NUREG-2163

Technical Basis for Regulatory 

Guidance on the Alternate 

Pressurized Thermal Shock Rule

Final Report

Office of Nuclear Regulatory Research
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NUREG-2163

Office of Nuclear Regulatory Research

Technical Basis for Regulatory 

Guidance on the Alternate 

Pressurized Thermal Shock Rule

Final Report

Manuscript Completed: December, 2016 

Date Published: September 2018 

Prepared by: 

G. Stevens1

M. Kirk

M. Modarres2

1 Structural Integrity Associates, Inc.

 11515 Vanstory Drive, Suite 125

 Huntersville, NC 28078

2 University of Maryland

 Clark School of Engineering

 College Park, MD 20742-7531

Mark Kirk, NRC Project Manager

iii

ABSTRACT

During plant operation, the walls of reactor pressure vessels (RPVs) are exposed to neutron 

radiation, resulting in embrittlement of the vessel steel and weld materials in the area of the 

RPV adjacent to the core. If an embrittled RPV had a flaw of critical size and if certain severe 

system transients were to occur, the flaw could rapidly propagate through the vessel, resulting 

in a through-wall crack that could challenge the integrity of the RPV. The severe transients of 

concern, known as pressurized thermal shock (PTS), are characterized by a rapid cooling of the 

internal RPV surface in combination with repressurization of the RPV. Advances in 

understanding material behavior, the ability to realistically model plant systems and operational 

characteristics, and the ability to better evaluate PTS transients to estimate loads on vessel 

walls led the U.S. Nuclear Regulatory Commission (NRC) to develop a risk-informed revision of 

the existing PTS Rule in Title 10 of the Code of Federal Regulations (10 CFR) 50.61a, 

“Alternate Fracture Toughness Requirements for Protection against Pressurized Thermal Shock 

Events.” 

This report explains the basis for the requirements that establish the entry conditions to permit 

the use of 10 CFR 50.61a and describes methods that licensees can use to meet the following 

four requirements:

(1) criteria related to the date of construction and design requirements

(2) criteria related to the evaluation of plant-specific surveillance data

(3) criteria related to inservice inspection data and nondestructive examination requirements

(4) criteria related to alternate screening criteria on embrittlement

v

FOREWORD

The reactor pressure vessel (RPV) is exposed to neutron radiation during normal operation. 

Over time, the RPV steel becomes progressively more brittle in the region adjacent to the core. 

If a vessel has a preexisting flaw of critical size and if certain severe system transients occur, 

this flaw could propagate rapidly through the vessel, resulting in a through-wall crack. The 

severe transients of concern, known as pressurized thermal shock (PTS), are characterized by 

rapid cooling (i.e., thermal shock) of the internal RPV surface that may be combined with 

repressurization. The simultaneous occurrence of flaws of critical size, embrittled steel, and a 

severe PTS transient is a low-probability event. U.S. pressurized-water reactors (PWRs) are 

not projected to approach the levels of embrittlement that would make them susceptible to PTS 

failure, even during extended operation beyond the original 40-year design life.

Advances in understanding material behavior, the ability to realistically model plant systems and 

operational characteristics, and the ability to better evaluate PTS transients to estimate loads on 

vessel walls led the U.S. Nuclear Regulatory Commission to develop a risk-informed revision of 

the existing PTS Rule in Title 10 of the Code of Federal Regulations (10 CFR) 50.61a, 

“Alternate Fracture Toughness Requirements for Protection against Pressurized Thermal Shock 

Events” (Alternate PTS Rule).

The Alternate PTS Rule provides revised PTS screening criteria in the form of an embrittlement 

reference temperature, RTMAX-X, which characterizes the RPV material’s resistance to 

flaw-initiated fractures. The Alternate PTS Rule is based on more comprehensive analysis 

methods than the existing PTS Rule in 10 CFR 50.61, “Fracture Toughness Requirements for

Protection against Pressurized Thermal Shock Events.” This alternate rule became desirable 

because the existing requirements, such as those in 10 CFR 50.61, are based on unnecessarily 

conservative assumptions. The Alternate PTS Rule reduces regulatory burden for those PWR 

licensees that expect to exceed the 10 CFR 50.61 embrittlement requirements before the 

expiration of their operating licenses while still maintaining adequate safety margins. PWR 

licensees may choose to comply with the Alternate PTS Rule as a voluntary alternative to 

complying with the requirements in 10 CFR 50.61.

This document explains the basis for the requirements that establish the entry conditions that 

allow licensees to use the Alternate PTS Rule. It also describes methods that licensees can 

use to meet the following four requirements:

(1) criteria related to the date of construction and design requirements

(2) criteria related to the evaluation of plant-specific surveillance data

(3) criteria related to inservice inspection data and nondestructive examination requirements

(4) criteria related to alternate screening criteria on embrittlement

Raymond Furstenau, Director

Director of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

vii

TABLE OF CONTENTS

ABSTRACT ................................................................................................................... iii

FOREWORD................................................................................................................... v

TABLE OF CONTENTS................................................................................................ vii

LIST OF FIGURES......................................................................................................... ix

LIST OF TABLES .......................................................................................................... xi

EXECUTIVE SUMMARY ............................................................................................. xiii

ABBREVIATIONS AND ACRONYMS........................................................................ xvii

SYMBOLS AND EXPRESSIONS................................................................................ xix

1 INTRODUCTION .................................................................................................... 1-1

1.1 Background ...............................................................................................................1-1

1.2 Scope of this Report ..................................................................................................1-3

2 OVERVIEW OF THE ALTERNATE PRESSURIZED THERMAL SHOCK 

RULE...................................................................................................................... 2-1

2.1 Background ...............................................................................................................2-1

2.2 Applicability of the Alternate Pressurized Thermal Shock Rule..................................2-1

2.3 Updated Embrittlement Correlation............................................................................2-2

2.4 Inservice Inspection Volumetric Examination and Flaw Assessments........................2-2

2.5 Uncertainties Related to Nondestructive Examination................................................2-4

2.6 Surveillance Data ......................................................................................................2-4

3 RESPONSES TO STAKEHOLDER FEEDBACK................................................... 3-1

4 GUIDANCE FOR CRITERIA RELATED TO THE DATE OF 

CONSTRUCTION AND DESIGN REQUIREMENTS.............................................. 4-1

4.1 Requirements in the Alternate Pressurized Thermal Shock Rule...............................4-1

4.2 Regulatory Guidance.................................................................................................4-1

5 GUIDANCE FOR CRITERIA RELATED TO THE EVALUATION OF PLANT 

SPECIFIC SURVEILLANCE DATA........................................................................ 5-1

5.1 Embrittlement Trend Curve........................................................................................5-2

5.2 Data Used in Statistical Tests....................................................................................5-4

5.3 Statistical Evaluation of Surveillance Data.................................................................5-6

5.4 How to Perform Statistical Tests of Surveillance Data ...............................................5-9

5.4.1 Type A Deviations..........................................................................................5-9

5.4.2 Type B Deviations........................................................................................ 5-10

5.4.3 Type D Deviations........................................................................................ 5-11

5.4.4 Comments on the Statistical Tests............................................................... 5-12

5.5 Evaluation of Plant Data Relative to the Statistical Tests......................................... 5-13

5.6 Considerations When Statistical Tests Are Failed.................................................... 5-14

5.6.1 Factors To Consider When Statistical Tests Are Failed................................ 5-15

5.6.2 Specific Procedures ..................................................................................... 5-16

5.7 Summary and Conclusions...................................................................................... 5-17
viii

6 GUIDANCE RELATED TO INSERVICE INSPECTION DATA AND 

NONDESTRUCTIVE EXAMINATION REQUIREMENTS....................................... 6-1

6.1 Background ...............................................................................................................6-1

6.2 Guidance on Criteria Related to Alternate Screening Criteria on Embrittlement.........6-7

6.2.1 Guidance on a Procedure To Preclude Brittle Fracture ..................................6-7

6.2.2 Guidance on Considerations To Include in a Plant-Specific Probabilistic 

Fracture Mechanics Analysis ....................................................................... 6-11

6.3 Guidance for Initial Evaluation of Nondestructive Examination Data........................ 6-14

6.4 Guidance for Further Evaluation of Nondestructive Examination Data..................... 6-23

6.4.1 Guidance on the Elements and Nondestructive Examination Techniques 

Associated with ASME Code Examinations ................................................. 6-23

6.4.2 Guidance on a Procedure To Adjust Nondestructive Examination Data 

and Comparison to Flaws Assumed in Probabilistic Fracture Mechanics 

Calculations ................................................................................................. 6-24

6.4.3 Guidance on the Application of Nondestructive Examination 

Uncertainties................................................................................................ 6-26

7 GUIDANCE RELATED TO ALTERNATE SCREENING CRITERIA ON 

EMBRITTLEMENT ................................................................................................. 7-1

8 SUMMARY ............................................................................................................. 8-1

9 REFERENCES ....................................................................................................... 9-1

APPENDIX A DERIVATION OF THE STATISTICAL TEST FOR TYPE D 

DEVIATIONS ...................................................................................... A-1

APPENDIX B REGULATORY ASSESSMENT OF STATISTICAL 

SURVEILLANCE TESTS.................................................................... B-1

APPENDIX C FLAW DEPTH AND DENSITY DISTRIBUTIONS CONSIDERING 

PROBABILITY OF DETECTION AND BIAS IN NDE DATA WITH 

APPLICATIONS ................................................................................. C-1

APPENDIX D SENSITIVITY STUDY RESULTS ON FLAW DISTRIBUTIONS 

CONSIDERING VFLAW DATA, POD, AND MEASUREMENT 

ERRORS IN NDE DATA..................................................................... D-1
ix

LIST OF FIGURES 

Figure 5-1 Four types of deviations between heat specific surveillance data and a 

∆T30 ETC...........................................................................................................5-8

Figure 5-2 Procedure used to assess Type B deviations.................................................. 5-10

Figure 5-3 Specific procedures to account for failure of the mean test (left) or 

low-fluence outlier statistical test (right)........................................................... 5-17

Figure 6-1 Flow diagram with recommendations for meeting the requirements of 

the Alternate PTS Rule .....................................................................................6-6

Figure 6-2 ASME Code, Section XI, examination and flaw evaluation process and 

identification of flaws for comparison to the Alternate PTS Rule...................... 6-17

Figure 6-3 Sample ASME Code, Section XI, MandatoryAppendix VIII, examination 

results for Plant J ............................................................................................ 6-18

xi

LIST OF TABLES

Table 1-1 RTMAX-X PTS Embrittlement Screening Criteria from the Alternate 

Table 1-2 Flaw Limit Tables from the Alternate PTS Rule [2]........................................... 1-5

Table 3-1 EPRI Recommendations for Addressing Alternate PTS Rule 

Requirements [10]............................................................................................ 3-2

Table 5-1 Standard Deviation of Residuals about Equation (1)........................................ 5-3

Table 5-2 Independent Variables in the Equation (1) ETC and the Ranges and Mean 

Values of the Calibration Dataset..................................................................... 5-3

Table 5-3 α = 1% Student’s t-Values ............................................................................. 5-11

Table 5-4 α = 1% Threshold Value for the Outlier Test .................................................. 5-12

Table 5-5 Heats of Material That Exhibit Statistically Significant Deviations (α = 1%) of 

Type A, B, or D .............................................................................................. 5-14

Table 5-6 Proportion of Material Heats in the Current Surveillance Database That 

Exhibit Statistically Significant Deviations (α = 1%) of Type A, B, or D ........... 5-14

Table 6-1 Sample Brittle Fracture Assessment .............................................................. 6-10

Table 6-2 Summary of the Revised Flaw Depth and Density VFLAW Parameters 

To Be Used in a Revised PFM Analysis for Beaver Valley, Unit 2 (from 

Appendix C)................................................................................................... 6-13

Table 6-3 Determination of Total Weld Length Examined for Plant J ............................. 6-19

Table 6-4 Determination of Total Plate Surface Area Examined for Plant J .................... 6-20

Table 6-5 Determination of the Flaw Positions for Plant J .............................................. 6-21

Table 6-6 Comparison of Flaws to the Flaw Tables in the Alternate PTS Rule for 

Plant J ............................................................................................................ 6-22

Table 6-7 Example for Plant J after Applying an Initial Alternate PTS Rule Flaw 

Table Check Using the Procedure in Section 6.3 ........................................... 6-26

PTS Rule [1].................................................................................................... 1-2 

xiii

EXECUTIVE SUMMARY

In early 2010, the U.S. Nuclear Regulatory Commission (NRC) promulgated Title 10 of the Code 

of Federal Regulations (10 CFR) 50.61a, “Alternate Fracture Toughness Requirements for 

Protection against Pressurized Thermal Shock Events” (Alternate Pressurized Thermal Shock 

(PTS) Rule) to amend existing regulations to provide alternate embrittlement requirements for 

protection against PTS events in pressurized-water reactor (PWR) pressure vessels. These 

requirements are based on more comprehensive, accurate, and realistic analysis methods than

those used by the NRC to establish the screening criteria in 10 CFR 50.61, “Fracture 

Toughness Requirements for Protection against Pressurized Thermal Shock Events.” This 

alternate rule became desirable because the existing requirements in 10 CFR 50.61 are based 

on unnecessarily conservative assumptions. The Alternate PTS Rule reduces regulatory 

burden for those PWR licensees that expect to exceed the 10 CFR 50.61 embrittlement 

requirements before the expiration of their operating licenses while still maintaining adequate 

safety margins. PWR licensees may choose to comply with the Alternate PTS Rule as a 

voluntary alternative to complying with the requirements in 10 CFR 50.61.

The Alternate PTS Rule provides revised PTS screening criteria in the form of embrittlement 

reference temperatures, RTMAX-X, that characterize the RPV material’s resistance to fracture 

initiating from flaws. Licensees may use the RTMAX-X embrittlement screening criteria as long as 

they meet the following four criteria:

(1) criteria related to the date of construction and design requirements

The Alternate PTS Rule applies to licensees whose construction permitswere issued

before February 3, 2010, and whose RPVs were designed andfabricatedto the

standards in the 1998 edition (or an earlier edition) of the American Society of

Mechanical Engineers Boiler and Pressure Vessel Code (ASME Code). The NRC

applied this restriction because the structural and thermal-hydraulic analyses that

established the basis forthe Alternate PTS Rule embrittlement screening criteria

represented only plantsconstructed before this date. Licensees are responsible for

demonstrating that their technical-basis calculations, developed in support of the

Alternate PTS Rule, address the risk-significant factors that control PTSfor any plant

constructed after February 3, 2010. Chapter 4 of this document describes methods by

which licensees can satisfy these criteria and identifies factors to be considered in such

an evaluation.

(2) criteria related to evaluation of plant-specific surveillance data

The Alternate PTS Rule includes statistical tests that licensees must perform on RPV

surveillance data to determine whether the surveillance data are sufficiently close to the

predictions of an embrittlement trend curve (ETC) that the ETC predictions are valid for

use. Of particular interest from a regulatory perspective is the use of these statistical

tests to determine whether plant-specific surveillance data deviate significantly from the

ETC predictions in a manner that suggests the ETC is likely to underpredict
xiv

• a detailed description of the mathematical procedures for use in assessing the

licensee’s compliance with the three statistical tests in the Alternate PTS Rule

• a list of factors to consider in diagnosing the reason why a particular surveillance

dataset might fail these statistical tests

• a description of certain situations under which the licensee can adjust the ETC

predictions

(3) criteria related to inservice inspection (ISI) data and nondestructive examination (NDE)

requirements

The Alternate PTS Rule describes a number of tests of and conditions on the collection

and analysis of ISI data that should provide reasonable assurance that the distribution of

flaws assumed to exist in the probabilistic fracture mechanics (PFM) calculations, which

provide the basis for the RTMAX-X screening criteria, provides an acceptable model of the

population of flaws in the RPV of interest. Chapter 6 of this document provides guidance

to help licensees satisfy these criteria. This document discusses the following guidance:

• guidance for initial evaluation of NDE data obtained from qualified ISI

examinations

• guidance for further evaluation of NDE data obtained from qualified ISI

examinations, including the following:

− elements and NDE techniques associated with the qualified ISI 

examinations in Mandatory Appendix VIII, “Performance Demonstration 

for Ultrasonic Examination Systems,” to Section XI, “Rules for Inservice 

Inspection of Nuclear Power Plant Components,” of the ASME Code that 

are performed to assess compliance with the requirements of the 

Alternate PTS Rule

− a mathematical procedure that can be used to adjust NDE data to 

account for flaw detection and sizing errors and comparison of the 

adjusted data to the population of flaws assumed in the PFM technical 

basis for the Alternate PTS Rule

• guidance for plants with RPV flaws that fall outside the applicability of the flaw

tables in the Alternate PTS Rule, including the following:

− a mathematical procedure that licensees can use to preclude brittle 

fracture based on RTNDT information

− a mathematical procedure that licensees can use to combine the NDE 

data with the population of flaws assumed in the PFM calculations to 

estimate the total flaw distribution that is predicted to exist in the RPV and 

guidance on how to apply this total flaw distribution as part of a PFM 

calculation using the Fracture Analysis of Vessels–Oak Ridge computer 

code

plant-specific data trends. Chapter 5 of this document describes guidance on

assessing the closeness of plant-specific data to the ETC using statistical tests, including

the following:
xv 

(4) criteria related to alternate screening criteria on embrittlement

Guidance is provided to help licensees estimate a plant-specific value of through-wall

cracking frequency for cases that do not satisfy the RTMAX-X screening criteria of the

Alternate PTS Rule. Chapter 7 of this document describes the two sets of guidance on

satisfying the embrittlement acceptability criteria.

This document provides guidance and the associated technical basis for methods that licensees 

can use to meet these requirements.

xvii

ABBREVIATIONS AND ACRONYMS

ADAMS Agencywide Documents Access and Management System

AP Advanced Passive

APWR Advanced Pressurized Water Reactor

ASME American Society of Mechanical Engineers

ASME Code American Society of Mechanical Engineers Boiler and Pressure Vessel Code

BWR Boiling Water Reactor

CFR Code of Federal Regulations

CVN Charpy V-Notch

E Energy

EPR Evolutionary Power Reactor

EPRI Electric Power Research Institute

ETC Embrittlement Trend Curve

F Degrees Fahrenheit

FAVOR Fracture Analysis of Vessels–Oak Ridge

HAZ Heat-Affected Zone

ISI Inservice Inspection

Mev Million Electron Volts

MRP Materials Reliability Program

N/cm2 Neutrons Per Square Centimeter

NDE Nondestructive Examination

NRC U.S. Nuclear Regulatory Commission

NRR Office Of Nuclear Reactor Regulation

ORNL Oak Ridge National Laboratory

PFM Probabilistic Fracture Mechanics

PNNL Pacific Northwest National Laboratory

POD Probability Of Detection

PRA Probabilistic Risk Assessment

PTS Pressurized Thermal Shock

PVRUF Pressure Vessel Research User Facility

PWR Pressurized Water Reactor

RPV Reactor Pressure Vessel

SCD Surveillance Capsule Data

TWCF Through Wall Cracking Frequency

TWE Through Wall Extent

UT Ultrasonic Testing

xix

SYMBOLS AND EXPRESSIONS

A Multiplier for determining ΔT30 based on the product form

ADJ An adjustment in the embrittlement prediction to account for a failure of the 

mean test

B Multiplier for determining ΔT30 based on the product form

C1 and C2 Critical values of the outlier test

CRP Intermediate term for determining ΔT30 in degrees Fahrenheit or Celsius

Cu Copper content in weight percent

Cue Effective copper content in weight percent

f(Cue,P) Intermediate term for determining ΔT30 based on effective copper content and 

phosphorus content

g(Cue,Ni, φte) Intermediate term for determining ΔT30 based on the effective copper content, 

nickel content, and effective fluence

m Slope of ΔT30 prediction residuals plotted versus the base-10 logarithm of 

fluence

MATLAB Matrix laboratory

Max(Cue) Intermediate term for determining ΔT30 based on the effective copper content

MD Intermediate term for determining ΔT30 based on degrees Fahrenheit or 

Celsius

Mn Manganese content in weight-percent

n Number of ΔT30 observations in a plant specific surveillance dataset

Ni Nickel content in weight-percent

P Phosphorus content in weight-percent

r* Normalized residual

r*1 and r*2 Calculated values of residuals for the outlier test

rLIMIT(1) and Critical values of the outlier test (the same as C1 and C2) 

rLIMIT(2)

rmax Maximum permissible ΔT30 prediction residual

rmean Mean ΔT30 prediction residual for a plant specific surveillance dataset

R(max1) The largest ΔT30 prediction residual for a plant specific surveillance dataset

R(max2) The second largest ΔT30 prediction residual for a plant specific surveillance 

dataset

RTMAX X Any or all of the values RTMAX–AW, RTMAX–PL, RTMAX–FO, RTMAX–CW, or sum of 

RTMAX–AW and RTMAX–PL for a particular reactor vessel, expressed as a 

temperature in degrees Fahrenheit or Celsius

RTMAX AW A value, expressed as a temperature in degrees Fahrenheit or Celsius, which 

characterizes the reactor vessel’s resistance to fracture initiating from flaws 

found along axial weld fusion lines

RTMAX PL A value, expressed as a temperature in degrees Fahrenheit or Celsius, which 

characterizes the reactor vessel’s resistance to fracture initiating from flaws 

found in plates remote from welds
xx 

RTMAX FO A value, expressed as a temperature in degrees Fahrenheit or Celsius, which 

characterizes the reactor vessel’s resistance to fracture initiating from flaws 

in forgings remote from welds

RTMAX CW A value, expressed as a temperature in degrees Fahrenheit or Celsius, which 

characterizes the reactor vessel’s resistance to fracture initiating from flaws 

found along circumferential weld fusion lines

RTNDT Nil ductility transition temperature in degrees Fahrenheit or Celsius

RTNDT(u) Unirradiated nil ductility transition temperature in degrees Fahrenheit or 

Celsius

RTPTS The RTNDT value at the end of a license, as defined in 10 CFR 50.61, in 

degrees Fahrenheit or Celsius

S Distance of flaw below surface in inches or millimeters

se(m) Standard error of m

te Effective time in seconds

TC Irradiated (coolant) temperature in degrees Fahrenheit or Celsius

TCRIT(α) Critical value of Student’s t distribution

Tm T statistic for m

t, TWALL Wall thickness in inches or millimeters

t(...) Student’s t distribution

TWE Through wall extent in inches or millimeters

TWEMAX Maximum through wall extent in inches or millimeters

TWEMIN Minimum through wall extent in inches or millimeters

VFLAW Vessel flaw

α Statistical significance level

ΔT30 Increase in the Charpy V notch energy transition temperature in degrees 

Fahrenheit or Celsius at 30 foot pounds or 41 joules caused by neutron 

irradiation embrittlement

ΔT30(ADJ) An adjusted value of ΔT30 in degrees Fahrenheit or Celsius that accounts for 

a failure in the mean slope test

ΔT30i(measured) A measured value of ΔT30 in degrees Fahrenheit or Celsius

ΔT30i(ETC mean) A value of ΔT30 predicted by Equation (1) in degrees Fahrenheit or Celsius

ΔYS Change in yield strength in thousands of pounds per square inch or 

megapascals 

φ Flux in neutrons per square centimeter per second

φt Fluence in neutrons per square centimeter

φte Effective fluence in neutrons per square centimeter

σ Standard deviation in degrees Fahrenheit or Celsius
1-1

1 INTRODUCTION

1.1 Background

The U.S. Nuclear Regulatory Commission (NRC) promulgated Title 10 of the Code of Federal 

Regulations (10 CFR) 50.61a, “Alternate Fracture Toughness Requirements for Protection 

against Pressurized Thermal Shock Events” (the Alternative Pressurized Thermal Shock (PTS) 

Rule) [1], on January 4, 2010 (Volume 75 of the Federal Register, pages 13–29 (75 FR 13–

29) [2]). The regulations at 10 CFR 50.61a amend existing regulations to provide alternate

fracture toughness requirements for protection against PTS events for pressurized-water reactor

(PWR) pressure vessels.

The Alternate PTS Rule provides alternate embrittlement requirements that are based on more 

comprehensive analysis methods. This regulatory action became desirable because the 

existing requirements, such as those in 10 CFR 50.61, “Fracture Toughness Requirements for 

Protection against Pressurized Thermal Shock Events” [3], are based on unnecessarily 

conservative assumptions. The Alternate PTS Rule reduces regulatory burden, while 

maintaining adequate safety, for those PWR licensees that expect to exceed the 10 CFR 50.61 

embrittlement requirements before the expiration of their operating licenses. PWR licensees 

may choose to comply with the Alternate PTS Rule as a voluntary alternative to complying with 

the requirements in 10 CFR 50.61.

The Alternate PTS Rule provides revised PTS screening criteria in the form of embrittlement 

reference temperatures, RTMAX-X, that characterize the resistance of the material in the reactor 

pressure vessel (RPV) to fracture initiating from flaws. Table 1 of the Alternate PTS Rule and

Table 1-1 of this document list the PTS screening criteria. The values in Table 1-1 of this 

document are based on up-to-date understandings and models of the many factors that affect 

the operating safety of PWRs. Chapter 2 of this report further discusses the provisions and use 

of the Alternate PTS Rule.
1-2

Table 1-1 RTMAX-X PTS Embrittlement Screening Criteria from the Alternate PTS Rule [1] 
1-3

1.2 Scope of this Report

Licensees may use the RTMAX-X embrittlement screening criteria shown in Table 1-1 as long as 

their RPV meets certain criteria outlined in the Alternate PTS Rule. This document explains the 

bases for the criteria that establish the entry conditions that allow licensees to use the Alternate 

PTS Rule and describes methods that licensees can use to meet the following four criteria: 

(1) criteria related to the date of construction and design requirements

The regulation at 10 CFR 50.61a(b) restricts the applicability of the Alternate PTS Rule

to reactors for which construction permits were issued before February 3, 2010, and that

have RPVs designed and fabricated to the 1998 edition (or an earlier edition) of the

ASME American Society of Mechanical Engineers Boiler and Pressure Vessel Code

(ASME Code). Chapter 4 describes the criteria related to the date of plant construction

by which licensees can use the Alternate PTS Rule.

(2) criteria related to the evaluation of plant-specific surveillance data

Under 10 CFR 50.61a(f), the NRC requires licensees to verify that their plant-specific

surveillance data for the RPV in question satisfy three statistical tests described in the

Alternate PTS Rule. These tests assess whether the embrittlement trend curve (ETC)

used in the Alternate PTS Rule adequately predicts these plant-specific surveillance

data. If the licensee cannot verify these predictions, it must submit an evaluation of

plant-specific surveillance data to the Director of the NRC Office of Nuclear Reactor

Regulation (NRR) that proposes a method to account for plant-specific surveillance data

when assessing the subject RPV relative to the Alternate PTS Rule screening criteria on

RTMAX-X. Chapter 5 of this document describes methods by which licensees can satisfy

these criteria.

(3) criteria related to inservice inspection (ISI) data and nondestructive examination (NDE)

requirements

Under 10 CFR 50.61a(e), the NRC requires the licensee to verify that the flaw density

and size distributions detected within the beltline region of the RPV during a qualified

examination under Section XI, “Rules for Inservice Inspection of Nuclear Power Plant

Components,” of the ASME Code [4] are bounded by flaw tables in the Alternate PTS

Rule. The Alternate PTS Rule requires that any flaws detected within the inner 1 inch or

10 percent of the wall thickness of the vessel base material, whichever is greater, do not

exceed the limits shown in Table 1-2. If the licensee cannot make this verification, it

must demonstrate that the RPV will have a through-wall cracking frequency (TWCF) of

less than 1x10-6 per reactor year. Chapter 6 of this document describes methods by

which licensees can satisfy these criteria.

(4) criteria related to alternate screening criteria on embrittlement

Chapter 7 of this document describes criteria by which licensees can assess

plant-specific TWCF for cases that do not satisfy the RTMAX-X screening criteria of the

Alternate PTS Rule.

References to the “beltline” region of the RPV throughout this report refer to all regions of the 

RPV adjacent to the reactor core that are exposed to a fluence of 1x1017 neutrons per square 
1-4

centimeter (n/cm2

) or higher during the operating lifetime of the reactor [24]. Fluence values 

should be determined using a methodology consistent with that specified in Regulatory 

Guide 1.190, “Calculational and Dosimetry Methods for Determining Pressure Vessel Neutron 

Fluence,” issued March 2001 [26], or by using methods otherwise acceptable to the staff.

The NRC solicited input from interested stakeholders regarding an alternate PTS regulation

during three public meetings in 2011 [16]. The Electric Power Research Institute’s (EPRI’s) 

Materials Reliability Program (MRP) developed recommended technical methods or approaches 

in seven areas. MRP-334, “Materials Reliability Program: Proposed Resolutions to the 

Analytical Challenges of Alternate PTS Rule (10 CFR 50.61a) Implementation,” issued 

January 2012 [10], describes those recommended technical methods. These methods reduce 

the resources needed by utilities and the NRC to implement the Alternate PTS Rule and provide 

a consistent and acceptable level of safety subsequent to implementation of the rule, especially 

in those instances in which a licensee must perform alternate evaluations to demonstrate its 

compliance with the Alternate PTS Rule. Chapter 3 of this document discusses the NRC’s

responses to the recommendations made in MRP-334.
1-5

Table 1-2 Allowable Flaw Tables from the Alternate PTS Rule [2] 

2-1

2 OVERVIEW OF THE ALTERNATE 

PRESSURIZED THERMAL SHOCK RULE

2.1 Background

PTS events are system transients in a PWR during which the RPV rapidly cools down, resulting

in cold vessel temperatures with or without repressurization of the RPV. The rapid cooling of 

the inside surface of the RPV causes thermal stresses that can combine with stresses caused 

by high pressure. The aggregate effect of these stresses is an increase in the potential for 

fracture if a preexisting flaw is present in a region of the RPV that has significant embrittlement.

The PTS Rule in 10 CFR 50.61 establishes screening criteria below which the potential for an 

RPV to fail because of a PTS event is deemed to be acceptably low. These screening criteria 

effectively define a level of embrittlement beyond which operation cannot continue without 

further plant-specific compensatory action or analysis. Compensatory actions include

(1) reducing the neutron flux, (2) modifying the plant to reduce the PTS event probability or

severity, and (3) RPV annealing. The regulations in 10 CFR 50.61(b)(3), (b)(4), and (b)(7) and

in 10 CFR 50.66, “Requirements for Thermal Annealing of the Reactor Pressure Vessel,”

address these actions [5].

Currently, no operating PWR RPV is projected to exceed the 10 CFR 50.61 screening criteria 

before the expiration of its original 40-year operating license. However, several PWR RPVs are 

approaching the screening criteria, whereas others are likely to exceed the screening criteria 

during the period of license renewal.

The NRC developed technical bases that support updating the PTS regulations ([6], [7], [8], [9], 

[14]). These technical bases conclude that the risk of through-wall cracking because of a PTS 

event is much lower than previously estimated. This finding indicates that the screening criteria 

in 10 CFR 50.61 are unnecessarily conservative. Therefore, the NRC developed 

10 CFR 50.61a, the Alternate PTS Rule, to provide alternate screening criteria based on the 

updated technical bases. These technical bases covered the following topics:

• applicability of the Alternate PTS Rule

• updated embrittlement correlation

• ISI volumetric examination and flaw assessments

• NDE-related uncertainties

• surveillance data

The following sections present a brief overview of these topics.

In addition, 10 CFR 50.61a(d) defines seven subsequent requirements that licensees must 

satisfy as a part of their implementation of the Alternate PTS Rule.

2.2 Applicability of the Alternate Pressurized Thermal Shock Rule

The Alternate PTS Rule is based, in part, on analysis of information from three currently 

operating PWRs. Because factors that are generally common to PWRs control the severity of 

the risk-significant transient classes (e.g., primary-side pipe breaks and stuck-open valves on 
2-2

the primary side that may later reclose), the NRC concluded that the results and screening 

criteria developed from these analyses could be applied with confidence to the entire fleet of 

operating PWRs. The NRC based this conclusion on an understanding of the characteristics of 

the dominant transients that drive their risk significance and on an evaluation of a larger 

population of high-embrittlement PWRs. This evaluation revealed no design, operational, 

training, or procedural factors that could credibly increase either the severity of these transients 

or the frequency of their occurrence in the general PWR population above the severity and 

frequency characteristic of the three plants that were modeled in detail. The NRC also 

concluded that PTS events that were insignificant risk contributors in these analyses are not 

expected to become dominant contributors in other plants.

The Alternate PTS Rule applies to licensees whose construction permits were issued before 

February 3, 2010, and whose RPVs were designed and fabricated to the 1998 edition or an 

earlier edition of the ASME Code. 

2.3 Updated Embrittlement Correlation

The technical basis for the Alternate PTS Rule used many different models and parameters to 

estimate the yearly probability that a PWR will develop a through-wall crack as a consequence 

of PTS loading. One of these models was a revised ETC that uses information on the chemical 

composition and neutron exposure of low-alloy steels in the RPV beltline region to estimate the 

fracture-mode transition temperature of these materials. Although the general trends predicted 

by the embrittlement models in 10 CFR 50.61 and the Alternate PTS Rule are similar, the 

mathematical form of the revised ETC in the Alternate PTS Rule differs substantially from the 

ETC in 10 CFR 50.61. The NRC updated the ETC in the Alternate PTS Rule to more accurately 

represent the substantial amount of RPV surveillance data that has accumulated between the 

last revision of the 10 CFR 50.61 ETC in the mid-1980s and the database supporting the 

10 CFR 50.61a ETC, which was finalized in 2002. Section 5.1 discusses the specifics of the 

updated ETC used in the Alternate PTS Rule. 

2.4 Inservice Inspection Volumetric Examination and Flaw Assessments

The Alternate PTS Rule differs from 10 CFR 50.61 in that it requires licensees that choose to 

follow its requirements to analyze the results from ISI volumetric examinations done in 

accordance with ASME Code, Section XI. The analyses of ISI volumetric examinations may be 

used to determine whether the flaw density and size distribution in the licensee’s RPV beltline 

region are bounded by the flaw density and size distribution used in the development of the 

Alternate PTS Rule.

The NRC developed the Alternate PTS Rule using flaw density, spatial, and size distributions 

determined from experimental data, from physical models, and from expert judgment. The 

experimental data were obtained by taking samples from RPV materials from canceled plants 

(i.e., from the Shoreham Nuclear Power Plant and the Pressure Vessel Research Users’ Facility 

(PVRUF) vessels). The NRC believes that a comparison of the results from qualified ASME 

Code, Section XI, ISI volumetric examinations is necessary to confirm that the flaw density and 

size distributions in the RPV to which the Alternate PTS Rule may be applied are consistent with 

the flaw density and size distributions used in the development of the Alternate PTS Rule.

Under 10 CFR 50.55a(g)(6)(ii)(C) [11], the NRC requires licensees to implement ISI 

examinations in accordance with Supplements 4 and 6 [12] to Mandatory Appendix VIII, 

“Performance Demonstration for Ultrasonic Examination Systems,” to Section XI of the ASME 
2-3

Code. Supplement 4 contains qualification requirements for the RPV ISI volume from the 

clad-to-base-metal interface to the inner 15 percent of the RPV base material wall thickness. 

Supplement 6 contains qualification requirements for RPV weld volumes that lie within the outer 

85 percent of the RPV base material wall thickness. 

A simplified representation of the flaw density and size distributions used in the development of 

the Alternate PTS Rule is summarized by numerical values in Tables 2 and 3 of the Alternate 

PTS Rule for weld and plate/forging materials, respectively, as duplicated here in Table 1-2. 

Hereafter, Tables 2 and 3 of the Alternate PTS Rule are collectively referred to as “the flaw 

tables.” These tables provide the number of flaws in each size range that were evaluated in the 

underlying technical bases. If the RPV has a distribution of flaws that have sizes and densities

greater than those in the flaw tables, the licensee must evaluate those flaws to ensure that they 

are not causing the TWCF to exceed a value of 1x10-6. 

The technical basis for the Alternate PTS Rule also indicated that flaws buried more deeply than 

1 inch from the clad-to-base interface are not as susceptible to brittle fracture as flaws of similar 

size located closer to the inner surface. Therefore, the Alternate PTS Rule does not require an 

assessment of the density of these flaws, but the rule still requires large flaws, if discovered, to 

be evaluated for contributions to TWCF if they are within the inner three-eighths (3/8t) of the 

vessel base material wall thickness. Section II, “Discussion,” of 75 FR 13–29 [2] for the 

Alternate PTS Rule indicates that the limitation for flaw acceptance, as specified in ASME Code, 

Section XI, Table IWB-3510-1, approximately corresponds to the threshold for the sizes of flaws 

that can contribute significantly to TWCF if they are present in RPV material at this depth. 

Therefore, the Alternate PTS Rule requires the licensee to evaluate flaws within the inner 3/8t of 

the vessel thickness that exceed the size limits in Table IWB-3510-1 for their contribution to 

TWCF, in addition to the other evaluations for such flaws that are prescribed in the ASME Code.

The Alternate PTS Rule also clarifies that, for consistency with ASME Code, Section XI, 

Mandatory Appendix VIII, the smallest flaws that must be sized are 0.075 inch in through-wall 

extent (TWE). For each flaw detected that has a TWE equal to or greater than 0.075 inch, the 

licensee is required to document the dimensions of the flaw, its orientation, its location within the 

RPV, and its depth from the clad-to-base-metal interface. Those planar flaws for which the 

major axis of the flaw is identified by a circumferentially oriented ultrasonic transducer must be 

categorized as ‘‘axial.’’ All other planar flaws may be categorized as ‘‘circumferential.’’ If the 

licensee is uncertain about which flaw dimension constitutes the major axis for a given flaw 

identified with an ultrasonic transducer oriented in the circumferential direction, the licensee 

should consider it an axial flaw. The NRC may also use this information to evaluate whether 

plant-specific information gathered suggests that the NRC staff should generically reexamine 

the technical basis for the Alternate PTS Rule.

The technical basis for the Alternate PTS Rule did not include surface cracks that penetrate 

through the RPV stainless steel clad and more than 0.070 inch into the welds or the adjacent 

RPV base metal because these types of flaws have not been observed in the beltline of any 

operating PWR vessel. However, flaws of this type were observed in a boiling-water reactor

(BWR) RPV head in 1990 and were attributed to intergranular stress-corrosion cracking of the 

stainless steel cladding. BWRs are not susceptible to PTS events and, therefore, are not 

subject to the requirements in 10 CFR 50.61. However, if similar cracks were found in the 

beltline region of a PWR, they would be a significant contributor to TWCF because of their size 

and location. As a result, the Alternate PTS Rule requires licensees to determine whether

cracks of this type exist in the beltline weld region as a part of each required ASME Code, 

Section XI, ultrasonic examination.
2-4

2.5 Uncertainties Related to Nondestructive Examination

The flaw sizes shown in Table 1-2 represent actual flaw dimensions, whereas the results from 

ASME Code, Section XI, examinations are estimated dimensions. The available information 

indicates that, for most flaw sizes in Table 1-2, qualified inspectors will oversize flaws. 

Comparing oversized flaws to the size and density distributions in Table 1-2 is conservative but 

not necessary.

As a result of stakeholder feedback received during the NRC’s solicitation for public comments 

on a preliminary draft of the Alternate PTS Rule, the final published Alternate PTS Rule permits 

licensees to adjust the flaw sizes estimated by inspectors qualified under ASME Code, 

Section XI, Mandatory Appendix VIII, Supplements 4 and 6. The NRC also determined that a 

licensee should be allowed to consider other NDE uncertainties, such as probability of detection 

(POD) and flaw density and location, because these uncertainties may affect the ability of the

licensee to demonstrate compliance with the Alternate PTS Rule. As a result, the language in 

10 CFR 50.61a(e) allows licensees to account for the effects of NDE-related uncertainties in 

meeting the flaw size and density requirements of Table 1-2. The Alternate PTS Rule does not 

provide specific guidance on a methodology to account for the effects of NDE-related 

uncertainties, but the rule notes that accounting for such uncertainties may be based on data 

collected from ASME Code inspector-qualification tests or any other tests that measure the 

difference between the actual flaw size and the size determined from the ultrasonic 

examination. Because collecting, evaluating, and using data from ASME Code 

inspector-qualification tests requires extensive engineering judgment, the Alternate PTS Rule 

requires that the Director of NRR review and approve the methodology used to adjust flaw sizes 

to account for the effects of NDE-related uncertainties.

2.6 Surveillance Data

The regulation at 10 CFR 50.61a(f) defines the process for calculating the values for the 

reference temperature, RTMAX–X, for a particular RPV material. These values may be based on 

the RPV material’s copper (Cu), manganese (Mn), phosphorus (P), and nickel (Ni) weight 

percentages; reactor cold-leg coolant temperature; fast neutron flux and fluence values, and

unirradiated nil-ductility transition reference temperature, RTNDT. 

The Alternate PTS Rule includes a procedure by which the RTMAX–X values, which are predicted 

for plant-specific RPV materials using an ETC, are compared to heat-specific surveillance data 

that are collected as part of surveillance programs under Appendix H, “Reactor Vessel Material 

Surveillance Program Requirements,” [13] to 10 CFR Part 50, “Domestic Licensing of 

Production and Utilization Facilities.” The purpose of this comparison is to assess how well the 

ETC represents the surveillance data. If the surveillance data are close (closeness is assessed 

statistically) to the ETC, the predictions of this ETC are used, which is most often expected to 

be the case. However, a significant and nonconservative deviation of heat-specific surveillance 

data from the predictions of the ETC indicates a need for alternative methods (i.e., other than 

the ETC) to reliably predict the temperature-shift trend (and to estimate RTMAX–X) for the 

conditions being assessed. Therefore, the Alternate PTS Rule includes three statistical tests to 

determine the significance of the differences between heat-specific surveillance data and the 

ETC.
3-1

3 RESPONSES TO STAKEHOLDER FEEDBACK

The NRC solicited input from interested stakeholders regarding an alternate PTS 

implementation regulatory guide during three public meetings in 2011 [16]. Based on those 

meetings, the EPRI’s MRP developed recommendations for technical methods or approaches 

that would be useful for Alternate PTS Rule implementation in seven areas. 

MRP-334 describes those recommended technical methods [10] and provides 15 specific 

recommendations that might reduce the resources that utilities and the NRC need to implement 

the Alternate PTS Rule. In addition, EPRI stated in MRP-334 that the recommendations would 

provide a consistent and acceptable level of safety subsequent to implementation of the 

Alternate PTS Rule, especially for those instances in which licensees must perform evaluations 

to demonstrate their compliance with the Alternate PTS Rule.

Table 3-1 includes EPRI’s recommendations from MRP-334. The last column of Table 3-1

includes the NRC’s responses to EPRI’s recommendations. As indicated by some of the 

responses to EPRI’s recommendations, the NRC further clarified some of the guidance in this 

document.
3-2

Table 3-1 EPRI Recommendations for Addressing Alternate PTS Rule Requirements [10] 

No. 10 CFR 50.61a 

Paragraph

MRP-334 

Recommendation

MRP-334

Justification

NRC

Respon

1 (f)(6), (a)(10) Adjustments should not

be made to sister-plant 

∆T30 values for the 

purpose of performing 

the surveillance data

tests in 10 CFR 50.61a.

The 10 CFR 50.61a ETC directly

considers the material properties and the

irradiation temperature in the calculation of

∆T30 and the residual for each point of

plant or sister-plant data. Section 3.1 

provides additional information. 

The NRC agrees with th

Sister-plant data are use

surveillance dataset (see 

surveillance procedure), 

to the data are made.

2 (f)(6), (a)(10) Limitations should be

placed on the variation in 

chemistry within a weld 

heat that must be 

considered when

considering sister-plant

data.

Appendix A to this report includes an

example of a weld heat with significant

variation. Section 3.1 provides additional 

information.

The NRC agrees that the 

consider variations in co

a need to explain or unde

that the statistical tests re

surveillance data. This is 

Step 2(d)(ii)(a) in the sec

to Consider When the St

Step 2 Are Failed” under 

“Composition and Expos

Specific limits are not pro

justified on a case-specif

3 (f)(6)(vi), (a)(11) If the licensee cannot 

meet the surveillance 

data tests using exact 

time-weighted average 

TC values, it should 

consider a tolerance that 

is equivalent to plus or 

minus one-half of the 

range of the operating 

temperatures over the 

irradiation time. If the 

surveillance data tests 

can be satisfied by using 

a temperature within this 

tolerance range on TC, 

∆T30 values should not 

require an adjustment.

Large differences in irradiation 

temperature can also have significant 

effects on the calculated ∆T30 values. The 

regulation at 10 CFR 50.61a defines TC as 

a time-weighted average of the cold-leg 

temperature under normal full-power 

operating conditions. However, the values 

used in the development of the ETC may 

not have reflected an accurate 

time-weighted average for each specific 

plant. This tolerance accounts for the 

uncertainty in the actual operating 

temperature when the largest changes in 

the embrittlement index occurred. 

Section 3.1 provides additional 

information.

The NRC agrees that the 

consider variations in co

there is a need to explai

deviations identified by t

that are required for surv

is pointed out in Step 2(d

section titled “Factors to 

Statistical Tests of Step 

the heading “Compositio

Variables.” Specific limit

but should be justified on 

basis.
3-3

No. 10 CFR 50.61a 

Paragraph

MRP-334 

Recommendation

MRP-334

Justification

NRC

Respon

4 (f)(6)(vi), 

(f)(6)(v)(A), 

(f)(6)(v)(C)

Section 3.2 of the report 

recommends 

a procedure to calculate

the ∆T30 adjustment to 

meet the requirements

of 

10 CFR 50.61a(f)(6)(vi) 

when either the mean

or outlier statistical tests 

are failed when the 

requirements in

10 CFR 50.61a(f)(6)(v) 

are applied. 

The surveillance capsule data (SCD)

statistical tests in 10 CFR 50.61a(f)(6) 

can be overly conservative; therefore,

any needed adjustments to ∆T30

and RTMAX-X for failing the SCD 

statistical tests should be minimal. 

The proposed procedure is simple to

implement and addresses the concerns

with deviation from the ETC without

excessive conservatism. Section 3.2 

provides additional information. 

The NRC adopted this re

to address failures of the 

Refer to Step 2(b)(i). Th

a different approach to a

failures caused by a low

Refer to Step 2(b)(ii). T

disagree with the propos

outlier failures but believ

this procedure should be 

case-specific basis.

5 (f)(6)(vi), 

(f)(6)(v)(B)

An industry-consensus 

ETC that addresses 

irradiation-induced 

shifts caused by fluence 

values up to 

1x1020 n/cm2

(E > 1 million electron 

volts (MeV)) should be 

used to calculate the 

predicted values of ∆T30

if the slope test is not 

satisfied.

Data from several plants with fluence 

exposures of up to 8.5x1019 n/cm2

have been evaluated, and no 

slope-test deviations were 

encountered. High-fluence SCD could 

possibly fail the statistical slope test. 

The industry has developed a 

coordinated surveillance program to 

obtain high-fluence data from power 

reactors for use in developing an 

industry-consensus ETC that 

addresses irradiation-induced shifts 

caused by fluence values up to 

1x1020 n/cm2 (E > 1 MeV). Section 3.3 

provides additional information.

As of the current date, a

by broad consensus bet

and industry stakeholde

In addition, the data from 

surveillance program wi

in large quantities until 2

agrees that, in the event 

failure, the best current 

irradiation damage mech

used to help explain the 

suggest corrective actio

because technical conse

matter has not been rea

not providing guidance o
3-4

No. 10 CFR 50.61a 

Paragraph

MRP-334 

Recommendation

MRP-334

Justification

NRC

Respon

6 (f)(6)(vi), 

(f)(6)(v)(A),

(f)(6)(v)(B), 

(f)(6)(v)(C)

Section 3.4 provides 

recommendations for 

possible criteria for not 

adjusting ∆T30 values in 

accordance with 

10 CFR 50.61a(f)(6)(vi) 

when the test 

requirements in 

10 CFR 50.61a(f)(6)(v)

(A), (B), and (C) cannot 

be satisfied.

There are several scenarios where an 

adjustment to ∆T30 values would not be 

appropriate. Section 3.4 discusses 

these scenarios and criteria.

As discussed in Step 2(d

regulatory guide, the NR

there are many situation

adjustment of the ΔT30 v

needed nor justifiable. S

discusses some of these 

does not provide specific 

These exceptions should 

case-specific basis.

7 (d)(4), (c)(3) A provision should be 

included in the 

proposed regulatory 

guide for the direct 

calculation of 

TWCF95-TOTAL using the 

plant-specific RTMAX-X

values for cases in 

which the RTMAX-X limits 

in Table 1 of 

10 CFR 50.61a cannot 

be met.

There are some conservatisms in the 

RTMAX-XX screening limits. In addition, 

plate and forging limited plants are 

likely to reach the more restrictive limit 

for circumferential welds before 

reaching the plate or forging limits. 

Section 3.5 provides additional 

information.

The NRC agrees with th

recommendation. The N

guidance to this regulato

Position 4, which refers 

appropriate formula and 

Section 3.5.1, “Limitation 

NUREG-1874, “Recomm

Screening Limits for Pre

Shock (PTS),” issued Ma

8 (e)(1) Any small flaws 

detected by ISI 

within +0.5 inch of the 

outer boundaries of the 

ASME Code, 

Section XI, inspection 

volume can be treated 

as potential plate flaws. 

All other flaws within 

the inspection volume 

should be treated as 

weld flaws.

The plate flaw limits in Table 3 of 

10 CFR 50.61a should be evaluated 

only for RPV base metal flaws that are 

not affected by welding but are 

detected by ISI. Section 3.6 provides 

additional information.

The NRC agrees, in par

comment. This NUREG 

guidance for establishing 

flaws are in the plate or 

Section 6.3, Step D).
3-5

No. 10 CFR 50.61a 

Paragraph

MRP-334 

Recommendation

MRP-334

Justification

NRC

Respon

9 (e)(1) Plate flaws that have a 

depth (TWE) of 0.4 inch 

or more should be 

evaluated as weld 

flaws.

This is necessary to ensure that the 

small flaws created during fabrication 

of the plates and forgings, which is 

what was simulated in the FAVOR 

probabilistic fracture mechanics 

analysis code, have not been 

expanded to larger sized flaws by the 

effects of welding, which were 

simulated by FAVOR as weld flaws. 

Section 3.6 provides additional 

information.

The NRC disagrees with 

recommendation becaus

A case-specific justificat

demonstrate why a plate 

recategorized as a weld 

10 (e)(4)(i) The proposed 

regulatory guide should 

provide criteria or 

methods for 

determining whether 

the deviation in flaw 

limits will have a 

detrimental effect on 

the applicability of the 

PTS screening criteria 

in Table 1 of 

10 CFR 50.61a.

Such criteria would reduce burden on 

both the NRC and industry while 

providing an acceptable level of safety 

and quality. Section 3.7 and 

Appendix E provide additional 

information.

The NRC agrees with th

Step 3(i) of this regulato

both simplified and more 

procedures that address 

may be performed when 

are exceeded. The indu

to justify alternatives to t

on a case-specific basis

11 (e)(4)(i) Deviations to the flaw 

limits for plants that 

have low embrittlement 

should be generically 

allowed. Low 

embrittlement can be 

defined as having 

RTMAX-X values that are 

equivalent to or less 

than a TWCF of 1% of 

the PTS risk objective 

or approximately 1x10-8

events per year.

The vessel material at these plants 

would still have high enough fracture 

toughness that even large increases in 

the number of flaws above the 

10 CFR 50.61a limits would not result 

in a plant reaching the PTS risk 

objective of 1x10-6 events per year. 

Section 3.7 provides additional 

information.

The NRC disagrees with 

recommendation and the 

justification. If the flaw l

would be inappropriate t

relationships between T

RTMAX-X that depend on 

being correct to address 

regulatory guide provide

criteria for assessing bri

may be used in this situa

valid alternative case-sp

may be proposed.
3-6

12 (e)(1) The flaw limits in 

Tables 2 and 3 of 

10 CFR 50.61a should 

be applied to axial flaws 

only.

This proposed approach addresses the 

real technical concern (i.e., the 

maximum number of axial flaws that 

could lead to potential vessel failure). 

The flaw-orientation discussion in 

Section 3.7.1 provides additional 

information.

The NRC disagrees with 

The comparison to Table

10 CFR 50.61a conside

whether such flaws are a

circumferential, because 

10 CFR 50.61a(e), “Exa

Flaw Assessment Requ

paragraph (e)(1)(iii), stat

For each flaw detecte

inspection volume de

paragraph (e)(1) with 

to or greater than 0.0

licensee shall docume

dimensions of the flaw

TWE and length, whe

axial or circumferentia

and its location within 

vessel, including its a

axial positions and its 

embedded from the 

clad-to-base-metal in

10 CFR 50.61a(e)(4) sta

following:

The licensee shall pe

to demonstrate that th

vessel will have a TW

1x10-6 per reactor yea

Code, Section XI, vol

examination required 

paragraph (c)(2) or (d

section indicates any 

following:

(i) The flaw density an

inspection volume de

paragraph (e)(1) exce

Tables 2 or 3 of this s
3-7

No. 10 CFR 50.61a 

Paragraph

MRP-334 

Recommendation

MRP-334

Justification

NRC

Respon

13 (e)(1), (e)(4) A qualitative 

assessment process 

should be provided for 

addressing a flaw that 

exceeds the maximum 

size allowed in the flaw 

limit tables but is less 

than 0.875 inch in TWE.

Section 3.7.1 proposes a qualitative 

process that considers flaw orientation, 

flaw location, flaw size, and material 

properties.

The NRC agrees with th

Step I of this regulatory 

the recommendation.

14 (e)(1), (e)(4), 

(e)(5)

A quantitative 

assessment process 

should be provided 

(1) for instances in

which multiple flaws

exceed the flaw limit

tables or (2) if the

requirements of the

qualitative process

cannot be satisfied.

Section 3.7.2 provides a quantitative 

process that considers the contribution 

of individual flaws to the total vessel 

TWCF. If needed, Appendix F 

provides an additional process that 

reduces some of the conservatisms in 

the Section 3.7.2 process.

The NRC agrees with th

Step I of this regulatory 

the recommendation.

15 (e)(1) When assessing the 

flaw-limit tables, 

multiple flaws that are 

combined into one flaw 

in accordance with the 

ASME Code, 

Section XI, proximity 

rules should not be 

counted as multiple ISI 

flaws.

The ASME Code, Section XI, proximity 

rules were considered in the 

development of the flaw distributions 

used in the technical basis for 

10 CFR 50.61a. Section 3.7.2 

provides additional information.

The NRC agrees with th

regulatory guide conside

proximity, as indicated in 

4-1

4 GUIDANCE FOR CRITERIA RELATED TO THE DATE OF 

CONSTRUCTION AND DESIGN REQUIREMENTS

The Alternate PTS Rule applies to plants with construction permits issued before 

February 3, 2010, and with RPVs designed and fabricated in accordance with the 1998 edition 

or an earlier edition of the ASME Code. This chapter provides guidelines and supporting bases 

for this requirement.

4.1 Requirements in the Alternate Pressurized Thermal Shock Rule

The regulation at 10 CFR 50.61a(b), “Applicability,” states that the Alternate PTS Rule applies to 

plants that were issued a construction permit after February 3, 2010. Section II of 75 FR 13–29 

[2] states the following:

The final rule is applicable to licensees whose construction permits were issued before 

February 3, 2010 and whose reactor vessels were designed and fabricated to the 

American Society of Mechanical Engineers Boiler and Pressure Vessel Code (ASME 

Code), 1998 Edition or earlier. This would include applicants for plants such as Watts 

Bar Unit 2 who have not yet received an operating license. However, it cannot be 

demonstrated, a priori, that reactor vessels that were not designed and fabricated to the 

specified ASME Code editions will have material properties, operating characteristics, 

PTS event sequences and thermal hydraulic responses consistent with those evaluated 

as part of the technical basis for this rule. Therefore, the NRC determined that it would 

not be prudent at this time to extend the use of the rule to future PWR plants and plant 

designs such as the Advanced Passive (AP) 1000, Evolutionary Power Reactor (EPR) 

and U.S. Advanced Pressurized Water Reactor (US APWR). These designs have 

different reactor vessels than those in the currently operating plants, and the fabrication 

of the vessels based on these designs may differ from the vessels evaluated in the 

analyses that form the bases for the final rule. Licensees of reactors who commence 

commercial power operation after the effective date of this rule or licensees with reactor 

vessels that were not designed and fabricated to the 1998 Edition or earlier of the ASME 

Code may, under the provisions of § 50.12, seek an exemption from § 50.61a(b) to apply 

this rule if a plant specific basis analyzing their plant operating characteristics, materials 

of fabrication, and welding methods is provided.

Section 4.2 discusses the regulatory guidance for the above requirements.

4.2 Regulatory Guidance 

The NRC applied the restriction in Section 4.1 on the applicability of the Alternate PTS Rule 

embrittlement screening criteria because the structural and thermal-hydraulic analyses that 

established the basis for the Alternate PTS Rule represented only plants constructed before 

February 3, 2010. A licensee that applies the Alternate PTS Rule to a plant with a construction 

permit issued after February 3, 2010, must demonstrate that the technical bases calculations in 

NUREG 1806, “Technical Basis for Revision of the Pressurized Thermal Shock (PTS) 

Screening Limit in the PTS Rule,” issued August 2007 [6], and its supporting technical reference 

adequately address the risk significant factors that control PTS for the plant in question. The 

factors that this evaluation should consider include, but might not be limited to, the following:

• the event sequences that may lead to overcooling of the RPV
4-2

• the thermal hydraulic response of the nuclear steam supply system in response to such

sequences

• characteristics of the RPV design (e.g., vessel diameter, vessel wall thickness, and

operating pressure) that influence the stresses that develop in the beltline region of the

vessel (as defined in Section 1.2) in response to the event sequences

• characteristics of the RPV materials and their embrittlement behavior
5-1

5 GUIDANCE FOR CRITERIA RELATED TO THE EVALUATION OF 

PLANT SPECIFIC SURVEILLANCE DATA

The NRC staff developed and published the information in this chapter to support the 

development of the Alternate PTS Rule. Chapter 5 repeats relevant information from this work 

for completeness and clarity [14] and, in some cases, further clarifies the information in 

Reference [14] compared to the technical bases supporting the Alternate PTS Rule. 

Additionally, the information presented in this chapter adds to the information in Reference [14] 

in two respects: (1) Section 5.2 describes procedures for grouping data (e.g., treatment of 

“sister plant” data) before performing the statistical tests, and (2) Section 5.6.2 describes 

procedures that can be used if the statistical tests are failed.

This chapter describes procedures that licensees can use to analyze the plant-specific 

surveillance data collected through surveillance programs (in accordance with 10 CFR Part 50, 

Appendix H) to assess how well the ETC represents these data . If the surveillance data are 

“close” (closeness is assessed statistically) to the prediction of the ETC, the predictions of the 

ETC are used. Statistically significant differences between plant-specific datasets and the ETC 

prediction identify situations that warrant more focused attention and are an indication that 

methods other than, or in addition to, the ETC may be needed to predict ∆T30 trends. Although

standard statistical procedures exist to assess the significance of differences between individual 

datasets and ETC predictions, similarly standard procedures are not as commonly available to 

assess the practical importance of such differences or to adjust the data to account for these 

differences. This chapter concludes by discussing (1) factors that licensees may consider if the 

statistical tests are failed and (2) procedures that licensees could use to adjust the predictions of 

the ETC in certain circumstances. 

The remainder of this chapter is divided into six sections:

• Section 5.1 describes the ΔT30 ETC. Oak Ridge National Laboratory (ORNL)

TM-2006/530, “A Physically Based Correlation of Irradiation-Induced Transition

Temperature Shifts for RPV Steels,” issued November 2007, describes the development

of this ETC [9].

• Section 5.2 describes entry conditions that licensees must meet to use the proposed

surveillance assessment procedure.

• Section 5.3 describes different types of deviations between plant-specific surveillance

data and the trends represented by the ∆T30 ETC from Reference [9].

• Section 5.4 describes procedures that statistically assess the deviations described in

Section 5.3.

• Section 5.5 applies the procedures of Section 5.4 to the surveillance database that

supported the development of the ETC [9].
5-2

• Section 5.6 discusses factors that licensees should consider if the statistical tests of

Section 5.4 are failed. In addition, it describes procedures that licensees could use to

adjust the predictions of the ETC in certain circumstances.

5.1 Embrittlement Trend Curve

As detailed in ORNL/TM-2006/530 [9], the numerical coefficients in the following equations were 

determined by fitting them to the ∆T30 data collected through the 10 CFR Part 50, Appendix H, 

surveillance programs that licensees have submitted to the NRC through approximately 2002. 

This ∆T30 ETC, which is used in the Alternate PTS Rule, has the following form:

ΔTT30 = MMMM + CCCCCC (5-1)

MMMM = A ⋅ (1 − 0.001718 TTcc)(1 + 6.13 P Mn2.471)φφφφee

0.5 (5-2)

AA = �

1.14x10−7 for forgings

1.561x10−7 for plates

1.417x10−7 for welds

(5-3) 

CCCCCC = B ⋅ �1 + 3.77 Ni1.191� f(Cue, P) ⋅ g�Cue, Ni, φφφφee� (5-4)

BB = 

⎩

⎪

⎨

⎪

⎧

102.3 for forgings

102.5 for plates in non-Combustion Engineering vessels

135.2 for plates in Combustion Engineering vessels

155.0 for welds

(5-5) 

Cue = �

0 if Cu ≤ 0.072

mmmmmm�Cu, MAX(Cue)� if Cu > 0.072 (5-6) 

MAX(Cue) = �

0.243 for Linde 80 welds

0.301 for all other materials (5-7) 

ff(CCCCee, ) = �

0 for CCCC ≤ 0.072

(CCCCee − 0.072)0.668 for CCCC > 0.072 and ≤ 0.008

[(CCCCee − 0.072) + 1.359( − 0.008) ]0.668 for CCCC > 0.072 and > 0.008

(5-8) 

gg(CCCCee, NN ,φφφφee) = 0.5 + 0.5

× tt h �

llll 10(φφφφee) + 1.1390 × CCCCee − 0.448 × NN − 18.120

0.629 � (5-9) 

ff(CCCCee, ) = �

0 for CCCC ≤ 0.072

(CCCCee − 0.072)0.668 for CCCC > 0.072 and ≤ 0.008

[(CCCCee − 0.072) + 1.359( − 0.008) ]0.668 for CCCC > 0.072 and > 0.008

(5-10) 

Equation (1) estimates the dependent variable, ∆T30, in degrees Fahrenheit (F). Table 5-1 lists 

the standard deviation of residuals about Equation (1) for different product forms and Cu
5-3

contents. Table 5-2 provides the units and descriptions of independent variables in these

equations. As with any equation calibrated to empirical data, inaccuracies have a greater

tendency to occur at the extremes of, or beyond the limits of, the calibration dataset. Users of

Equation (1) should therefore exercise caution when applying it to conditions near or beyond the

extremes of its calibration dataset, which appears in Table 5-2. For example, for materials that

have Cu contents below 0.072 weight percent (wt%), Equation (1) predicts negative ∆T30 values

when the irradiation temperature exceeds 582.1 degrees F. Clearly, negative shift values are

incorrect. 

Table 5-1 Standard Deviation of Residuals about Equation (1) 

Product Form

Standard Deviation, σ (°F)

Cu ≤ 0.072 wt% Cu > 0.072 wt%

Weld

18.6

26.4

Plate 21.2

Forging 19.6

Table 5-2 Independent Variables in the Equation (1) ETC and 

the Ranges and Mean Values of the Calibration Dataset

Variable Symbol Units

Values of Surveillance Database

Average Standard 

Deviation Minimum Maximum

Neutron Fluence

(E > 1 MeV) φt n/cm2 1.24x10+19 1.19x10+19 9.26x10+15 1.07x10+20

Neutron Flux 

(E > 1 MeV) φ n/cm2/s 8.69x10+10 9.96x10+10 2.62x10+08 1.63x10+12

Irradiation Temperature Tc °F 545 11 522 570

Copper Content Cu wt% 0.140 0.084 0.010 0.410

Nickel Content Ni wt% 0.56 0.23 0.04 1.26

Manganese Content Mn wt% 1.31 0.26 0.58 1.96

Phosphorus Content P wt% 0.012 0.004 0.003 0.031
5-4

5.2 Data Used in Statistical Tests

Licensees should apply the following requirements for the use of surveillance data to perform 

the statistical tests outlined in this chapter:

(1) Materials Evaluated (i.e., the Meaning of “Plant Specific”)

• When performing the statistical tests required by the Alternate PTS Rule, the

licensee should evaluate each shell and weld material in the RPV beltline region

for which 10 CFR Part 50, Appendix H, surveillance data exist. The statistical

tests should be performed separately for each heat.

• For each heat that has available data, the ΔT30 values used in the statistical tests

should include data from the following sources:

- data obtained for the heat of material in question as part of a

10 CFR Part 50, Appendix H, surveillance program conducted for the

plant in question

- data obtained for the heat of material in question as part of a

10 CFR Part 50, Appendix H, surveillance program conducted for any

other plant that is operating, or has operated, under a license issued by

the NRC

Data from this source is often referred to as having come from a “sister

plant.” Such data may have different best-estimate chemistry values and

different irradiation temperatures (e.g., the Cu and Tc values for

heat “123” at plant “XYZ” may be 0.23 and 553 degrees F, respectively,

whereas the Cu and Tc values for heat “123” at plant “ABC” may be 0.21

and 544 degrees F, respectively). The statistical tests described in

Sections 5.3 and 5.4 operate on the residuals (i.e., the difference

between the surveillance measurement of ΔT30 and the prediction of the

ETC). In so doing, the ETC takes account of these plant-specific

variations in chemistry and/or temperature, so there is no need to make

further adjustments to account for so-called “sister plant” data (see

Reference [10]).

(2) Data Quantity Requirements

To perform these statistical tests, at least three plant-specific ∆T30 values, each

measured at a unique fluence value, should be available. If this condition is not met, the

licensee should use the ETC described in the Alternate PTS Rule to estimate ∆T30.

(3) Data Binning Requirements

• As discussed in item 1, these statistical evaluations should bin together and

consider data obtained for the heat of material in question as part of a

10 CFR Part 50, Appendix H, surveillance program conducted for any plant that

is operating, or has operated, under a license issued by the NRC.
5-5

• For plates and forgings, Charpy data are often obtained for different orientations

of the notch relative to the primary working direction of the plate or forging. For

these statistical tests, ΔT30 values for a particular plate or forging should be

computed from unirradiated specimens that have the same notch orientation.

Once ΔT30 values are calculated, different notch orientation data from the same

heat of material should be binned together for the statistical tests described in

Sections 5.3 and 5.4. This is appropriate because the differences in unirradiated

transition temperature caused by notch orientation will be subtracted out when

ΔT30 values are calculated.

(4) Data Characterization Requirements

For all materials meeting the requirements of the three preceding items, the following

information is needed:

• heat identification

• plant identification

• capsule identification

• product form

• notch orientation

• the unirradiated reference temperature, RTNDT(U)

• ∆T30

• Charpy V-notch (CVN) energy data used to estimate ΔT30

• fluence

• flux

• operating time

• cold-leg temperature under normal full-power operating conditions (Tc) (i.e., Tc

(degrees F) is determined as the time-weighted average coolant temperature of

the reactor coolant system cold leg that covers the time period when the capsule

was in the reactor)

• Cu content

• Ni content

• P content

• Mn content

• citation (i.e., the reference, or references, for all of the information listed above)
5-6

The values of Cu, Ni, P, and Mn are the best-estimate values for the material. For a 

plate or forging, the best-estimate value is normally the mean of the measured values for 

that plate or forging. For a weld, the best-estimate value is normally the mean of the 

measured values for a weld deposit that are obtained using the same weld wire heat 

number as the critical vessel weld. If these values are not available, the licensee should 

use either the upper limiting values given in the material specifications to which the 

vessel material was fabricated or conservative estimates (i.e., mean plus one standard 

deviation) based on generic data. Table 4 of 10 CFR 50.61a provides the upper-bound 

estimates for P and Mn. Similarly, 10 CFR 50.61 provides the upper-bound estimates 

for Cu and Ni.

5.3 Statistical Evaluation of Surveillance Data

In developing this surveillance assessment procedure, consideration was given to the 

development of statistical tests capable of detecting the four types of deviations between 

heat-specific surveillance data and the ∆T30 ETC expressed by Equations (1) through (10). 

Figure 5-1 illustrates these deviations and identifies them as Type A, B, C, and D. The list 

below describes the potential origins and implications of these types of statistical deviations. 

Figure 5-1 illustrates only situations in which the data suggest that the ∆T30 ETC may provide a 

nonconservative prediction (i.e., situations in which the data exceed the ETC prediction). The 

opposite situation is also possible (i.e., situations in which the ETC underestimates the data). 

However, only nonconservative predictions are important from a regulatory viewpoint.

• Type A Deviations. For Type A deviations, measurements differ from the mean ETC

prediction more or less uniformly at all fluence levels. Additionally, the magnitude of this

deviation is larger than would be expected based on the population of data used to

calibrate the ETC. Potential origins of Type A deviations may include, but are not limited

to, errors in the chemical composition values or errors in the unirradiated ∆T30 value

associated with the surveillance sample. A statistically significant Type A deviation

(Section 5.4.1 describes procedures for evaluating statistical significance) implies that

the ETC may systematically underestimate the value of ∆T30 for the heat of steel being

evaluated.

• Type B Deviations. For Type B deviations, measurements differ from the mean ETC

prediction by an amount that increases as fluence increases. Additionally, the

magnitude of this deviation is larger than would be expected based on the population of

data used to calibrate the ETC. Potential origins of Type B deviations may include, but

are not limited to, (1) errors in the temperature value associated with the surveillance

sample or (2) the existence of an embrittlement mechanism that is not represented in the

ETC calibration dataset. A statistically significant Type B deviation (Section 5.4.2

describes procedures for evaluating statistical significance) implies that the ETC may

systematically underestimate the value of ∆T30 for the heat of steel being evaluated and

that the magnitude of this underestimation will increase as the plant operation continues.
5-7

• Type C Deviations. For Type C deviations, measurements differ from the mean ETC by

exhibiting more scatter than would be expected based on the population of data used to

calibrate the ETC. Potential origins of Type C deviations may include, but are not limited

to, errors made in testing, labeling, or controlling the notch orientation of surveillance

specimens. Statistically significant Type C deviations do not imply that the ETC may

systematically underpredict the true embrittlement; instead, such deviations imply that

the ability of the surveillance data to provide insight into embrittlement trends is called

into question for a specific heat of material.

• Type D Deviations. For Type D deviations, one or more of the ∆T30 measurements differ

significantly from the mean ETC prediction even though all other measurements for the

heat of steel being evaluated agree well with that prediction. The magnitude of the

deviation of these outliers is larger than would be expected based on the population of

data used to calibrate the ETC. Potential origins of Type D deviations may include, but

are not limited to, (1) a large measurement error in the single datum or (2) the rapid

emergence of an embrittlement mechanism in the surveillance sample that is not

represented in the calibration dataset (e.g., rapid emergence of a Type B deviation). A

statistically significant Type D deviation (Section 5.4.3 describes procedures for

evaluating statistical significance) implies that the ETC may systematically

underestimate the value of ∆T30 for the heat of steel being evaluated.

If they are statistically significant, Type A, B, and D deviations all give rise to concerns that the 

embrittlement trends predicted by the ETC may produce nonconservative estimates of the 

embrittlement experienced by materials that are used to construct the RPV under evaluation. 

For this reason, Sections 5.4.1 through 5.4.3 describe the methods used to assess the 

statistical significance of these deviations. Type C deviations, if they are statistically significant, 

suggest that the surveillance program for the material in question may not reliably indicate 

embrittlement trends for that material. Because 10 CFR Part 50, Appendix H, requires the 

performance of surveillance on the “limiting” (meaning “most irradiation-sensitive”) materials 

used to construct the RPV beltline, the existence of a Type C deviation is important from a 

regulatory viewpoint but not in the context of indicating a potential nonconservatism in the 

predictions of the ∆T30 ETC adopted in the Alternate PTS Rule. For this reason, the Alternate 

PTS Rule does not include statistical procedures to detect Type C deviations (see 

Reference [1]); therefore, Section 5.4 does not describe such procedures. 
5-8

Figure 5-1 Four types of deviations between heat specific surveillance data and a ∆T30 ETC 

– 30(MEAS)

T

∆

30(ETC,mean)

T

∆

φt

30

T

∆

φt

Mean ETC Prediction 

Surveillance 

Measurements 

ETC Confidence Bounds

– 30(MEAS)

T

∆

30(ETC,mean)

T

∆

φt

30

T

∆

φt

– 30(MEAS)

T

∆

30(ETC,mean)

T

∆

30

T

∆

– 30(MEAS)

T

∆

30(ETC,mean)

T

∆

φt

30

T

∆

φt

Type A

(measurements 

uniformly offset 

from ETC)

Type B

(measurements diverge 

from ETC; different 

fluence trend)

Type C

(measurements have 

more uncertainty than 

ETC calibration data)

(out
5-9

5.4 How to Perform Statistical Tests of Surveillance Data

This section describes how to perform the Type A (mean test), Type B (slope test), and Type D 

(outlier test) assessments of surveillance data are required by the Alternate PTS Rule.

5.4.1 Type A Deviations

As illustrated by Figure 5-1, Type A deviations are characterized by measurements that differ 

from the mean ETC prediction more or less uniformly at all fluence levels. The following 

procedure can be used to detect Type A deviations when the ∆T30 measurements for a specific 

heat of material are uniformly underpredicted by Equation (1). A statistical significance level of 

α = 1% (i.e., 2.33 standard deviations) is recommended for this one-sided test. Section 5.4.4

discusses the rationale for this selection.

A-1. Ensure that the entry conditions of Section 5.2 have been met.

A-2. Estimate the residual (r) for each datum using the following formula:

rr = ΔTT30(MM MMMMMMMM MM) − ΔTT30(PP PPPPPP ), (5-11)

where ∆T30(measured) represents each individual measurement, and ∆T30(predicted) is 

the value of ∆T30 predicted by Equation (1) using the best-estimate composition 

for the surveillance material and the best-estimate exposure values for the plant 

from which the companion ∆T30(measured) value was obtained.

A-3. Estimate the mean residual (rmean) for the ∆T30 dataset using the following 

formula:

rrmm mm = 1�{rr }

=1

, (5-12)

where n is the number of ∆T30 measurements for the specific heat of material

under assessment. 

A-4. Estimate the maximum allowable residual (rmax) using the following formula:

rrmm mm = 2.33σσ

√ , (5-13)

where n is the number of ∆T30 measurements for the specific heat of material 

under assessment and σ is the population standard deviation taken from

Table 5-1. 

A-5. If rmean exceeds rmax, the subject dataset shows a Type A deviation.
5-10

5.4.2 Type B Deviations

As illustrated by Figure 5-1, Type B deviations are characterized by measurements that differ 

from the ETC prediction by an amount that increases as fluence increases. The following 

procedure is used to detect Type B deviations. Similar to the test for Type A deviations, a 

statistical significance level of α = 1% is recommended for this one-sided test. Section 5.4.4

discusses the rationale for this selection.

B-1. Ensure that the entry conditions of Section 5.2 have been met.

B-2. For each measured ∆T30 value, calculate the difference between the measured 

and predicted value of ∆T30 using Equation (11). As illustrated in Figure 5-2, plot 

r versus the log10 value of fluence. The abscissa is expressed in this manner

because embrittlement, as quantified by ∆T30, increases approximately linearly 

with the logarithm of fluence.

B-3. Using the method of least squares, estimate the slope (m) of the data plotted as 

shown in Figure 5-2. In addition, estimate the standard error of the estimated 

value of the slope, se(m).

B-4. Estimate the T-statistic for the slope as follows:

TTSSSSSSSS = mm

ss (mm) (5-14)

B-5. Establish the critical T-value as follows:

TTCC CCCC(αα) = (αα, − 2), (5-15)

where t(...) represents Student’s t-distribution, α is the selected significance 

level, and n is the number of ∆T30(Measured) values. Adoption of α = 1% is 

recommended for regulatory implementation of this procedure. Section 5.4.4

discusses the rationale for this selection. Table 5-3 provides values of TCRIT(1%). 

Log10(φt)

Figure 5-2 Procedure used to assess Type B deviations 

m

r
5-11

Table 5-3 α = 1% Student’s t-Values 

Number of 

∆T30 Values, n

n-2 One-Tailed TCRIT

(1%, n-2)

3 1 31.82

4 2 6.96

5 3 4.54

6 4 3.75

7 5 3.36

8 6 3.14

9 7 3.00

10 8 2.90

11 9 2.82

12 10 2.76

13 11 2.72

14 12 2.68

15 13 2.65

B-6. If Tm exceeds TCRIT(α), the subject dataset shows a Type B deviation.

5.4.3 Type D Deviations

As illustrated by Figure 5-1, Type D deviations are characterized by one or more of the 

∆T30 measurements differing significantly from the mean ETC prediction even though all other 

measurements for the heat of steel under evaluation agree well with the ETC. Similar to the 

tests for both Type A and Type B deviations, a statistical significance level of α = 1% is 

recommended for this one-sided test. Section 5.4.4 discusses the rationale for this selection.

D-1. Ensure that the entry conditions of Section 5.2 have been met.

D-2. Estimate the normalized residual, r*, for each or the n observations in the 

∆T30 dataset using the following formula:

rr∗ = rr

σσ

(5-16)

where r is defined from Equation (11) and σ is the population standard deviation 

taken from Table 5-1. 

D-3. Find the largest and second largest r* values from Step D-2; designate these as

r*1 and r*2, respectively.

D-4. Find the limit values rLIMIT(1) and rLIMIT(2) corresponding to n in Table 5-4. These 

threshold values correspond to a significance level of α = 1%. Appendix A to this 

document describes how the values of C1 and C2 in Table 5-4 were derived.

D-5. If r*1 ≤ rLIMIT(1) and r*2 ≤ rLIMIT(2), the dataset is judged to not show a Type D 

deviation. Otherwise the surveillance dataset is judged to show a Type D 

deviation. 
5-12

Table 5-4 α = 1% Threshold Value for the Outlier Test 

n rLIMIT(2) rLIMIT(1)

3 1.55 2.71

4 1.73 2.81

5 1.84 2.88

6 1.93 2.93

7 2.00 2.98

8 2.05 3.02

9 2.11 3.06

10 2.16 3.09

11 2.19 3.12

12 2.23 3.14

13 2.26 3.17

14 2.29 3.19

15 2.32 3.21

17 2.37 3.24

26 2.53 3.36

64 2.83 3.62

Note that Appendix A refers to rLIMIT(1) as C2

and rLIMIT(2) as C1. The notation is changed 

here to improve clarity.

5.4.4 Comments on the Statistical Tests

The significance level recommended for regulatory implementation of the Type A, B, and D tests 

is α = 1%. At this significance level, there is less than a 1-percent chance that the underlying 

cause of the detected difference (Type A, B, or D) between the plant-specific surveillance data 

and the value of ∆T30 predicted by Equation (1) has occurred as a result of chance alone. The 

following considerations informed this recommendation:

• A 1-percent significance level makes it more difficult for plant-specific surveillance data

to be declared “different” from the predictions of the ETC than has traditionally been the

case. For example, both 10 CFR 50.61 [3] and Regulatory Guide 1.99, “Radiation

Embrittlement of Reactor Vessel Materials,” Revision 2, issued May 1988 [15], use a

“2σ” criterion which, for a one-sided test, implies an α = 2.5% significance level. The

staff views this change in significance level from 2.5 percent to 1 percent as appropriate

in view of the greater physical and empirical support of Equation (1) than that available

when the NRC adopted both 10 CFR 50.61 and Regulatory Guide 1.99, Revision 2.

• The selection of the α = 1% significance level represents a conscious tradeoff between

the competing goals of providing high confidence in the determination of a statistically

significant difference between plant-specific surveillance data and the predictions of

Equation (1) versus limiting the risk of judging that a particular set of plant-specific

surveillance data are similar to the ∆T30 ETC when, in fact, they are not. The former

goal is achieved by adopting a small value for α, whereas the latter goal is achieved by

increasing the α value.

• If a plant-specific dataset is determined by these statistical tests to be “different” from the

predictions of Equation (1), the alternatives that are available to licensees to either
5-13

troubleshoot the cause of the difference or develop new/replacement data are limited, 

expensive, or have long lead times. Consequently, although the NRC recognizes the 

importance of comparing plant-specific data to generic trends and taking action when 

such comparisons show differences, the agency believes that reserving such actions to

cases in which the differences are the clearest and are the most practically significant is 

justified. 

Considering all of these factors, the Alternate PTS Rule adopted a significance level for Type A, 

B, and D deviations of α = 1%.

5.5 Evaluation of Plant Data Relative to the Statistical Tests

This section presents information that appeared previously in Reference [14]. It is repeated 

here for clarity and completeness.

The plant surveillance data used in ORNL/TM-2006/530 [9] to calibrate Equation (1) were 

evaluated according to the statistical tests detailed in Section 5.4. After filtering the data to 

remove heats having less than three ∆T30 observations at three different fluence values, 

159 datasets remained for evaluation. These sets included data from both PWRs and BWRs 

and from plants that are no longer in operation. Although the BWR and ex-plant data are not 

directly pertinent to the Alternate PTS Rule, this analysis retained them for information. 

Appendix B contains the detailed results of these analyses. 

Table 5-5 summarizes the 14 heats of material from 12 plants that show a statistically significant 

deviation of Type A, B, or D, whereas Table 5-6 summarizes the proportion of heats in the 

surveillance database that exhibit statistically significant deviations at the α = 1% level. The 

information in Table 5-6 demonstrates that both the mean and the outlier tests exhibit a rate of 

deviation above the expected value for a population of 159 datasets (i.e., 1 percent of 159, or 

1.59), whereas the deviation rate of the slope test is close to this expected value. These 

observations suggest that, for the mean and outlier tests, the assumption that the residuals are 

distributed normally about the ETC (Equation (1)) may be incorrect. One possible explanation 

for this situation could be the presence of systematic biases in some of the unirradiated 

T30 values (e.g., arising from measurement error or imprecision). Such biases, if present, would 

have no effect on the detection rate of the slope test because it operates on the differences 

between ∆T30 residuals, not on their absolute values. Therefore, any systematic biases in the 

unirradiated ∆T30 values would be subtracted from the ∆T30 difference values that are used to 

perform the slope test and, consequently, could not affect the outcome of the test. Conversely, 

the mean and outlier tests both operate on the absolute values of ∆T30 residuals. Consequently, 

systematic biases in the unirradiated values of ∆T30 could affect the normalcy of the 

∆T30 residuals and, thereby, the detection rate of the mean and outlier tests.
5-14

Table 5-5 Heats of Material That Exhibit Statistically Significant Deviations 

(α = 1%) of Type A, B, or D 

Plant Name Heat ID Product 

Form

Population 

σ (°F)

Number 

of ∆T30

Values

Test Results

A -

Mean 

Test

B -

Slope 

Test

D -

Outlier 

Test

 Operating PWRs

San Onofre Unit 3 PSO301 Plate 18.6 3 FAIL PASS FAIL

D.C. Cook, Unit 2 PCK201 Plate 21.2 8 FAIL PASS PASS

Beaver Valley, Unit 1 PBV101 Plate 21.2 8 FAIL PASS FAIL

Callaway WCL101 Weld 18.6 4 FAIL PASS FAIL

Surry, Unit 1 WSU101 Weld 26.4 3 FAIL PASS FAIL

Indian Point, Unit 2 PIP203 Plate 21.2 3 FAIL PASS PASS

Sequoyah, Unit 1 FSQ101 Forging 19.6 8 FAIL PASS PASS

Sequoyah, Unit 1 WSQ101 Weld 26.4 4 FAIL PASS PASS

Sequoyah, Unit 2 WSQ201 Weld 26.4 4 PASS PASS FAIL

 Operating BWRs

River Bend, Unit 1 and 

Oyster Creek WRB01 Weld 18.6 3 FAIL PASS FAIL

 Decommissioned PWRs

Maine Yankee PMY01 Plate 21.2 6 FAIL PASS PASS

Zion, Unit 1 WZN101 Weld 18.6 5 PASS FAIL PASS

 Decommissioned BWRs

Big Rock Point PBR01 Plate 21.2 5 FAIL FAIL FAIL

Table 5-6 Proportion of Material Heats in the Current Surveillance Database That Exhibit 

Statistically Significant Deviations (α = 1%) of Type A, B, or D 

Test Type Datasets that Show Statistically 

Significant (α = 1%) Deviation

Count Percent

A Mean Test 11 6.9%

B Slope Test 2 1.3%

D Outlier Test 7 4.4%

5.6 Considerations When Statistical Tests Are Failed

Failure of plant-specific surveillance data to pass any of these statistical tests indicates a 

situation in which Equation (1) may underestimate the embrittlement magnitude. Using

Equation (1) in such situations without additional justification is not advisable. Such failures 

warrant a more focused assessment of the surveillance data and indicate that methods other 

than, or in addition to, the ETC may be necessary to reliably predict ∆T30 trends. However, the 

most appropriate approach may not be a heat-specific adjustment of the ETC predictions in all 

cases. For example, statistically significant differences may indicate situations in which the 

available data (i.e., the ΔT30 measurements or the composition and exposure values associated 
5-15

with the ΔT30 measurements, or both) are incorrect; therefore, adjusting the ETC predictions to 

match these data would be unwise.

This section divides the discussion into two parts. First, it lists the factors that could help in 

diagnosing the reason why the surveillance data failed the statistical tests. Second, it discusses 

situations in which adjustments of the ETC predictions may be made using simple procedures. 

5.6.1 Factors To Consider When Statistical Tests Are Failed

Before the licensee considers adjusting the ETC predictions to match surveillance data, the 

NRC suggests that the licensee conduct a detailed assessment of the accuracy and 

appropriateness of the ∆T30 data. Such an assessment should consider, but not be limited to, 

the following factors:

• Unirradiated RTNDT Value. As noted in Section 5.5, the occurrence of mean and outlier

failures in the available surveillance data exceeds the statistically expected value. Both

of these tests are sensitive to the accuracy of the unirradiated RTNDT value. In these

cases, a records investigation of the unirradiated RTNDT value or the performance of

additional testing of archival material, or both, may provide a more accurate estimate of

RTNDT, which may explain the reason for failure of the mean test or outlier test, or both.

• Irradiated ∆T30 Values. Although most CVN energy versus temperature curves from

which ∆T30 values are estimated are based on 8 to 12 individual measurements, some

datasets are more limited and, therefore, can increase uncertainty in the ∆T30 estimate.

If any of the statistical tests are not satisfied, a review of the individual CVN

energy versus temperature curves may help to reveal the cause of the failure.

• Composition and Exposure Variables. The input variables to Equation (1) are subject to

variability and are often based on limited data. However, the predictions of Equation (1)

depend on these input variables, particularly Cu content, fluence, temperature, and

Ni content. If a sensitivity analysis reveals that small variations of the values input to

Equation (1) rationalize the failure of the statistical tests, this might indicate that more

refined information concerning input values (e.g., additional measurements) could

explain the reason for the failure of the statistical tests.

• Notch Orientation. The ∆T30 value for plate and forging materials is sensitive to the

orientation of the notch in the CVN specimen relative to the primary working direction of

the plate or forging. Differences in notch orientation between the unirradiated ∆T30 value

and the ∆T30 value of all the irradiated specimens could explain why the mean test is not

satisfied. Similarly, differences in notch orientation between the unirradiated ∆T30 value

and the ∆T30 value of the irradiated specimens in a single capsule could explain why the

outlier test is not satisfied. In these situations, the outcome of a records search or

metallurgical investigation of the tested specimens might be useful to explain the reason

for the failure of the statistical tests.

• Comparative Trends Analysis. In addition to CVN specimens, surveillance capsules also

contain tensile specimens that are part of the capsule testing program. Like ΔT30, the

increase in yield strength with irradiation (ΔYS) also follows certain trends. If the

ΔYS data for a particular material that failed the statistical tests follow the trends
5-16

exhibited by ΔYS data for a similar composition, this information might indicate that the 

CVN specimens were taken from the wrong material or have been somehow mislabeled.

5.6.2 Specific Procedures

If a statistical test is failed, licensees may use any of the following three procedures: 

(1) Mean Test (Type A) Failure. Figure 5-3 (left side) illustrates the following procedure

used to adjust ETC predictions to account for a failure of the mean test:

• Calculate the value ADJ as follows:

AA AA = rrmm mm − rrmm mm (5-17)

• Adjust the prediction of Equation (1) as follows:

ΔTT30(AAAAAA) = MMMM + CCCCCC + AA AA (5-18) 

• Use the value ΔT30(ADJ) in place of ΔT30 in all calculations required by the

Alternate PTS Rule for the material that failed the mean test.

(2) Slope Test (Type B) Failure. One procedure for adjusting ETC predictions to account for

a failure of the slope test is to adjust the ETC predictions, Equation (1), based on the

greater increase of embrittlement with fluence suggested by the plant-specific data. The

licensee should technically justify and document the specific procedure used.

(3) Outlier Test (Type D) Failure (Not Satisfied at Low Fluence). Figure 5-3 (right side)

illustrates a situation in which a ΔT30 value measured at low fluence is the cause of

failing the outlier test. Such a failure is not considered structurally relevant to a PTS

evaluation and, therefore, may be ignored as long as both of the following conditions are

satisfied:

• The fluence of the datum that caused the outlier test failure, φtLOW, is less than

10 percent of the fluence at which the PTS evaluation is being performed, φtEVAL

• After elimination of the datum measured at φtLOW, the entry conditions for the

surveillance tests are still met (i.e., at least three data points measured at three

different fluence levels remain), and all three statistical tests are satisfied with the

reduced dataset.

Other approaches to assessment of surveillance data in which all surveillance measurements 

are bounded are subject to review and approval by the NRC. 
5-17

Figure 5-3 Specific procedures to account for failure of the mean test (left) or low-fluence 

outlier statistical test (right)

5.7 Summary and Conclusions

This chapter discussed the three statistical tests required by the Alternate PTS Rule and 

methods by which data can be evaluated relative to these tests. The aim of these tests is to 

determine whether the surveillance data are sufficiently “close” to the predictions of the ETC to 

allow use of the ETC predictions. From a regulatory perspective, it is of particular interest to 

determine whether plant-specific surveillance data deviate significantly from the predictions of 

the ETC in a manner that suggests that the ETC is likely to underpredict plant-specific trends. 

To this end, a statistical significance level of α = 1% was adopted, which represents a conscious 

tradeoff between the competing goals of providing high confidence in the determination of a 

statistically significant difference between plant-specific surveillance data and the ∆T30 ETC 

versus limiting the risk of judging that a particular set of plant-specific surveillance data are 

similar to the ETC when, in fact, they are not. The α = 1% tests will show fewer statistically 

significant deviations than did 10 CFR 50.61 or Regulatory Guide 1.99, Revision 2, both of 

which use a “2σ” criterion that, for a one-sided test, implies a significance level of α = 2.5%. 

The staff views this change in significance level (from 2.5 percent to 1 percent) as appropriate in 

view of the greater empirical support for the ETC used in the Alternate PTS Rule than that

available when the NRC adopted 10 CFR 50.61 or Regulatory Guide 1.99, Revision 2.

∆

T30(MEAS)

–

∆

T30(ETC,mean)

φt

∆

T30

φt

Mean ETC Prediction 

Surveillance 

Measurements 

ETCConfidence Bounds

∆

T30(MEAS)

–

∆

T30(ETC,mean)

φt

∆

T30

φt

Mean Test Failure

rmean

rmax

ADJ = rmean + rmax

C2

r(max1)

φ φtEVAL tLOW

Low Fluence Outlier Test Failure
5-18

The Alternate PTS Rule adopted three statistical tests because, collectively, they indicate when 

an underprediction of embrittlement magnitude by the ETC may have occurred. Appendix B 

applies these statistical tests to the operating plant surveillance database assembled through 

(approximately) 2002. Of the heats of material considered, only 14 heats from 12 plants failed

one or more of the three statistical tests. Failure of plant-specific surveillance data to pass any 

of the statistical tests indicates a situation in which the ETC may underestimate the 

embrittlement magnitude. Using Equation (1) in such situations without additional justification is 

not advisable. Such failures warrant a more focused assessment of the surveillance data and 

indicate that methods other than, or in addition to, the ETC may be necessary to reliably predict 

∆T30 trends. However, the most appropriate approach may not be a heat-specific adjustment of 

the ETC predictions in all cases. For example, statistically significant differences may indicate 

situations in which the available data (i.e., the ΔT30 measurements or the composition and 

exposure values associated with the ΔT30 measurements, or both) are incorrect; therefore, 

adjusting the ETC predictions to match these data would be unwise. This chapter listed the

factors that could help in diagnosing the reason why the surveillance data failed the statistical 

tests and discusses certain situations for which adjustments of the ETC predictions can be 

made.
6-1

6 GUIDANCE RELATED TO INSERVICE INSPECTION DATA AND 

NONDESTRUCTIVE EXAMINATION REQUIREMENTS

6.1 Background

The technical basis for the Alternate PTS Rule concludes that flaws as small as 0.1 inch in TWE

contribute to the TWCF, and nearly all of the contributions come from flaws buried less than 

1 inch below the inner diameter surface of the reactor vessel wall. Therefore, the Alternate PTS 

Rule specifies flaw limits for such flaws as indicated in Table 1-2 in this document. For weld 

flaws that exceed the sizes and numbers prescribed in Table 1-2, the risk analyses indicated 

that a single flaw contributes a significant fraction of the 1x10-6 per reactor year screening 

criteria on TWCF. Therefore, if a flaw that exceeds the sizes and quantities described in the 

flaw tables is found in a reactor vessel, it is important to assess it individually.

The technical basis for the Alternate PTS Rule also indicated that flaws buried deeper than 

1 inch from the clad-to-base interface did not contribute as significantly to total risk as flaws of 

similar size located closer to the inner surface. Therefore, the Alternate PTS Rule does not 

require a comparison of the density of these flaws, but the rule still requires an evaluation of 

large flaws, if any are discovered, for their contributions to TWCF if they are within the inner 3/8t

of the vessel wall thickness. Because flaws greater than 3/8t of the vessel wall thickness from 

the inside surface do not contribute to TWCF, the rule does not require an analysis of larger 

flaws.

The limitation for flaw acceptance, specified in ASME Code, Section XI, Table IWB-3510-1, 

approximately corresponds to the threshold for flaw sizes that can contribute significantly to 

TWCF if flaws of such sizes are present in reactor vessel material at this depth. Therefore, the 

final rule requires that flaws exceeding the size limits in Table IWB-3510-1 be evaluated for their 

contribution to TWCF in addition to the other evaluations for such flaws that are prescribed in 

the ASME Code.

The regulation at 10 CFR 50.61a(e) describes a number of tests and conditions on the 

collection and analysis of NDE data. These data provide reasonable assurance that the 

distribution of flaws assumed to exist in the probabilistic fracture mechanics (PFM) calculations, 

which provided the basis for the RTMAX-X screening criteria in Table 1-1 of this document, 

provides an appropriate, or bounding, model of the population of flaws in the RPV of interest. 

These tests and conditions, the totality of which the diagram in Figure 6-1 illustrates, go beyond 

a simple comparison of the NDE data to the flaw table limits in Table 1-2. 

The steps below summarize the process depicted in Figure 6-1. For each step in Figure 6-1, 

reference is made to the paragraph in the Alternate PTS Rule that contains the requirement 

addressed by that step.

Step A. All recordable flaw data (see Figure 6-2) should be collected for the inner 3/8t of the 

wall thickness for the base material and weld metal examination volumes within the RPV beltline 

region using procedures, equipment, and personnel as required by ASME Code, Section XI, 

Mandatory Appendix VIII, Supplements 4 and 6 [7], using ultrasonic testing (UT) volumetric 

examinations. (Note that the evaluation required by the flaw tables in 10 CFR 50.61a should 

include any flaws that are detected within the ultrasonic transducer scan paths. This includes 

any flaws located outside of the required ASME Code, Section XI, examination volume (see 

Step D of this procedure)).
6-2

Step B. The plant-specific flaw data from Step A should be evaluated for axial flaw surface 

connection. Any flaws with a TWE greater than or equal to 0.075 inch that are axially oriented 

and located at the clad-to-base metal interface should be assessed to determine whether they 

connect to the RPV inner surface using examination techniques that can detect and 

characterize service-induced cracking of the RPV cladding. Eddy current and visual 

examination methods are acceptable to the staff for detecting cladding cracks. The licensee 

shall implement an appropriate quality standard to ensure that these examinations can 

effectively identify surface cracking as required by 10 CFR Part 50, Appendix B, “Quality 

Assurance Criteria for Nuclear Power Plants and Fuel Reprocessing Plants,” Criterion IX, 

“Control of Special Processes.” Criterion IX requires the licensee to establish measures to 

ensure that special processes, including nondestructive testing, are controlled and 

accomplished by qualified personnel using qualified procedures in accordance with applicable 

codes, standards, specifications, criteria, and other special requirements. Appropriate quality 

standards for surface examinations are identified in the ASME Code, Section XI, or ASME 

Code, Section V, “Nondestructive Examination,” or both.

• If surface connected flaws do not exist then proceed to Step C.

• Conversely, if surface connected flaws do exist then proceed to Step G.

− If the outcome of Step G is a pass, proceed to Step C.

− If the outcome of Step G is a failure, proceed to Step H. 

Step C. The plant-specific flaw data from Step A should be evaluated for acceptability in 

accordance with the ASME Code, Section XI, Table IWB-3510-1, flaw acceptance standards.

• If all flaws are acceptable in accordance with the flaw acceptance standards, proceed to

Step D.

• Conversely, if some flaws are not acceptable in accordance with the ASME flaw

acceptance standards, proceed to Step G.

− If the outcome of Step G is a pass, proceed to Step D.

− If the outcome of Step G is a failure, proceed to Step H. Additionally, the 

licensee must demonstrate that it has satisfied the requirements of ASME Code, 

Section XI, before the vessel could be approved for a return to service.

Step D. The plant-specific flaw data should be compared to Tables 2 and 3 of 10 CFR 50.61a. 

Section 6.3 of this document provides an example of how this step may be performed and 

explains how the plant-specific flaw data are categorized as weld flaws or plate flaws.

• If all flaws are acceptable in accordance with the flaw tables of 10 CFR 50.61a, proceed

to Step I.

• Conversely, if some flaws are not acceptable in accordance with the flaw tables, proceed

to Step E.
6-3

Step E. The evaluation may account for NDE uncertainties such as flaw sizing errors, a flaw 

detection threshold, or POD. Appendix C to this document describes the development and 

application of one methodology acceptable to the NRC that accounts for uncertainties in NDE 

data. The licensee may use this method to develop more realistic vessel-specific flaw depth 

and density distributions for comparison to Tables 2 and 3 of 10 CFR 50.61a and may use them

in a plant-specific PFM analysis. The methodology considers flaw sizing errors, a flaw detection 

threshold, POD, and a prior flaw distribution assumption. It applies a Bayesian updating 

methodology to combine the observed NDE data with the available flaw data and models used 

as part of the PTS reevaluation effort. The licensee must submit the adjustments made to the 

volumetric test data to account for NDE-related uncertainties, as described in 

10 CFR 50.61a(c)(2).

• At the conclusion of this step, proceed to Step F.

Step F. The revised flaw distribution results of Step E should be compared to Tables 2 and 3 of 

10 CFR 50.61a.

• If all flaws are acceptable in accordance with the flaw tables of 10 CFR 50.61a, proceed

to Step I.

• Conversely, if some flaws are not acceptable in accordance with the flaw tables, proceed

to Step G.

Step G. A demonstration that the TWCF is less than 1x10-6 events per reactor year is 

necessary to satisfy 10 CFR 50.61a(e)(4). The staff considers the two approaches described 

below to be acceptable for providing assurance that the TWCF is less than 1x10-6 events per 

reactor year. Therefore, all flaws should be evaluated for acceptability using one of the 

following two approaches:

(1) Preclusion of Brittle Fracture. The licensee can satisfactorily demonstrate upper-shelf

behavior, which precludes brittle fracture, by maintaining temperature above

RTNDT + 60 degrees F using the following steps:

• Compute the irradiated RTNDT for all flaws as follows:

− Determine the unirradiated value of RTNDT and RTNDT(U) for the material at 

each flaw location.

− Determine the fluence at each flaw location.

− Compute ∆T30 for each flaw using Equation (5) and the fluence at each 

flaw location.

− Compute the flaw-specific value of RTNDT as RTNDT(U) + ∆T30 for each flaw.

• Assuming a lower bound PTS transient temperature of 75 degrees F, upper-shelf

behavior is assured if RTNDT + 60 ≤ 75° F. Therefore, the flaw-specific value of

RTNDT should be less than or equal to 15° F. This evaluation is considered

acceptable if the flaw-specific values of RTNDT are less than or equal to 15° F for

all flaws.
6-4

(2) Calculation of the Plant-Specific TWCF Using a Plant-Specific PFM Analysis. A

plant-specific PFM analysis to calculate TWCF is complex, and many variations of inputs

are possible for such an analysis. Therefore, guidance for plant-specific PFM analysis to

calculate TWCF is not provided. Section 6.2.2 provides general considerations for a

plant-specific PFM analysis. Several sources discuss the methodology used in

performing TWCF calculations for PTS. These include NUREG-1806; NUREG-1807,

“Probabilistic Fracture Mechanics—Models, Parameters, and Uncertainty Treatment

Used in FAVOR Version 04.1,” issued June 2007 [20]; and NUREG/CR-6854, “Fracture

Analysis of Vessels—Oak Ridge FAVOR, v04.1, Computer Code: Theory and

Implementation of Algorithms, Methods, and Correlations,” issued August 2007 [21].

The steps associated with conducting a plant-specific PFM calculation are as follows:

• Perform a Bayesian update of the flaw distribution:

− Apply the procedures of Appendix C to this document and obtain revised 

flaw depth and density parameters (similar to those shown in Table 6-2

below).

• Calculate the TWCF using a PFM computer code (e.g., ORNL/TM-2012/566,

“Fracture Analysis of Vessels—Oak Ridge (FAVOR), v12.1, Computer Code:

User’s Guide,” issued 2012) [19]:

− Run the generalized procedure for generating flaw-related inputs (see

Ref. 12) using the revised flaw depth and density parameters.

− Develop necessary plant-specific inputs using the guidance in 

NUREG-1806, NUREG-1807, and NUREG/CR-6854.

− Run a plant-specific PFM analysis.

− Calculate the TWCF.

• Compare the plant-specific TWCF to the TWCF screening criteria specified in

10 CFR 50.61a:

− The evaluation associated with Step I is acceptable if the calculated 

TWCF is less than or equal to the 1x10-6 events per reactor year 

screening criteria specified in 10 CFR 50.61a.

• If the outcome of this step is a pass, proceed to Step I.

• If the outcome of this step is a failure, proceed to Step H.

Step H. The licensee should perform a plant-specific assessment for PTS and submit 

the assessment to the Director of NRR for review and approval as required by 

10 CFR 50.61a(d)(4).
6-5

Step I. The screening criteria in Table 1 of 10 CFR 50.61a may be applied to the plant in 

question. Under 10 CFR 50.61a(c), the NRC requires licensees to submit their 

plant-specific assessments, including explicit details and results, to the Director of NRR 

for review and approval in the form of a license amendment at least three years before 

RTMAX–X is projected to exceed the Alternate PTS Rule screening criteria.

Based on this process, the guidelines discussed in this chapter include the following three 

components:

(1) guidance for plants in which RPV flaws fall outside the applicability of the flaw tables in

the Alternate PTS Rule, including the following:

• guidance on a procedure to preclude brittle fracture

• guidance on considerations to include in a plant-specific PFM analysis

(2) guidance for initial evaluation of NDE data obtained from qualified ISI examinations

(3) guidance on methods for further evaluation of NDE data obtained from qualified ISI

examinations, including the following:

• guidance on the elements and NDE techniques associated with the qualified ISI

examinations performed in accordance with ASME Code, Section XI, Mandatory

Appendix VIII, to assess compliance with the requirements of the Alternate PTS

Rule

• guidance on a mathematical procedure that can be used to adjust NDE data to

account for flaw detection errors and sizing errors and guidance on comparison

of the adjusted data to the population of flaws assumed in the PFM analysis used

to develop the Alternate PTS Rule

The sections below describe guidance for these topics.
6-6

Figure 6-1 Flow diagram with recommendations for meeting the requirements of the Alternate PTS Rule 
6-7

6.2 Guidance on Criteria Related to Alternate Screening Criteria on

Embrittlement

This section describes guidance for situations in which plant-specific NDE results do not meet 

the acceptance standards of ASME Code, Section XI, Table IWB-3510-1, or are not within the 

limits prescribed by the flaw tables in the Alternate PTS Rule. In such situations, additional 

efforts beyond those described in Section 6.1 may still allow application of the PTS screening 

criteria in Table 1-1 of this document. 

The guidelines discussed in this section include the following components: 

• guidance on a procedure that can be used to preclude brittle fracture based on RTNDT

information for RPV flaws that fall outside the applicability of the Alternate PTS Rule flaw

tables

• guidance on a procedure that can be used to combine the NDE data with the population

of flaws assumed in the TWCF calculations to estimate a total flaw distribution that is

predicted to exist in the RPV and guidance on the use of the total flaw distribution if a

licensee chooses to conduct a PFM calculation

The sections below discuss these topics in detail.

6.2.1 Guidance on a Procedure To Preclude Brittle Fracture

This section provides guidance on a mathematical procedure to preclude brittle fracture for 

flaws that exceed the acceptance standards of ASME Code, Section XI, Table IWB-3510-1, as 

identified by Step I in Figure 6-1 of this document. Such guidance is based on information in 

Section II of 75 FR 13–29 [2], which states the following in regard to ISI volumetric examination 

and flaw assessments: 

The technical basis for the final rule also indicates that flaws buried deeper than 

1 inch from the clad-to-base interface are not as susceptible to brittle fracture as 

similar size flaws located closer to the inner surface. Therefore, the final rule 

does not require the comparison of the density of these flaws, but still requires 

large flaws, if discovered, to be evaluated for contributions to TWCF if they are 

within the inner three-eighths of the vessel thickness. The limitation for flaw 

acceptance, specified in ASME Code, Section XI, Table IWB-3510-1, 

approximately corresponds to the threshold for flaw sizes that can make a 

significant contribution to TWCF if present in reactor vessel material at this depth. 

Therefore, the final rule requires that flaws exceeding the size limits in ASME 

Code, Section XI, Table IWB-3510-1 be evaluated for contribution to TWCF in 

addition to the other evaluations for such flaws that are prescribed in the ASME 

Code.

This section describes a simplified procedure for the situation in which the as-found NDE data 

for a plant reveal that one or more flaws fall outside the maximum range of the flaw tables in the

Alternate PTS Rule and that the flaws do not satisfy the flaw-acceptance criteria of ASME Code, 

Section XI. Therefore, the following situations occur: 

• The NDE data were obtained using a qualified examination in accordance with ASME

Code, Section XI, Mandatory Appendix VIII, thereby satisfying Step A in Figure 6-1.
6-8

• All recordable flaws are located away from the clad-to-base-metal interface. Therefore,

Step B is satisfied with a result of “NO” in Figure 6-1.

• Some of the recordable flaws do not meet the flaw-acceptance criteria of ASME Code,

Section XI. Therefore, Step C is not satisfied with a result of “NO” in Figure 6-1.

Thus, based on the above information, Step F in Figure 6-1 requires the licensee to perform a 

flaw evaluation with acceptable results in accordance with ASME Code, Section XI, for those 

recordable flaws that do not meet the flaw-acceptance criteria of ASME Code, Section XI. In 

addition, further evaluation for acceptability using Step I is required. For the purposes of this 

example, a flaw evaluation in accordance with ASME Code, Section XI, is assumed to be 

successful and, therefore, is not described in the assessment that follows.

For the further evaluation required by Step I in Figure 6-1, one approach is to determine 

whether brittle fracture can be precluded. For this situation, a recommended evaluation could 

be the following: 

Step I—Preclude Brittle Fracture Option

• The licensee can satisfactorily demonstrate upper-shelf behavior, which precludes brittle

fracture, by maintaining temperature above RTNDT + 60 degrees F [22].

• The licensee should compute the irradiated RTNDT for all flaws as follows:

− Determine the unirradiated value of RTNDT and RTNDT(u) for the material at each 

flaw location.

− Determine the fluence at each flaw location.

− Compute ∆T30 for each flaw using Equation (1) and the fluence at each flaw 

location.

− Compute the flaw-specific value of RTNDT as RTNDT(u) + ∆T30 for each flaw.

• Assuming a lower-bound PTS transient temperature of 75° F, upper-shelf behavior is

assured if RTNDT + 60 ≤ 75° F. Therefore, the flaw-specific value of RTNDT should be less

than or equal to 15° F.

• Flaws are acceptable if the flaw-specific value of RTNDT is less than or equal to 15° F.

For this situation, the decision at Step F is “ACCEPTABLE” in Figure 6-1.

• Flaws are not acceptable if the flaw-specific value of RTNDT is greater than 15° F. For

this situation, the decision at Step F is “NOT ACCEPTABLE” in Figure 6-1, another

assessment is required (Step E in Figure 6-1), and the provisions of the Alternate PTS

Rule may not be used.

• For the case in which Step F is “ACCEPTABLE,” all recordable flaws less than the

maximum of 0.1 times the vessel wall thickness or 1 inch must be checked against the

flaw tables (Step D in Figure 6-1).
6-9

• If the result of Step D is “PASS,” the RTMAX-X screening criteria of the Alternate PTS Rule

may be used (Step K in Figure 6-1).

Table 6-1 provides a sample calculation that demonstrates acceptability by Step I above. 
6-10

Table 6-1 Sample Brittle Fracture Assessment 

STEP D: Preclude Brittle Fracture for J-2 Flaws

Height on 

RPV (inches)

RPV Circumferential 

Position (°)

Depth Below Clad, 

x (inches)

X 235.00 150.1 1.66 1.02E+19 0.6714 6.85E+18 54.0 4.02E+09

Y 235.14 157.7 2.70 1.02E+19 0.5231 5.34E+18 54.0 3.13E+09

RTNDT(u) (°F) Cu

(wt %)

Ni

(wt %)

Mn

(wt%)

P

(wt%)

X -40 0.09 0.48 1.300 0.004

Y -40 0.09 0.48 1.300 0.004

Flaw No. Temperature

(°F)

φ te

Effective Fluence 

(n/cm2

)

A B Max(Cue) Cue f(Cue,P) g(Cue,Ni,φ te) Mfterm

(°F)

C

X 550.0 1.272E+19 1.417E-07 155.0 0.2430 0.0900 0.0683 9.412E-01 29.2 

Y 550.0 1.057E+19 1.417E-07 155.0 0.2430 0.0900 0.0683 9.253E-01 26.6 

Notes: a. Determined from a plant-specific fluence map.

b. From RPV surveillance program.

Flaw No.

Attenuated Fluence 

at Flaw Location 

(n/cm2

)

LINDE 80 Weld Chemistryb

End-of-Life 

Effective Full 

Power Years 

(EFPY)

Attenuated 

Flux at Flaw 

Location 

(n/cm2

-sec)

Flaw Position Flaw No. Fluence at Clad/Base 

Metal Interface at 

Flaw Location (n/cm2

)

a

Attenuation 

Factor,

e-0.24x
6-11

6.2.2 Guidance on Considerations To Include in a Plant-Specific Probabilistic Fracture

Mechanics Analysis 

This section provides guidance on the key considerations that should be included in a 

plant-specific PFM analysis to calculate TWCF, as identified by Step I in Figure 6-1. Such 

guidance includes a mathematical procedure to combine NDE data with the PFM flaw

distribution used to develop the Alternate PTS Rule. A plant-specific TWCF analysis might be

necessary based on 10 CFR 50.61a(d)(4) [1], which states the following:

(4) If the analysis required by paragraph (d)(3) of this section indicates that no

reasonably practicable flux reduction program will prevent the RTMAX–X value for

one or more reactor vessel beltline materials from exceeding the PTS screening

criteria, then the licensee shall perform a safety analysis to determine what, if

any, modifications to equipment, systems, and operation are necessary to

prevent the potential for an unacceptably high probability of failure of the reactor

vessel as a result of postulated PTS events. In the analysis, the licensee may

determine the properties of the reactor vessel materials based on available

information, research results and plant surveillance data, and may use

probabilistic fracture mechanics techniques.

The PFM computer code, FAVOR [19], was developed by ORNL with NRC funding to predict 

failure probabilities for embrittled vessels subject to PTS transients. The NRC used FAVOR in 

the underlying TWCF analyses for the development of the Alternate PTS Rule. Critical inputs to 

FAVOR are the number and sizes of fabrication flaws in the RPVs of interest and the 

characteristics of cooldown scenarios. The TWCF analysis further requires the expected 

frequencies of the cooldown scenarios. Work on flaw distributions was coordinated with another 

NRC research program conducted by Pacific Northwest National Laboratory (PNNL) to perform 

examinations of RPV materials to detect and measure the numbers and sizes of fabrication 

flaws in welds and base metal. To supplement the limited data from flaw detection and 

measurements, PNNL applied an expert judgment elicitation process and the PRODIGAL flaw 

simulation model developed in the United Kingdom by Rolls-Royce and Associates. PNNL’s 

experimental work on flaw distributions provided fabrication flaw data from NDE and destructive 

examinations, which were used to develop statistical distributions to characterize the numbers 

and sizes of flaws in the various regions of RPVs. Based on these statistical distributions, 

PNNL developed the computer program VFLAW, which generated flaw distributions that were 

used as inputs to the FAVOR computer code [18]. These input files for FAVOR describe flaw 

distributions based on PNNL’s research activities. Therefore, the VFLAW program and the 

incorporation of plant-specific NDE data are critical input elements for performing plant-specific 

TWCF analyses.

Appendix C provides a recommended methodology for combining plant-specific NDE data with 

the PFM flaw distribution used to develop the Alternate PTS Rule. For the sample application to 

Beaver Valley Power Station, Unit 2 (Beaver Valley), discussed in Appendix C (Table C-4), 

Table 6-2 lists the revised flaw parameters that represent a plant-specific flaw distribution. The 

revised parameters on the flaw uncertainty distribution may be used to generate a revised flaw 

distribution for Beaver Valley, Unit 2, that is consistent with the flaw distribution used in the PTS 

FAVOR analyses. The revised parameters will lead to revised flaw distributions that may be 

input to a FAVOR PFM analysis. These parameters have been customized using the 

Appendix C procedure based on the specific geometry of Beaver Valley, Unit 2, and as-found 

NDE data. The revised flaw distributions may be generated and used as input to FAVOR by 

re-running the VFLAW program with the revised parameters listed in Table 6-2. Re-running the 
6-12

VFLAW program allows adjustment of the generic VFLAW flaw distribution used to develop the 

Alternate PTS Rule into a plant-specific flaw distribution based on the updated knowledge of 

flaws obtained from plant-specific ISI. As shown in Table 6-2, this yields a Bayesian updated 

flaw distribution for use in the plant-specific PFM required at Step I in Figure 6-1. 

As described in Appendix C, it is important to note that, although the VFLAW data represent 

generic values of flaw characteristics (based on expert judgment and the PVRUF and 

Shoreham RPVs), such data should be specialized to a specific RPV by using RPV-specific 

weld length, weld bead thickness, geometry, and other weld characteristics. Therefore, the 

specialized VFLAW data that result from this evaluation are the most representative information 

that can be used to describe a prior distribution of flaw depth and flaw density for a 

plant-specific PFM assessment. If other prior information is available, such information may 

also be used instead of, or in addition to, the specialized VFLAW data.

A PFM analysis that calculates TWCF also requires (1) the thermal-hydraulic characteristics of 

the cooldown scenarios as input to FAVOR and (2) the frequency of those scenarios as input to 

the TWCF calculation. The characteristics and frequency of excessive cooldown scenarios are 

not developed by existing probabilistic risk assessments (PRAs), which model only the end 

states of core damage and containment failure. The PTS rulemaking relied on extensive PRA 

analyses to explore, identify, and characterize excessive cooldown end states.

A plant-specific PFM analysis that calculates TWCF is complex, and many variations of inputs 

are possible for such an analysis. Therefore, this report does not include guidance for a 

plant-specific PFM analysis to calculate TWCF. NUREG-1806 [6], NUREG-1807 [21], and 

NUREG/CR-6854 [22] discuss the methodology used in performing a PFM analysis to calculate 

TWCF for PTS. As indicated in the Alternate PTS Rule, the plant-specific PFM analysis used to 

calculate TWCF and the description of the modifications made to the plant-specific inputs must 

be submitted to the Director of NRR in the form of a license amendment at least 3 years before 

RTMAX–X is projected to exceed the PTS screening criteria.

The steps associated with conducting a plant-specific PFM evaluation are as follows:

(1) Perform the Bayesian update of the flaw distribution.

• Apply the procedures of Appendix C and obtain revised flaw depth and density

parameters (similar to those shown in Table 6-2).

(2) Calculate the TWCF using FAVOR.

• Run VFLAW using the revised flaw depth and density parameters.

• Develop necessary plant-specific input using the guidance in NUREG-1806,

NUREG-1807, and NUREG/CR-6854.

• Run a plant-specific FAVOR analysis.

• Calculate the TWCF.
6-13

(3) Compare the plant-specific TWCF from the FAVOR analysis to the screening criteria.

• If the calculated TWCF value is less than or equal to the screening criteria of 1x10-6 per

reactor year as specified in the Alternate PTS Rule, the NDE data are acceptable, and

the licensee may use the PTS screening criteria in Table 1-1 (Step K in Figure 6-1).

• If the TWCF value is greater than the screening criteria of 1x10-6 per reactor year as

specified in the Alternate PTS Rule, the NDE data are unacceptable, and the PTS

screening criteria in Table 1-1 may not be used. Alternate actions are required to

resolve PTS embrittlement issues; such actions may include changes to the facility to

reduce the likelihood or severity of the cooldown transients. The licensee must submit

its plant-specific PTS assessment to the Director of NRR for review and approval (Step J

in Figure 6-1).

Table 6-2 Summary of the Revised Flaw Depth and Density VFLAW Parameters To Be 

Used in a Revised PFM Analysis for Beaver Valley, Unit 2 (from Appendix C)

Case Flaw Size 

Category

Original VFLAW Parameters of 

Uncertainty Distribution Used in 

PTS Work

(Flaw Depth Parameters Specialized to 

Beaver Valley, Unit 2)

Revised Parameters of Uncertainty 

Distribution Based on Beaver 

Valley, Unit 2, NDE Data

1 Small

(a ≤ Δ)

α3 = 0.180

α4 = 1,419

α'3 = 0.230

α'4 = 1,909

2 Large

(a > Δ)

α3 = 0.180

α4 = 4 

α'3 = 0.230

α'4 = 5 

3 Small

(a ≤ Δ)

U1 = 34

U2 = 8 

U3 = 1 

U'1 = 513.75

U'2 = 17.71

U'3 = 1.54

4 Large

(a > Δ)

α1 = 4.615

α2 = 4 

α'1 = 4.563

α'2 = 5 
6-14

6.3 Guidance for Initial Evaluation of Nondestructive Examination Data

This section provides guidance for initial evaluation of NDE data obtained from qualified ISI 

examinations, as identified in Steps A through F in Figure 6-1. These steps are expected to be 

the most common use of the Alternate PTS Rule, and they represent a comparison of the 

as-reported NDE results with the flaw tables. Successful comparison of the NDE data to the 

flaw tables provides reasonable assurance that the plant-specific flaw distribution is bounded by 

the flaw distribution used in the development of the Alternate PTS Rule, therefore justifying 

application of the alternate PTS screening criteria in Table 1-1 to the plant in question.

As indicated under 10 CFR 50.61a(e), the licensee must acquire volumetric examination results 

evaluated under 10 CFR 50.61a(e)(1), (e)(2), and (e)(3) using procedures, equipment, and 

personnel qualified under ASME Code, Section XI, Mandatory Appendix VIII, Supplements 4 

and 6, as specified in 10 CFR 50.55a(b)(2)(xv). Under 10 CFR 50.55a(g)(6)(ii)(C), the NRC

requires licensees to implement ASME Code, Section XI, Mandatory Appendix VIII, 

Supplements 4 and 6. Supplement 4 contains qualification requirements for the RPV ISI 

volume from the clad-to-base-metal interface to the inner 15% of the RPV base-metal wall 

thickness. Supplement 6 contains qualification requirements for RPV weld volumes that lie 

within the outer 85% of the RPV base-metal wall thickness.

Figure 6-2 shows the examination and flaw evaluation process in ASME Code, Section XI, and 

identifies the flaws from that process that should be used for comparison to the flaw tables in 

the Alternate PTS Rule. As noted in Figure 6-2, the process used to identify flaws for 

comparison to the flaw tables is a subset of the process outlined in the ASME Code. All 

recordable flaws, subsequent to application of the flaw proximity rules of ASME Code, 

Section XI, Subarticle IWA-3300 (Flaw Characterization), are used for comparison to the flaw 

tables in the Alternate PTS Rule [16b].

A letter from N.A. Palm and M.G. Semmler (Westinghouse Electric Company) to A. Csontos 

(NRC), dated September 7, 2011, includes a sampling of RPV weld examinations from 13 PWR 

RPVs, conducted in accordance with ASME Code, Section XI, Mandatory Appendix VIII [17]. 

This sampling is a compilation of several RPV beltline weld examinations performed since 2000 

that were provided by Westinghouse Electric Company in response to a request from the NRC. 

These results form the basis for the example comparison to the flaw tables shown in Figure 6-3

and Table 6-3 through Table 6-6 in this document. The following paragraphs discuss this figure 

and these tables.

The following evaluation process was used (Steps A through D and Step K in Figure 6-1) for the 

example shown in Figure 6-3 and Table 6-3 through Table 6-6: 

Step A. Perform a qualified examination in accordance with ASME Code, Section XI, Mandatory 

Appendix VIII. 

• Figure 6-3 shows the ASME Code, Section XI, Appendix VIII, examination results for

Plant J.

• Eleven welds (two girth welds and nine intersecting axial welds) were examined in the

RPV beltline region. A total of eight combined recordable flaws (as defined by the

process shown in Figure 6-2) were detected.
6-15

Step B. Do axial flaws greater than 0.075 inch in depth at the clad-to-base-metal interface open 

to the RPV inside surface?

• Based on the S dimension (distance of flaw below the clad-to-base-metal interface)

shown in Figure 6-3 for all flaws, no flaws at the clad-to-base-metal interface require

supplemental examination to confirm that they are not connected to the RPV inside

surface.

• If supplemental examination is required, perform a demonstrated surface or visual

examination of the clad surface within the examination volume required by ASME Code,

Section XI (e.g., Figures IWB-2500-1 and IWB-2500-2) to identify potential axial

indications in the cladding surface that may extend into the base metal. A demonstrated

visual or surface examination is capable of detecting and characterizing inservice

cracking in a clad surface representative of the reactor vessel cladding process. An

eddy current test is one acceptable examination method for performing this verification.

• The licensee shall document the method that it used for determining the uncertainty in

locating the position of axial flaws identified by surface or visual examination and the

location of axial flaws identified by UT examination. Any axial flaws located by UT within

the uncertainty bounds of an axial crack shall be considered to be the same axial flaw.

• If the licensee confirms that no axial flaws are connected to the RPV inside surface,

Step B is “NO” in Figure 6-1.

Step C. Are all flaws acceptable according to ASME Code, Section XI, Table IWB-3510-1? 

• As indicated in Figure 6-3 in the column titled, “ASME Code Disposition,” in the second

table, all recordable flaws are acceptable for meeting the requirements of ASME Code,

Section XI, Table IWB-3510-1. The details of this determination are not shown.

• Therefore, the outcome of Step C is “YES” in Figure 6-1.

Step D. Check the flaw tables for flaws located in the inner 1 inch or 0.1t (whichever is greater).

• Compute the total weld length examined. The total weld examination length is

determined in Table 6-3 based on the circumference of the RPV and the percentage of

the weld examined (i.e., the coverage amount) for each of the 11 welds.

• Compute the total plate surface area examined. Table 6-4 lists the total plate surface

area examined based on the surface area of the ASME Code, Section XI, examination

volume less the surface area of the weld for each of the 11 welds examined.
6-16

• Determine the position of flaws. The position of all flaws is determined (Table 6-5) as

follows:

− Determine whether the flaw resides in plate or weld material. This determination 

is based on the flaw position with respect to the weld centerline and the 

maximum weld crown width1 on either surface of the inspected weld. If the flaw 

position resides within the span of the weld centerline ± one-half of the weld 

crown width, the flaw was considered to be a WELD flaw. Otherwise, it was 

treated as a PLATE flaw.

− Determine whether the flaw resides within the inner 1 inch or 10% of the 

base-metal wall thickness, whichever is greater, for comparison to the flaw tables 

in the Alternate PTS Rule.

− Determine whether the flaw resides between the inner 1 inch or 10% of the 

base-metal thickness, whichever is greater, and the inner 37.5% of the 

base-metal wall thickness (3/8t) for potential evaluation of brittle fracture.

− Based on the results shown in Table 6-5, two flaws should be compared to Table 

2 (the weld flaw table) of the Alternate PTS Rule, and one flaw should be 

compared to Table 3 (the plate/forging flaw table) of the Alternate PTS Rule. 

Although two flaws reside between the inner 1 inch or 10 percent of the 

base-metal thickness (whichever is greater) and the inner 37.5% of the 

base-metal wall thickness (3/8t) from the clad-base-metal interface, they do not 

require further assessment for acceptability because they were found to be 

acceptable in accordance with ASME Code, Section XI, Table IWB-3510-1.

• Assess flaws.

− The flaws determined in the previous step to be located in the inner 1 inch or 

10% of the base-metal wall thickness (whichever is greater) are compared to the 

flaw tables from the Alternate PTS Rule in Table 6-6 and are found to be 

acceptable.

− The remaining two flaws located between the inner 1 inch or 10% of the 

base-metal thickness (whichever is greater) and the inner 37.5% of the 

base-metal wall thickness (3/8t) from the clad-base-metal interface are 

acceptable in accordance with ASME Code, Section XI, Table IWB-3510-1.

− Therefore, the outcome of Step D is “PASS” in Figure 6-1. 

1 The weld crown width was used in this example for the entire RPV base-metal wall thickness, which can 

potentially classify flaws located midwall as weld flaws rather than plate flaws in single-groove or 

double-V-groove weld configurations. This approach is conservative with respect to the flaw limits in Table 

1-2. Consideration should also be given to the proximity of the flaw to the weld’s heat-affected zone (HAZ).

For example, the licensee should consider that any flaw located in the plate material but within some

technically justified minimum distance from the edge of the weld is affected by the HAZ and, therefore, is a

weld flaw. In addition, if there are any weld-repair areas located within the examination volume, the licensee

should classify any flaws detected within those areas as weld flaws.
6-17

Step K. Plant J can apply the PTS screening criteria in Table 1 of 10 CFR 50.61a. The 

licensee must submit the PTS evaluation to the NRC for review and approval.

Figure 6-2 ASME Code, Section XI, examination and flaw evaluation process and 

identification of flaws for comparison to the Alternate PTS Rule
6-18

Figure 6-3 Sample ASME Code, Section XI, MandatoryAppendix VIII, 

examination results for Plant J 

Step A: Plant J Examination Results: (see Westinghouse Letter LTR-AMLRS-11-71 [18])

Circumferential Weld Axial Weld
6-19

Table 6-3 Determination of Total Weld Length Examined for Plant J 

STEP D: Compute Total Weld Length Examined

Weld ID Direction

Radius, Ri

(inches)

Length

(inches) Comments

Examination 

Coverage

Ex

L

J-1 Circumferential 86.5 543.5 Length computed as 2πRi 100% 

J-2 Circumferential 86.5 543.5 Length computed as 2πRi 100% 

J-3 Axial N/A 70 Length assumed 100% 

J-4 Axial N/A 70 Length assumed 100% 

J-5 Axial N/A 70 Length assumed 100% 

J-6 Axial N/A 70 Length assumed 100% 

J-7 Axial N/A 70 Length assumed 100% 

J-8 Axial N/A 70 Length assumed 100% 

J-9 Axial N/A 70 Length assumed 77.8% 

J-10 Axial N/A 70 Length assumed 77.8% 

J-11 Axial N/A 70 Length assumed 77.8% 

Total, L = 
6-20

Table 6-4 Determination of Total Plate Surface Area Examined for Plant J 

Notes: (1) The weld width, WW, is defined as the maximum weld crown width from both sides of the RPV wall. From Figure 6-3, WW i

circumferential welds and 1.38 inches for axial welds.

(2) The examination width, WE, is defined as the ASME Code, Section XI, examination volume width, which is one-half of the w

sides of the weld. From Figure 6-3, the RPV base-metal wall thickness, which is equal to WE, is 8.60 inches.

STEP D: Compute Total Plate Surface Area Examined

Weld ID

Examined 

Length, L

Weld Width, 

WW

(1) 

(inches)

Examination 

Width, WE

(2) 

(inches)

P

J-1 543.5 1.65 8.60 

J-2 543.5 1.65 8.60 

J-3 70.0 1.38 8.60 

J-4 70.0 1.38 8.60 

J-5 70.0 1.38 8.60 

J-6 70.0 1.38 8.60 

J-7 70.0 1.38 8.60 

J-8 70.0 1.38 8.60 

J-9 54.5 1.38 8.60 

J-10 54.5 1.38 8.60 

J-11 54.5 1.38 8.60 

Total, A = 

Plate surface area computed as L x (WE - WW)

Plate surface area computed as L x (WE - WW)

Plate surface area computed as L x (WE - WW)

Plate surface area computed as L x (WE - WW)

Plate surface area computed as L x (WE - WW)

Plate surface area computed as L x (WE - WW)

Comments

Plate surface area computed as L x (WE - WW)

Plate surface area computed as L x (WE - WW)

Plate surface area computed as L x (WE - WW)

Plate surface area computed as L x (WE - WW)

Plate surface area computed as L x (WE - WW)
6-21

Table 6-5 Determination of the Flaw Positions for Plant J 

STEP D: Determine Position of Flaws

Height on RPV 

(inches)

RPV Circumferential 

Position (°)

Depth Below 

Clad (inches)

J-2 1 235 in 1.65 235.00 150.1 1.66 WELD NO YES 0.16 

2 235 in 1.65 235.14 157.7 2.70 WELD NO YES 0.12 

3 235 in 1.65 235.80 129.3 8.60 WELD NO NO 0.50 

4 235 in 1.65 235.50 332.1 4.49 WELD NO NO 0.24 

J-7 1 120 ° 1.38 123.60 123.6 0.63 PLATE YES N/A 0.22 

J-9 1 60 ° 1.38 256.50 60.3 0.11 WELD YES N/A 0.25 

2 60 ° 1.38 240.30 60.4 0.79 WELD YES N/A 0.34 

J-11 1 300 ° 1.38 312.61 300.3 3.60 WELD NO NO 0.27 

Flaw Position Through Wall 

Extent (TWE) 

= 2a (inches) Weld or Plate Flaw?

Is Flaw Within First 

1.0" or 0.10t?

Is Flaw Within 

First 3/8t?

Weld Width

(inches) Weld Centerline Indication No. Weld No.
6-22

Table 6-6 Comparison of Flaws to the Flaw Tables in the Alternate PTS Rule for Plant J 

STEP D: Compare Flaws to 10 CFR 50.61a Flaw Tables

Table 2 Comparison = Weld Flaws

(Allowable) (Cumulative)

Bin Minimum TWE Maximum TWE Max. # of Flaws # of Flaws # of Flaws / L

No. (inches) (inches) per 1,000 inches Detected x 1,000

1 0 0.075 No limit 0 0.00 YES

2 0.075 0.475 166.70 2 1.20 YES 

3 0.125 0.475 90.80 2 1.20 YES 

4 0.175 0.475 22.82 2 1.20 YES 

5 0.225 0.475 8.66 2 1.20 YES 

6 0.275 0.475 4.01 2 1.20 YES 

7 0.325 0.475 3.01 1 0.60 YES 

8 0.375 0.475 1.49 0 0.00 YES

9 0.425 0.475 1.00 0 0.00 YES

10 0.475 Infinite 0.00 0 0.00 YES

Table 3 Comparison = Plate/Forging Flaws

(Allowable) (Cumulative)

Bin Minimum TWE Maximum TWE Max. # of Flaws # of Flaws # of Flaws / A

No. (inches) (inches) per 1,000 inches Detected x 1,000

1 0 0.075 No limit 0 0.00 YES

2 0.075 0.375 8.05 1 0.08 YES 

3 0.125 0.375 3.15 1 0.08 YES 

4 0.175 0.375 0.85 1 0.08 YES 

5 0.225 0.375 0.29 0 0.00 YES

6 0.275 0.375 0.08 0 0.00 YES

7 0.325 0.375 0.01 0 0.00 YES

8 0.375 Infinite 0.00 0 0.00 YES

Acceptab

Acceptab
6-23

6.4 Guidance for Further Evaluation of Nondestructive Examination Data

This section provides guidance for further evaluation of NDE data (Steps G through I in Figure 

6-1). Such guidance is based on Section II of 75 FR 13–29 [2], which states the following in

regard to NDE-related uncertainties:

The flaw sizes in Tables 2 and 3 represent actual flaw dimensions while the 

results from the ASME Code examinations are estimated dimensions. The 

available information indicates that, for most flaw sizes in Tables 2 and 3, 

qualified inspectors will oversize flaws. Comparing oversized flaws to the size 

and density distributions in Tables 2 and 3 is conservative and acceptable, but 

not necessary.

As a result of stakeholder feedback received on the NRC solicitation for 

comments published in the August 2008 supplemental proposed rule, the final 

rule will permit licenses to adjust the flaw sizes estimated by inspectors qualified 

under the ASME Code, Section XI, Appendix VIII, Supplement 4 and 

Supplement 6.

The NRC determined that, in addition to the NDE sizing uncertainties, licensees 

should be allowed to consider other NDE uncertainties, such as probability of 

detection and flaw density and location, because these uncertainties may affect 

the ability of a licensee to demonstrate compliance with the rule. As a result, the 

language in § 50.61a(e) will allow licensees to account for the effects of 

NDE-related uncertainties in meeting the flaw size and density requirements of 

Tables 2 and 3. The methodology to account for the effects of NDE-related 

uncertainties must be based on statistical data collected from ASME Code 

inspector qualification tests or any other tests that measure the difference 

between the actual flaw size and the size determined from the ultrasonic 

examination. 

The sections below provide specific guidance on various elements of NDE data evaluation. 

6.4.1 Guidance on the Elements and Nondestructive Examination Techniques

Associated with ASME Code Examinations 

The NRC developed the Alternate PTS Rule using a flaw density, spatial distribution, and size 

distribution determined from experimental data and from physical models and expert judgment.

To implement the Alternate PTS Rule, actual flaw densities and distributions need to be

estimated from the results of periodic ISI performed on RPV welds and adjacent base material.

UT is the method used for these examinations. As discussed in Section 6.3, the licensee must

acquire the data necessary to evaluate the Alternate PTS Rule using procedures, equipment, 

and personnel qualified under ASME Code, Section XI, Mandatory Appendix VIII,

Supplements 4 and 6. Mandatory Appendix VIII provides requirements for demonstrating UT

examination procedures, equipment, and personnel used to detect and size flaws.

Supplement 4 specifies qualification requirements for examining the inner 15% of clad ferritic

reactor vessels and may be applied to the inner 15% of unclad ferritic reactor vessels.

Supplement 6 specifies qualification requirements for examining unclad ferritic components and 

the outer 85% of clad ferritic components.
6-24

Supplement 4 provides performance-demonstration rules intended to produce effective 

procedures, personnel, and equipment for detection and sizing of flaws typical of those that 

might form under service conditions. These rules result in targeting flaws that are primarily 

planar in orientation and emanate from the inside surface (clad-to-base-metal interface) of the 

RPV specimens that are used for the qualification process. The aspect ratio of flaws used for 

performance demonstration also closely follows the acceptance criteria of ASME Code, 

Section XI, Article IWB-3000. These flaws are the focus of the performance demonstration 

because they are of structural significance under standard operating conditions. Therefore, the 

objective of ASME Code, Section XI, Supplement 4, qualification is to demonstrate UT 

capabilities on planar flaws. Examinations using ASME Code, Section XI, Mandatory 

Appendix VIII, qualification may also detect larger fabrication flaws, which often occurs in 

practice because no known credible subcritical cracking mechanisms affect the RPV material for 

the current fleet of U.S. reactors.

The PFM analyses supporting the Alternate PTS Rule assumed all flaws were planar in nature. 

Because the empirical evidence on which the flaw distribution used in these analyses was 

based included both planar flaws and fabrication flaws [18], this assumption was considered

conservative because it produced a higher density of planar flaws than typically found in nuclear 

RPVs. Fabrication flaws are considerably smaller than those within current Supplement 4 

qualification specimens and are not typically connected to the clad-to-base-metal interface. 

Nevertheless, it is probable that parameters associated with qualified UT methods may be 

optimized to enhance the method’s capability to detect and size small fabrication flaws in the 

inner 1 inch of RPV base material. Therefore, licensees should consider enhancements to 

Mandatory Appendix VIII-qualified procedures to ensure accurate detection and sizing of the 

flaws inferred by the Alternate PTS Rule while maintaining the essential variables for which the 

procedure was qualified.

Within the context of a Mandatory Appendix VIII-qualified RPV examination, the licensee might 

be able to vary the elements and NDE techniques associated with the examination to provide 

better NDE data for comparison with the flaw limits in Tables 2 and 3 of the Alternate PTS Rule.

Such elements and techniques may include, but are not limited to, the following:

• reduction of the scan index

• use of an ultrasonic straight-beam examination technique

• use of an enhanced recording criterion (lower threshold)

The NRC staff has been working with UT/NDE experts at PNNL to assess RPV examination 

and implementation of the Alternate PTS Rule. A technical letter report [23] addresses the 

assessment, including enhancements to procedures and examination techniques. Licensees 

that choose to apply the Alternate PTS Rule should consider the elements and techniques listed 

above when establishing the protocols and procedures for Mandatory Appendix VIII 

examinations to maximize the usefulness of the resulting NDE data and to provide reasonable 

assurance of the acceptability of the NDE data comparisons required by the Alternate PTS 

Rule.

6.4.2 Guidance on a Procedure To Adjust Nondestructive Examination Data and

Comparison to Flaws Assumed in Probabilistic Fracture Mechanics

Calculations 

This section provides guidance on a mathematical procedure that licensees can use to adjust 

NDE data to account for flaw detection and sizing errors, as identified by Step G in Figure 6-1. 

This evaluation adjusts the as-found NDE data by taking into account flaw-sizing errors, POD 
6-25

uncertainties, and prior flaw distributions such as those used in the development of the Alternate 

PTS Rule (i.e., VFLAW [18]). The licensee may consider any or all of these uncertainties, 

depending on the level of detail needed for flaw assessment. After making such an adjustment, 

the licensee may again compare the adjusted NDE results with the flaw tables (Step H in Figure 

6-1) because NDE techniques tend to oversize smaller flaws, thereby distributing detected flaws

into larger bins where the allowed number of flaws is smaller. In such cases, adjustment for

NDE flaw detection and sizing uncertainties may result in a less conservative distribution of flaw

sizes and possibly result in a successful comparison of the adjusted NDE data to the flaw

tables. The NRC staff would view a successful comparison of the revised NDE data to the flaw

tables as providing reasonable assurance that the plant-specific flaw distribution is bounded by

the flaw distribution used in the development of the Alternate PTS Rule, thus indicating that

applying the alternate PTS screening criteria is appropriate (Step K in Figure 6-1).

Appendix C describes the development and application of a methodology for assessing 

uncertainties in NDE data, analyzing such data for the purpose of developing more realistic 

vessel-specific flaw depth and density distributions for comparison to the flaw tables, and 

performing a plant-specific PFM analysis (discussed in Section 6.2.2). The methodology 

considers POD, flaw-measurement error, and flaw-detection threshold in its application and 

uses Bayesian updating to combine the observed NDE data with the available flaw data and 

models used as part of the PTS reevaluation effort. Appendix C describes the Bayesian 

framework that this methodology uses, the application details of the NDE data uncertainties, 

(i.e., the POD and measurement/sizing error) and the Bayesian updating procedure. 

Appendix C demonstrates the application of the methodology using the ultrasonic NDE data 

obtained from a previous ISI examination of the Beaver Valley, Unit 2, RPV and a MATLAB 

software routine that uses the Bayesian equations developed in Appendix C. Appendix C also 

includes the MATLAB software listing.

As an example of this procedure, assume that Plant J performs an initial NDE assessment using 

the guidance of Section 6.3 with the results shown in Table 6-7. These results indicate that

Plant J fails the flaw table check in the Alternate PTS Rule because it violated the flaw

acceptance limit for Flaw Bin No. 2 (i.e., 170.10 actual flaws per 1,000 inches of weld versus

166.70 allowed flaws per 1,000 inches of weld). Therefore, Step D in Figure 6-1 yields a “FAIL” 

decision, thereby necessitating the evaluations associated with Step G in Figure 6-1. As a 

result, the licensee could choose to apply procedures similar to those described in Appendix C.

A key input for this procedure is a POD and associated flaw-sizing error data appropriate to the 

methods and techniques used to examine the RPV. EPRI has previously developed example 

PODs and flaw-sizing error data based on Performance Demonstration Initiative (PDI) 

qualification data [25]. Similar information should be obtained for the examination technique 

being applied and technically justified for use as a part of implementing the procedures 

described in Appendix C.
6-26

Table 6-7 Example for Plant J after Applying an Initial Alternate PTS Rule Flaw Table 

Check Using the Procedure in Section 6.3

Flaw

Bin No.

Flaw Depth

(inches)

Observed 

(Detected)

Number of Flaws 

from NDE ISI

10 CFR 50.61a 

Flaw Limits

(number of 

flaws per 

1,000 inches

of weld)

Acceptable?

(Is the number

of flaws less 

than the

limit?)

1 0.000 < a ≤ 0.075 234.45 No limit Yes

2 0.075 < a ≤ 0.475 170.10 166.70 No

3 0.125 < a ≤ 0.475 11.23 90.80 Yes

4 0.175 < a ≤ 0.475 0.90 22.82 Yes

5 0.225 < a ≤ 0.475 0.05 8.66 Yes

6 0.275 < a ≤ 0.475 0.01 4.01 Yes

7 0.325 < a ≤ 0.475 0.00 3.01 Yes

8 0.375 < a ≤ 0.475 0.00 1.49 Yes

9 0.425 < a ≤ 0.475 0.00 1.00 Yes

6.4.3 Guidance on the Application of Nondestructive Examination Uncertainties

Appendix D discusses the results of sensitivity analyses that apply the Bayesian updating 

methodology in Appendix C to systematically assess the effect of NDE uncertainties such as the 

POD and measurement (sizing) error on the estimated flaw populations. The sensitivity 

analyses were performed for a base case and 12 sensitivity cases that investigated variations in 

observed NDE data and application of prior PDFs, POD, and flaw-sizing error. 

As a part of the sensitivity studies, lower NDE detection limits of 0.04 inch and 0.075 inch were 

also evaluated and found to have no significant effect on the observed data.

The results obtained from the 12 sensitivity cases consistently show that a small (i.e., 10%) 

overpopulation of flaws in Bins 2 and 3 of the Alternate PTS Rule flaw tables, as might be 

expected from actual plant inspections because of oversizing of small flaws, would be shifted to 

Flaw Bin Nos. 1 and 2 after accounting for the measurement error in the Bayesian update. 

When the POD was also considered, the effects of small flaws that might be missed by NDE 

methods were clearly seen in Flaw Bin Nos. 1 and 2, with an additional number of flaws in the 

posterior estimates as compared to the observed flaws. However, the results are sensitive to 

the POD used, especially the portion of the POD for smaller flaw sizes. Therefore, if a licensee 

uses a POD, this use must be sufficiently justified.

The effects of the choice of prior distributions of flaw density and flaw depth were significant. 

When no prior information was used to describe the flaw density and flaw depth distributions, 

the POD and measurement error were very sensitive and significantly amplified the number of 

flaws that resulted in Flaw Bin Nos. 1 and 2. However, when prior PDFs were used, existence 

of the prior PDFs significantly moderated the posterior PDFs, and the POD and measurement 

errors played less significant roles.
6-27

The results of the sensitivity analysis documented in Appendix D reveal the following:

• Neglecting consideration of prior PDFs in the evaluation provides a conservative

assessment.

• Neglecting consideration of flaw-sizing error in the evaluation provides a conservative

assessment.

• The POD significantly affects the evaluation, and it should be included for cases in which

PDFs are not considered. For the evaluation of PDFs, the effect of the POD is relatively

small and may be neglected.

• Consideration of flaw-sizing error, POD, or prior PDFs (identified as “NDE uncertainties”

in the Alternate PTS Rule) using methods similar to those shown in Appendix C is

successful in removing conservatisms that may unnecessarily prevent a licensee from

passing the flaw tables in the Alternate PTS Rule.

7-1

7 GUIDANCE RELATED TO ALTERNATE SCREENING 

CRITERIA ON EMBRITTLEMENT 

The regulation at 10 CFR 50.61a(c)(3) states the following (note that the highlighting is, as 

explained below, added for emphasis; the highlighting does not appear in the CFR):

Each licensee shall compare the projected RTMAX–X values for plates, forgings, 

axial welds, and circumferential welds to the PTS screening criteria in Table 1 of 

this section, for the purpose of evaluating a reactor vessel’s susceptibility to 

fracture due to a PTS event. If any of the projected RTMAX–X values are greater 

than the PTS screening criteria in Table 1 of this section, then the licensee 

may propose the compensatory actions or plant-specific analyses as required 

in paragraphs (d)(3) through (d)(7) of this section, as applicable, to justify 

operation beyond the PTS screening criteria in Table 1 of this section.

This section describes one method by which licensees can perform the plant-specific analyses 

indicated by the highlighted text. This method is acceptable to the staff as long as the 

licensee satisfies all other requirements of 10 CFR 50.61a concerning flaw evaluations, flaw 

assessment, statistical evaluation of surveillance data, and plant corrective actions. 

The RTMAX-X screening criteria in Table 1 of 10 CFR 50.61a were established in NUREG-1874 

based on a TWCF of 1x10-6 per reactor year. As described in NUREG-1874, the RTMAX-X

screening criteria are based on the results of PFM analyses; they account for the combined 

TWCF contributions from various flaw populations in the RPV. Some simplifications of the PFM 

data underlying these screening criteria were necessary to permit their expression in a tabular 

form. As an example, the TWCF attributable to circumferentially oriented flaws that occur in 

circumferential welds was held below 1x10-8 per reactor year rather than 1x10-6 per reactor year. 

This simplification was made for expedience and was not intended to address a safety concern. 

Therefore, the licensee can use the following procedure, which eliminates similar simplifying 

assumptions, to demonstrate compliance with the RTMAX-X screening criteria in 10 CFR 50.61a, 

Table 1. Section 3.5.1 of NUREG-1874 describes this procedure as follows:

(1) Determine RTMAX-X for all axial welds (RTMAX-AW), plates (RTMAX-PL), circumferential welds

(RTMAX-CW), and forgings (RTMAX-FO) (as applicable) in the RPV beltline region according

to the requirements of 10 CFR 50.61a. These RTMAX-X values must be expressed in

units of Rankine (R) (degrees F plus 459.69).

(2) Use the RTMAX-X values from Step 1 to estimate the 95th percentile TWCF contribution

from each component in the beltline using the following formulas:

(7-1) 

(7-2) 

(7-3) 

(7-4) 

TWCF95−AW = exp{ .5 5198⋅ ln(RT −AWMAX ) 40616 .542}⋅−− β

TWCF95−PL = exp{23.737 ⋅ ln(RT −PLMAX ) 162300 .38}⋅−− β

TWCF95−CW = exp{ .9 1363⋅ln(RTMAX −CW ) 65616 .066}⋅−− β

TWCF95−FO = exp{23.737 ⋅ ln(RT −FOMAX ) 162300 .38}⋅−− β

η { ⋅×⋅+ }⋅ β − − ⋅RTMAX FO 137 185.0 3.1 1010
7-2

where: 

η = 0 if the forging is compliant with Regulatory Guide 1.43, “Control of 

Stainless Steel Weld Cladding of Low-Alloy Steel Components”; otherwise, 

η = 1.

β = 1 if TWALL ≤ 9.5 inches

β = 1 + 8 x (TWALL – 9.5) if 9.5 < TWALL < 11.5 inches

β = 17 if TWALL ≥ 11.5 inches

(3) Estimate the total 95th percentile TWCF for the RPV using the following formulae (noting

that, depending on the type of vessel in question, certain terms in the following formula

will be zero):

(7-5) 

where: 

α = 2.5 if RTMAX-xx ≤ 625 R

if 625 R < RTMAX-xx < 875 R

α = 1 if RTMAX-xx ≥ 875 R

(4) If the calculated TWCF95-TOTAL from Step 3 is less than 1x10-6 per reactor year, the

requirements of Table 1 of 10 CFR 50.61a are considered to have been met.

























⋅

⋅ +

⋅ +

⋅ +

=

−

−

−

−

−

FO FO

CW CW

PL PL

AW AW

TOTAL

TWCF

TWCF

TWCF

TWCF

TWCF

95

95

95

95

95

α

α

α

α

( 625) 250

5.1

α 5.2 −= RTMAX −xx −
8-1

8 SUMMARY

In early 2010, the NRC promulgated the Alternate PTS Rule in 10 CFR 50.61a, which amended 

existing regulations to provide alternate embrittlement requirements for protection against PTS 

events for PWR RPVs. These requirements are based on more comprehensive, accurate, and 

realistic analysis methods than those used to establish the screening criteria in 10 CFR 50.61. 

This action became desirable because the existing requirements, as contained in 

10 CFR 50.61, are based on unnecessarily conservative assumptions. While still maintaining 

adequate safety margins, the Alternate PTS Rule reduces regulatory burden for those PWR 

licensees that expect to exceed the 10 CFR 50.61 embrittlement requirements before the 

expiration of their operating licenses. PWR licensees may choose to comply with the Alternate 

PTS Rule as a voluntary alternative to complying with the requirements in 10 CFR 50.61.

The Alternate PTS Rule provides revised PTS screening criteria in the form of embrittlement 

reference temperatures, RTMAX-X, that characterize the RPV material’s resistance to fracture 

initiating from flaws. Licensees may use the RTMAX-X embrittlement screening criteria provided 

that they meet the following criteria:

(1) criteria related to the date of construction and design requirements

The Alternate PTS Rule applies to licensees whose construction permits were issued

before February 3, 2010, and whose RPVs were designed and fabricated to the

1998 edition or an earlier edition of the ASME Code. The reason for this applicability

restriction is that the structural and thermal-hydraulic analyses that established the basis

for the Alternate PTS Rule’s embrittlement screening criteria represented only plants

constructed before this date. The licensee is responsible for demonstrating that the

technical basis calculations developed in support of the Alternate PTS Rule adequately

address the risk-significant factors that control PTS for any plant constructed after

February 3, 2010. Chapter 4 of this document describes methods by which licensees

can satisfy these criteria and identifies factors to be considered in such an evaluation.

(2) criteria related to plant-specific surveillance data

(3) The Alternate PTS Rule includes statistical tests that licensees must perform on RPV

surveillance data to determine whether the surveillance data are sufficiently “close” to

the predictions of an ETC to validate such predictions for use. Of particular interest from

a regulatory perspective is the use of these statistical tests to determine whether

plant-specific surveillance data deviate significantly from the predictions of the ETC in a

manner that suggests that the ETC is very likely to underpredict plant-specific data

trends. Chapter 5 of this document describes guidance by which licensees can assess

the closeness of plant-specific data to the ETC using statistical tests, including the

following:

• a detailed description of the mathematical procedures to use to assess

compliance with the three statistical tests in the Alternate PTS Rule

• a list of factors to consider in diagnosing the reason why particular surveillance

datasets may fail these statistical tests
8-2

• a description of certain situations in which routine adjustments of the ETC

predictions can be made

(4) criteria related to ISI data and NDE requirements

(5) The Alternate PTS Rule describes a number of tests of and conditions on the collection

and analysis of ISI data that should provide reasonable assurance that the distribution of

flaws assumed to exist in the PFM calculations, which provide the basis for the RTMAX-X

screening criteria, provides an appropriate, or bounding, model of the population of flaws

in the RPV of interest. Chapter 6 of this document includes guidance to help licensees

satisfy these criteria. This document discusses the following guidance:

• guidance for plants with RPV flaws that fall outside the applicability of the flaw

tables in the Alternate PTS Rule, including the following:

− a mathematical procedure that can be used to preclude brittle fracture 

based on RTNDT information

− a mathematical procedure that can be used to combine the NDE data 

with the population of flaws assumed in the PFM calculations to estimate 

the total flaw distribution predicted to exist in the RPV and guidance on 

the use of this total flaw distribution as part of a PFM calculation using the 

FAVOR computer code

• guidance for initial evaluation of NDE data obtained from qualified ISI

examinations

• guidance for further evaluation of NDE data obtained from qualified ISI

examinations, as follows:

− the elements and NDE techniques associated with the qualified ISI 

examinations performed in accordance with ASME Code, Section XI, 

Mandatory Appendix VIII, to assess compliance with the requirements of 

the Alternate PTS Rule

− a mathematical procedure that can be used to adjust NDE data to 

account for flaw-detection and -sizing errors and comparison of the 

adjusted data to the population of flaws assumed in the PFM technical 

basis for the Alternate PTS Rule

(6) criteria related to alternate screening criteria on embrittlement

Guidance is provided by which licensees can estimate a plant-specific value of TWCF

for cases that do not satisfy the RTMAX-X screening criteria of the Alternate PTS Rule.

Chapter 7 of this document describes these two sets of guidance to enable licensees to

satisfy the embrittlement acceptability criteria.

This document provides guidance and the associated technical basis for methods by which 

licensees can satisfy the above criteria.
9-1

9 REFERENCES

[1] U.S. Code of Federal Regulations, “Alternate Fracture Toughness Requirements for

Protection against Pressurized Thermal Shock Events, Section 50.61a, Chapter I,

Title 10, “Energy.”

[2] U.S. Nuclear Regulatory Commission, “Alternate Fracture Toughness Requirements for

Protection against Pressurized Thermal Shock Events,” Federal Register, Vol. 75, No. 1,

January 4, 2010, pp. 13–29.

[3] U.S. Code of Federal Regulations, “Fracture Toughness Requirements for Protection

against Pressurized Thermal Shock Events,” Section 50.61, Chapter I, Title 10,

“Energy.”

[4] American Society of Mechanical Engineers, Boiler and Pressure Vessel Code,

2013 edition, Section XI, “Rules for Inservice Inspection of Nuclear Power Plant

Components,” New York, NY.

[5] U.S. Code of Federal Regulations, “Requirements for Thermal Annealing of the Reactor

Pressure Vessel,” Section 50.66, Chapter I, Title 10, “Energy.”

[6] U.S. Nuclear Regulatory Commission, “Technical Basis for Revision of the Pressurized

Thermal Shock (PTS) Screening Limit in the PTS Rule (10 CFR 50.61): Summary

Report,” NUREG-1806, August 2007.

[7] U.S. Nuclear Regulatory Commission, “Recommended Screening Limits for Pressurized

Thermal Shock (PTS),” NUREG-1874, March 2010.

[8] Elliot, B.J., Senior Materials Engineer (NRC), memorandum to M.A. Mitchell, Branch

Chief (NRC), “Development of Flaw Size Distribution Tables for Draft Proposed Title 10

of the Code of Federal Regulations (10 CFR) 50.61a,” April 3, 2007, Agencywide

Documents Access and Management System (ADAMS) Accession No. ML070950392.

[9] Eason, E.D., et al., “A Physically Based Correlation of Irradiation-Induced Transition

Temperature Shifts for RPV Steels,” ORNL/TM-2006/530, Oak Ridge National

Laboratory, Oak Ridge, TN, November 2007, ADAMS Accession No. ML081000630.

[10] Electric Power Research Institute, “Materials Reliability Program: Proposed Resolutions

to the Analytical Challenges of Alternate PTS Rule (10 CFR 50.61a) Implementation

(MRP-334),” Technical Update No. 1024811, Palo Alto, CA, January 2012.

[11] U.S. Code of Federal Regulations, “Codes and Standards,” Section 50.55a, Chapter I,

Title 10, “Energy.”

[12] American Society of Mechanical Engineers, Boiler and Pressure Vessel Code,

2013 edition, Section XI, “Rules for Inservice Inspection of Nuclear Power Plant

Components,” Mandatory Appendix VIII, “Performance Demonstration for Ultrasonic

Examination Systems,” New York, NY.
9-2

[13] U.S. Code of Federal Regulations, “Domestic Licensing of Production and Utilization

Facilities,” Part 50, Appendix H, “Reactor Vessel Material Surveillance Program

Requirements,” Chapter I, Title 10, “Energy.”

[14] U.S. Nuclear Regulatory Commission, “Statistical Procedures for Assessing Surveillance

Data for 10 CFR Part 50.61a,” June 9, 2008, ADAMS Accession No. ML081290654.

[15] U.S. Nuclear Regulatory Commission, “Radiation Embrittlement of Reactor Vessel

Materials,” Regulatory Guide 1.99, Revision 2, May 1988, ADAMS Accession

No. ML003740284.

[16] U.S. Nuclear Regulatory Commission Public Meeting Summary Reports:

a. U.S. Nuclear Regulatory Commission, “Category 2 Public Meeting—Discussion of

Reactor Pressure Vessel Integrity Issues for Operating Nuclear Power Plants,”

August 5, 2011, ADAMS Accession No. ML112170262.

b. U.S. Nuclear Regulatory Commission, “Category 2 Public Meeting—Discussion of

Nondestructive Examination Aspects of Reactor Pressure Vessel Integrity Issues for

Operating Nuclear Power Plants,” October 6, 2011, ADAMS Accession

No. ML112790501.

c. U.S. Nuclear Regulatory Commission, “Category 2 Public Meeting—Discussion of

Reactor Pressure Vessel Integrity Issues for Operating Nuclear Power Plants,”

November 18, 2011, ADAMS Accession No. ML113220295.

[17] Palm, N.A., Fellow Engineer, and M.G. Semmler, Acting Manager (Westinghouse

Electric Company), letter to Dr. Aladar Csontos, Branch Chief (NRC), “Inspection Data

for Use in Development of Alternate Pressurized Thermal Shock (PTS) Rule

Implementation Regulatory Guide,” LTR-AMLRS-11-71, September 7, 2011, ADAMS

Accession No. ML112560145.

[18] U.S. Nuclear Regulatory Commission, “A Generalized Procedure for Generating

Flaw-Related Inputs for the FAVOR Code,” NUREG/CR-6817 (PNNL-14268),

March 2004, ADAMS Accession No. ML040830499.

[19] Oak Ridge National Laboratory, “Fracture Analysis of Vessels–Oak Ridge

FAVOR, v12.1, Computer Code: Theory and Implementation of Algorithms, Methods,

and Correlations,” ORNL/TM-2012/567, Oak Ridge, TN, November 2012, ADAMS

Accession No. ML13008A015.

[20] U.S. Nuclear Regulatory Commission, “Probabilistic Fracture Mechanics—Models,

Parameters, and Uncertainty Treatment Used in FAVOR Version 04.1,” NUREG-1807,

June 2007.

[21] U.S. Nuclear Regulatory Commission, “Fracture Analysis of Vessels—Oak Ridge

FAVOR, v04.1, Computer Code: Theory and Implementation of Algorithms, Methods,

and Correlations,” NUREG/CR-6854 (ORNL/TM-2004/244), August 2007.
9-3

[22] Pellini, W.S., and P.P. Puzak, “Fracture Analysis Diagram Procedures for the

Fracture-Safe Engineering Design of Steel Structures,” Bulletin 88, Welding Research

Council, Shaker Heights, OH, May 1963.

[23] Pacific Northwest National Laboratory, “Evaluation on the Feasibility of Using Ultrasonic

Testing of Reactor Pressure Vessel Welds for Assessing Flaw Density/Distribution per

10 CFR 50.61a, Alternate Fracture Toughness Requirements for Protection Against

Pressurized Thermal Shock,” PNNL-19666, Richland, WA, June 2014, ADAMS

Accession No. ML14162A001.

[24] NRC Regulatory Issue Summary 2014-11, “Information on Licensing Applications for

Fracture Toughness Requirements for Ferritic Reactor Coolant Pressure Boundary

Components,” ADAMS ML14149A165.

[25] Electric Power Research Institute, “Nondestructive Evaluation: Probabilistic Analysis of

Performance Demonstration Ultrasonic Flaw Detection and Through-Wall Sizing Results

for Reactor Pressure Vessel Inspections,” EPRI Report No. 1025787, Palo Alto, CA,

September 2012.

[26] U.S. Nuclear Regulatory Commission, “Calculational and Dosimetry Methods for

Determining Pressure Vessel Neutron Fluence,” Regulatory Guide 1.190, March 2001,

ADAMS Accession No. ML010890301.

A-1

APPENDIX A DERIVATION OF THE STATISTICAL TEST FOR 

TYPE D DEVIATIONS 

The value C2 is defined so that the probability that all the normalized residuals are less than C2

is 1 - α = 0.99, assuming that the embrittlement shift model is correct. Under this assumption,

the normalized residuals all have a standard normal distribution with a mean of 0 and standard

deviation of 1. The cumulative distribution function of the standard normal distribution, denoted 

by F, is then:

C2 = F-1 (0.99)1/n A-1

For any n and C2 as determined above, define:

p = Prob {C1 < X ≤ C2} A-2

for any C1 < C2 and where X has a standard normal distribution, then:

1-p = Prob {X ≤ C1} + Prob {X > C2} A-3

However, the second term in (1-p) is negligible compared to the first term. In fact, from Table 

5-4 in the main body of the text, C2 ≥ 2.71 for n ≥ 3 and, therefore, Prob {X > C2} < 0.0034 for

n ≥ 3. Thus, the following equation applies:

1-p ≈ Prob {X ≤ C1} A-4

The probability that the subject dataset does not show a Type D deviation can be expressed in 

terms of p. Because all of the n normalized residuals should be less than or equal to C1 to pass 

the Outlier Test, the following may be written:

Prob {x[1] ≤ C1} = (1-p)

n A-5

In addition, the outlier test indicates that it is acceptable to have a single normalized residual 

between C1 and C2 while the other (n – 1) normalized residuals are all less than C1. Therefore, 

the following equation applies: 

Prob {x[2] < C1 ≤ x[1] ≤ C2} = np (1-p)

n-1 A-6

Because A-5 and A-6 are mutually exclusive, the sum of their probabilities is the probability of a 

Type D deviation, or 1 - α = 0.99. This sum, denoted by G(p), is as follows: 

G(p) = (1-p)

n + np (1-p)n-1 = (1-p)n-1 [1 + (n-1)p] A-7

By iteration, the value p0 may be found that yields G(p0) = 0.99. To calculate C1 in Table 5-4, 

Prob {X ≤ C1} is set to 1-p0. The following equation then applies: 

C1 = F-1 (1-p0) A-8

B-1

Note that this appendix summarizes the evaluations provided for review only; they were performed to evaluate t

statistical surveillance tests. These calculations do not include an assessment of sister plant data, the licensee 

as a replacement of licensing-basis evaluations for each plant, and they do not represent the U.S. Nuclear Regu

official position.

Table B-1 Type A Deviations (Mean Test)

General Information Type A De

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) rmean (

oF) 

Arkansas Nuclear 1 PWR PAN101 P 6 21 -13 

Arkansas Nuclear 1 PWR WAN101 W 3 26 6 

Arkansas Nuclear 2 PWR PAN201 P 3 21 -3 

Beaver Valley 1 PWR PBV101 P 8 21 23.0 

Beaver Valley 1 PWR WBV101 W 4 26 -3 

Beaver Valley 2 PWR PBV201 P 6 19 -7 

Beaver Valley 2 PWR WBV201 W 3 26 -37 

Braidwood 1 PWR FBD101 F 6 19 -7 

Braidwood 1 PWR WBD101 W 3 19 3 

Braidwood 2 PWR FBD201 F 6 19 -9 

Braidwood 2 PWR WBD201 W 3 19 -8 

Brunswick 1 BWR PBR_01 P 5 21 31.3 

Brunswick 1 BWR WBR_01 W 3 26 35 

Byron 1 PWR FBY101 F 6 19 15 

Byron 1 PWR WBY101 W 3 19 0 

Byron 2 PWR FBY201 F 6 19 -5 

Byron 2 PWR WBY201 W 3 19 -1 

Callaway PWR PCL101 P 8 19 -2 

Callaway PWR WCL101 W 4 19 27.0 

Calvert Cliffs 1 PWR PCC103 P 3 21 -6 

Calvert Cliffs 1 PWR WCC101 W 3 26 -17 
B-2

General Information Type A De

Plant Name Unit Reactor 

Type

Heat Product 

Form

n

σ(

o

F) 

rmean(

o

F)

Calvert Cliffs2 PWR PCC202P3 21-7 

Catawba1 PWR FCB101F6 20-16 

Catawba1 PWR WCB101W3 19-8 

Catawba2 PWR PCB201P6 21-1 

Catawba2 PWR WCB201W3 191 

Commanche Peak1 PWR PCP101P4 19-5 

Connecticut Yankee ex-PWR PCTY04P3 21-4 

Connecticut Yankee ex-PWR PCTY02P3 21-13 

Crystal River3 PWR PCR301P4 21 17 

Crystal River3 PWR WCR301W4 26 12 

Crystal River3 PWR WHSS66W4 26-20 

Crystal River3 PWR WHSSCRW3 26-6 

Crystal River & Surry 3 & 2 PWR WHSS65W3 263 

D.C. Cook1 PWR PCK101P8 21-4 

D.C. Cook1 PWR WCK101W3 26-103 

D.C. Cook2 PWR PCK201P8 21 24.6 

D.C. Cook2 PWR WCK201W4 19 17 

Davis Besse PWR FDB102F4 19-7 

Davis Besse PWR WDB101W5 261 

Davis Besse PWR PRS101P3 21-6 

Davis Besse PWR WRS101W3 26-14 

Diablo Canyon1 PWR PDC103P3 21-24 

Diablo Canyon1 PWR WDC101W3 26-2 

Diablo Canyon2 PWR PDC201P8 21-5 

Diablo Canyon2 PWR WDC201W4 26-3 

Dresden3 BWR WDR302W3 26-17 

Dresden2 BWR PDR201P5 21-32 

Dresden3 BWR PDR301P6 21-10 

Dresden3 BWR WDR301W5 26-5 

Duane Arnold BWR PDAC01P3 21 10 

Duane Arnold BWR WDAC01W3 19-4 
B-3

General Information Type A De

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) rmean (

oF) 

Farley 1 PWR PFA101 P 8 21 13 

Farley 1 PWR WFA101 W 4 26 -7 

Farley 2 PWR PFA201 P 8 21 15 

Farley 2 PWR WFA201 W 4 19 -51 

FitzPatrick BWR PFTZ01 P 6 21 -11 

Fort Calhoun PWR PFC101 P 5 21 -10 

Fort Calhoun PWR WFC101 W 4 26 -1 

Ginna PWR FGIN02 F 4 19 -18 

Ginna PWR FGIN01 F 4 19 17 

Ginna PWR WGIN01 W 4 26 13 

H.B. Robinson 2 PWR WHB201 W 3 26 6 

Indian Point 2 PWR PIP202 P 3 21 -1 

Indian Point 2 PWR PIP203 P 3 21 32.6 

Indian Point 3 PWR PIP304 P 5 21 13 

Indian Point 3 PWR WIP301 W 3 26 33 

Kewaunee PWR FKWE02 F 4 19 -7 

Kewaunee PWR FKWE01 F 4 19 -9 

Kewaunee PWR WKWE01 W 4 26 16 

Maine Yankee ex-PWR PMY_01 P 6 21 28.5 

Maine Yankee ex-PWR SHSS01 SRM 17 21 1 

Maine Yankee ex-PWR WMY_01 W 4 26 -8 

McGuire 1 PWR PMC101 P 8 21 13 

McGuire 1 PWR WMC101 W 4 26 -11 

McGuire 2 PWR FMC201 F 8 20 1 

McGuire 2 PWR WMC201 W 4 19 3 

Millstone 1 ex-BWR PML101 P 4 21 -6 

Millstone 2 PWR PML201 P 5 21 13 

Millstone 2 PWR WML201 W 3 26 -27 

Nine Mile Point 1 BWR PNM101 P 5 21 -10 

North Anna 1 PWR FNA101 F 6 20 -14 

North Anna 1 PWR WNA101 W 3 26 21 
B-4

General Information Type A De

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) rmean (

oF) 

North Anna 2 PWR FNA201 F 6 20 -18 

North Anna 2 PWR WNA201 W 3 26 -23 

Oconee 1 PWR POC102 P 6 21 5 

Oconee 1 PWR SHSS02 SRM 64 21 -14 

Oconee 1 PWR WOC101 W 3 26 5 

Oconee 2 PWR FOC201 F 5 19 -3 

Oconee 2 PWR WOC201 W 3 26 -23 

Oconee 3 PWR FOC301 F 4 19 2 

Oconee 3 PWR FOC302 F 3 19 21 

Oconee 3 PWR WOC301 W 4 26 -28 

Oyster Creek BWR PGG_01 P 4 19 2 

Oyster Creek BWR PCPR02 P 4 21 -3 

Oyster Creek BWR PEP2JP P 5 19 -3 

Oyster Creek BWR WGG_01 W 4 19 -8 

Oyster Creek BWR WML101 W 6 26 -23 

Oyster Creek BWR WQC102_1 W 4 26 26 

Oyster Creek BWR WQC201_1 W 4 26 17 

Oyster Creek BWR WRB_01 W 3 19 34.6 

Palisades PWR PPAL01 P 7 21 -33 

Palisades PWR WPAL01 W 4 26 -5 

Point Beach 2 PWR FPB202 F 4 20 19 

Point Beach 1 PWR PPB102 P 4 21 -28 

Point Beach 1 PWR PPB101 P 4 21 9 

Point Beach 1 PWR WPB101 W 4 26 -42 

Point Beach 2 PWR FPB201 F 4 19 16 

Point Beach 2 PWR WPB201 W 4 26 6 

Prarie Island 1 PWR FPI101 F 8 19 -2 

Prarie Island 1 PWR WPI101 W 4 26 -19 

Prarie Island 2 PWR FPI201 F 8 20 -4 

Prarie Island 2 PWR WPI201 W 4 26 -11 

Quad Cities 1 BWR PQC101 P 6 21 1 
B-5

General Information Type A De

Plant Name Unit Reactor 

Type

Heat Product 

Form

n

σ(

o

F) 

rmean(

o

F)

Quad Cities1 BWR WQC101W4 26-16 

Quad Cities2 BWR PQC201P4 21-18 

Quad Cities2 BWR WQC201W4 26 18 

Saint Lucie1 PWR PSL101P5 21-19 

Saint Lucie1 PWR WSL101W3 26-18 

Saint Lucie2 PWR PSL201P3 21 14 

Salem1 PWR PSA103P3 21-30 

Salem1 PWR PSA101P3 216 

Salem2 PWR PSA201P8 21 10 

Salem2 PWR WSA201W4 26-18 

San Onofre2 PWR PSO201P3 21-7 

San Onofre3 PWR PSO301P3 19 40.1 

Seabrook1 PWR PSB101P4 19 19 

Sequoyah1 PWR FSQ101F8 20 18.3 

Sequoyah1 PWR WSQ101W4 26 32.4 

Sequoyah2 PWR FSQ201F8 207 

Sequoyah2 PWR WSQ201W4 26 23 

South Texas1 PWR PST101P4 193 

South Texas2 PWR PST201P4 194 

Surry1 PWR PSU101P3 215 

Surry1 PWR WSU101W3 26 43.5 

Surry2 PWR PSU201P6 210 

Surry2 PWR WSU201W3 26-14 

Three Mile Island1 PWR PTM101P3 21-17 

Trojan ex-PWR PTRO01P6 211 

Trojan ex-PWR WTRO01W3 198 

Turkey Point3 PWR FTP302F3 20 10 

Turkey Point3 PWR SASTM SRM 26 215 

Turkey Point3 PWR WTP301W4 26 13 

Virgil Summer1 PWR PVS101P8 21-20 

Virgil Summer1 PWR WVS101W4 190 
B-6

General Information Type A De

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) rmean (

oF) 

Vogtle 1 PWR PVO101 P 6 19 -1 

Vogtle 1 PWR WVO101 W 3 19 -4 

Vogtle 2 PWR PVO201 P 6 19 -14 

Vogtle 2 PWR WVO201 W 3 19 -13 

Waterford 3 PWR PWF301 P 3 19 -13 

Watts Bar 1 PWR FWB101 F 4 20 -6 

Wolf Creek 1 PWR PWC101 P 8 19 8 

Wolf Creek 1 PWR WWC101 W 4 19 17 

Zion 1 ex-PWR PZN101 P 8 21 -2 

Zion 1 ex-PWR WZN101 W 5 26 -6 

Zion 2 ex-PWR PZN201 P 6 21 3 

Zion 2 ex-PWR WZN201 W 3 26 3 
B-7

Table B-2 Type B Deviations (Slope Test) 

General Information Type B Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) m se(m) Tm 

Arkansas Nuclear 1 PWR PAN101 P 6 21 -26.06 10.09 -2.58 

Arkansas Nuclear 1 PWR WAN101 W 3 26 -37.69 19.02 -1.98 

Arkansas Nuclear 2 PWR PAN201 P 3 21 -5.72 16.85 -0.34 

Beaver Valley 1 PWR PBV101 P 8 21 -37.91 21.46 -1.77 

Beaver Valley 1 PWR WBV101 W 4 26 -56.91 15.54 -3.66 

Beaver Valley 2 PWR PBV201 P 6 19 4.78 6.63 0.72 

Beaver Valley 2 PWR WBV201 W 3 26 -50.14 20.08 -2.50 

Braidwood 1 PWR FBD101 F 6 19 26.30 21.44 1.23 

Braidwood 1 PWR WBD101 W 3 19 8.25 8.49 0.97 

Braidwood 2 PWR FBD201 F 6 19 14.24 22.91 0.62 

Braidwood 2 PWR WBD201 W 3 19 6.66 19.20 0.35 

Brunswick 1 BWR PBR_01 P 5 21 67.73 13.28 5.10 

Brunswick 1 BWR WBR_01 W 3 26 41.69 45.09 0.92 

Byron 1 PWR FBY101 F 6 19 7.34 15.79 0.46 

Byron 1 PWR WBY101 W 3 19 26.54 8.12 3.27 

Byron 2 PWR FBY201 F 6 19 0.03 19.60 0.00 

Byron 2 PWR WBY201 W 3 19 27.60 8.32 3.32 

Callaway PWR PCL101 P 8 19 -8.04 14.97 -0.54 

Callaway PWR WCL101 W 4 19 -41.68 12.80 -3.26 

Calvert Cliffs 1 PWR PCC103 P 3 21 13.74 2.75 4.99 

Calvert Cliffs 1 PWR WCC101 W 3 26 37.90 2.00 18.95 

Calvert Cliffs 2 PWR PCC202 P 3 21 11.27 12.00 0.94 

Catawba 1 PWR FCB101 F 6 20 24.31 20.63 1.18 

Catawba 1 PWR WCB101 W 3 19 7.91 2.47 3.20 

Catawba 2 PWR PCB201 P 6 21 0.93 10.27 0.09 

Catawba 2 PWR WCB201 W 3 19 91.48 9.59 9.54 

Comanche Peak 1 PWR PCP101 P 4 19 -19.21 15.89 -1.2

Connecticut Yankee ex-PWR PCTY04 P 3 21 -63.22 2.55 -24.79 

Connecticut Yankee ex-PWR PCTY02 P 3 21 -47.44 1.52 -31.24 

Crystal River 3 PWR PCR301 P 4 21 22.02 11.98 1.84 
B-8

General Information Type B Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) m se(m) Tm 

Crystal River 3 PWR WCR301 W 4 26 46.92 13.65 3.44 

Crystal River 3 PWR WHSS66 W 4 26 -110.03 117.85 -0.93 

Crystal River 3 PWR WHSSCR W 3 26 -116.65 31.01 -3.76 

Crystal River & Surry 3 & 2 PWR WHSS65 W 3 26 2.10 14.59 0.14 

D.C. Cook 1 PWR PCK101 P 8 21 -8.31 11.44 -0.73 

D.C. Cook 1 PWR WCK101 W 3 26 -27.17 98.72 -0.28 

D.C. Cook 2 PWR PCK201 P 8 21 1.58 17.98 0.09 

D.C. Cook 2 PWR WCK201 W 4 19 -14.88 17.64 -0.84 

Davis Besse PWR FDB102 F 4 19 33.72 23.70 1.42 

Davis Besse PWR WDB101 W 5 26 10.23 58.55 0.17 

Davis Besse PWR PRS101 P 3 21 19.87 18.23 1.09 

Davis Besse PWR WRS101 W 3 26 24.78 24.12 1.03 

Diablo Canyon 1 PWR PDC103 P 3 21 -2.29 33.31 -0.07 

Diablo Canyon 1 PWR WDC101 W 3 26 23.50 74.96 0.3

Diablo Canyon 2 PWR PDC201 P 8 21 -1.49 7.64 -0.19 

Diablo Canyon 2 PWR WDC201 W 4 26 -34.17 7.34 -4.66 

Dresden 3 BWR WDR302 W 3 26 -25.60 231.23 -0.1

Dresden 2 BWR PDR201 P 5 21 2.15 5.51 0.39 

Dresden 3 BWR PDR301 P 6 21 -2.52 4.90 -0.5

Dresden 3 BWR WDR301 W 5 26 7.60 7.66 0.99 

Duane Arnold BWR PDAC01 P 3 21 -2.02 13.71 -0.15 

Duane Arnold BWR WDAC01 W 3 19 20.21 6.54 3.09 

Farley 1 PWR PFA101 P 8 21 21.46 8.51 2.52 

Farley 1 PWR WFA101 W 4 26 -27.48 10.40 -2.64 

Farley 2 PWR PFA201 P 8 21 20.33 15.54 1.3

Farley 2 PWR WFA201 W 4 19 -25.24 19.69 -1.28 

FitzPatrick BWR PFTZ01 P 6 21 8.83 10.75 0.82 

Fort Calhoun PWR PFC101 P 5 21 -22.33 33.89 -0.66 

Fort Calhoun PWR WFC101 W 4 26 -73.25 49.46 -1.48 

Ginna PWR FGIN02 F 4 19 39.26 74.20 0.53 

Ginna PWR FGIN01 F 4 19 -33.49 29.11 -1.15 

Ginna PWR WGIN01 W 4 26 13.77 24.57 0.56 
B-9

General Information Type B Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) m se(m) Tm 

H.B. Robinson 2 PWR WHB201 W 3 26 7.86 33.97 0.23 

Indian Point 2 PWR PIP202 P 3 21 -59.41 46.88 -1.27 

Indian Point 2 PWR PIP203 P 3 21 -17.19 2.14 -8.05 

Indian Point 3 PWR PIP304 P 5 21 2.30 29.72 0.08 

Indian Point 3 PWR WIP301 W 3 26 -0.18 79.92 0.00 

Kewaunee PWR FKWE02 F 4 19 5.09 6.32 0.8

Kewaunee PWR FKWE01 F 4 19 -3.54 28.08 -0.13 

Kewaunee PWR WKWE01 W 4 26 -15.96 19.26 -0.83 

Maine Yankee ex-PWR PMY_01 P 6 21 -6.49 15.82 -0.4

Maine Yankee ex-PWR SHSS01 SRM 17 21 -4.95 15.22 -0.33 

Maine Yankee ex-PWR WMY_01 W 4 26 10.14 12.08 0.84 

McGuire 1 PWR PMC101 P 8 21 24.92 19.19 1.30 

McGuire 1 PWR WMC101 W 4 26 -43.26 13.24 -3.27 

McGuire 2 PWR FMC201 F 8 20 4.68 13.50 0.35 

McGuire 2 PWR WMC201 W 4 19 -34.72 13.01 -2.67 

Millstone 1 ex-BWR PML101 P 4 21 -46.63 28.45 -1.64 

Millstone 2 PWR PML201 P 5 21 23.17 31.56 0.73 

Millstone 2 PWR WML201 W 3 26 -56.09 3.80 -14.77 

Nine Mile Point 1 BWR PNM101 P 5 21 41.45 22.11 1.87 

North Anna 1 PWR FNA101 F 6 20 8.37 20.75 0.40 

North Anna 1 PWR WNA101 W 3 26 -40.22 70.03 -0.57 

North Anna 2 PWR FNA201 F 6 20 18.17 12.92 1.4

North Anna 2 PWR WNA201 W 3 26 -5.18 23.10 -0.22 

Oconee 1 PWR POC102 P 6 21 -19.62 25.32 -0.77 

Oconee 1 PWR SHSS02 SRM 64 21 1.87 4.39 0.43 

Oconee 1 PWR WOC101 W 3 26 41.08 14.09 2.92 

Oconee 2 PWR FOC201 F 5 19 -15.62 13.86 -1.13 

Oconee 2 PWR WOC201 W 3 26 30.52 12.69 2.4

Oconee 3 PWR FOC301 F 4 19 -2.79 5.78 -0.48 

Oconee 3 PWR FOC302 F 3 19 -21.76 32.80 -0.66 

Oconee 3 PWR WOC301 W 4 26 41.81 33.82 1.24 

Oyster Creek BWR PGG_01 P 4 19 21.14 22.39 0.94 
B-10

General Information Type B Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) m se(m) Tm 

Oyster Creek BWR PCPR02 P 4 21 -8.62 42.21 -0.20 

Oyster Creek BWR PEP2JP P 5 19 -32.14 8.29 -3.88 

Oyster Creek BWR WGG_01 W 4 19 39.71 61.15 0.65 

Oyster Creek BWR WML101 W 6 26 10.03 20.07 0.50 

Oyster Creek BWR WQC102_1 W 4 26 6.48 11.60 0.56 

Oyster Creek BWR WQC201_1 W 4 26 57.46 59.89 0.96 

Oyster Creek BWR WRB_01 W 3 19 20.94 63.55 0.33 

Palisades PWR PPAL01 P 7 21 -77.49 15.02 -5.16 

Palisades PWR WPAL01 W 4 26 -42.23 5.32 -7.93 

Point Beach 2 PWR FPB202 F 4 20 41.30 12.36 3.34 

Point Beach 1 PWR PPB102 P 4 21 -76.91 8.77 -8.77 

Point Beach 1 PWR PPB101 P 4 21 -55.54 23.06 -2.4

Point Beach 1 PWR WPB101 W 4 26 -12.46 53.53 -0.23 

Point Beach 2 PWR FPB201 F 4 19 -0.70 8.03 -0.09 

Point Beach 2 PWR WPB201 W 4 26 38.35 27.60 1.39 

Prarie Island 1 PWR FPI101 F 8 19 -0.54 17.08 -0.03 

Prarie Island 1 PWR WPI101 W 4 26 57.84 38.91 1.49 

Prarie Island 2 PWR FPI201 F 8 20 8.36 9.37 0.89 

Prarie Island 2 PWR WPI201 W 4 26 -40.19 12.22 -3.29 

Quad Cities 1 BWR PQC101 P 6 21 7.70 2.14 3.59 

Quad Cities 1 BWR WQC101 W 4 26 10.12 7.81 1.30 

Quad Cities 2 BWR PQC201 P 4 21 -10.04 3.17 -3.17 

Quad Cities 2 BWR WQC201 W 4 26 -3.89 4.21 -0.92 

Saint Lucie 1 PWR PSL101 P 5 21 -5.59 16.17 -0.35 

Saint Lucie 1 PWR WSL101 W 3 26 -46.07 12.84 -3.59 

Saint Lucie 2 PWR PSL201 P 3 21 49.57 1.95 25.45 

Salem 1 PWR PSA103 P 3 21 -6.76 19.49 -0.35 

Salem 1 PWR PSA101 P 3 21 5.06 24.98 0.20 

Salem 2 PWR PSA201 P 8 21 -3.87 21.39 -0.18 

Salem 2 PWR WSA201 W 4 26 -45.51 9.34 -4.87 

San Onofre 2 PWR PSO201 P 3 21 11.38 26.39 0.43 

San Onofre 3 PWR PSO301 P 3 19 15.75 21.22 0.74 
B-11

General Information Type B Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n

σ (

o

F) 

m se(m)T

m

Seabrook1 PWR PSB101P4 19-6.15 14.03-0.44 

Sequoyah1 PWR FSQ101F8 20 31.83 17.01 1.87 

Sequoyah1 PWR WSQ101W4 26-8.36 4.54-1.84 

Sequoyah2 PWR FSQ201F8 20 12.09 14.40 0.84 

Sequoyah2 PWR WSQ201W4 26-71.71 89.12-0.80 

South Texas1 PWR PST101P4 19-9.15 21.18-0.43 

South Texas2 PWR PST201P4 19 16.33 4.60 3.55 

Surry1 PWR PSU101P3 21 10.46 20.36 0.5

Surry1 PWR WSU101W3 26 9.51 7.62 1.25 

Surry2 PWR PSU201P6 21-2.98 13.63-0.22 

Surry2 PWR WSU201W3 26 7.37 24.69 0.30 

Three Mile Island1 PWR PTM101P3 21-41.07 2.89-14.23 

Trojan ex-PWR PTRO01P6 21-2.31 12.00-0.19 

Trojan ex-PWR WTRO01W3 19-14.97 10.82-1.38 

Turkey Point3 PWR FTP302F3 20 52.36 70.45 0.74 

Turkey Point3 PWR SASTM SRM 26 21 10.59 8.87 1.19 

Turkey Point3 PWR WTP301W4 26 15.55 35.61 0.44 

Virgil Summer1 PWR PVS101P8 21-12.14 16.33-0.74 

Virgil Summer1 PWR WVS101W4 19-20.29 23.75-0.85 

Vogtle1 PWR PVO101P6 19 20.85 19.05 1.09 

Vogtle1 PWR WVO101W3 19-41.81 19.81-2.1

Vogtle2 PWR PVO201P6 19 15.57 10.12 1.54 

Vogtle2 PWR WVO201W3 19 25.29 19.30 1.3

Waterford3 PWR PWF301P3 19-87.52 64.25-1.36 

Watts Bar1 PWR FWB101F4 20 41.28 90.57 0.46 

Wolf Creek1 PWR PWC101P8 19-8.38 9.54-0.88 

Wolf Creek1 PWR WWC101W4 19 4.70 8.95 0.53 

Zion1 ex-PWR PZN101P8 21 14.89 14.97 0.99 

Zion1 ex-PWR WZN101W5 26 43.23 8.52 5.07 

Zion2 ex-PWR PZN201P6 21 19.41 15.57 1.25 

Zion2 ex-PWR WZN201W3 26 17.59 31.94 0.55 
B-12

Table B-3 Type D Deviations (utlier Test) 

General Information Type D Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) ri(max1) ri(max2) C1 

Arkansas Nuclear 1 PWR PAN101 P 6 21 0.98 -0.13 1.93 

Arkansas Nuclear 1 PWR WAN101 W 3 26 1.47 0.03 1.55 

Arkansas Nuclear 2 PWR PAN201 P 3 21 0.36 -0.32 1.55 

Beaver Valley 1 PWR PBV101 P 8 21 2.52 2.26 2.05 

Beaver Valley 1 PWR WBV101 W 4 26 0.83 0.14 1.73 

Beaver Valley 2 PWR PBV201 P 6 19 -0.04 -0.06 1.93 

Beaver Valley 2 PWR WBV201 W 3 26 -0.61 -1.39 1.55 

Braidwood 1 PWR FBD101 F 6 19 0.41 0.23 1.93 

Braidwood 1 PWR WBD101 W 3 19 0.42 0.03 1.55 

Braidwood 2 PWR FBD201 F 6 19 0.85 0.41 1.93 

Braidwood 2 PWR WBD201 W 3 19 0.04 -0.59 1.55 

Brunswick 1 BWR PBR_01 P 5 21 4.09 2.99 1.84 

Brunswick 1 BWR WBR_01 W 3 26 2.56 1.53 1.55 

Byron 1 PWR FBY101 F 6 19 1.67 1.58 1.93 

Byron 1 PWR WBY101 W 3 19 0.38 0.37 1.55 

Byron 2 PWR FBY201 F 6 19 0.46 0.36 1.93 

Byron 2 PWR WBY201 W 3 19 0.59 -0.10 1.55 

Callaway PWR PCL101 P 8 19 1.06 0.70 2.05 

Callaway PWR WCL101 W 4 19 3.03 0.98 1.73 

Calvert Cliffs 1 PWR PCC103 P 3 21 -0.10 -0.19 1.55 

Calvert Cliffs 1 PWR WCC101 W 3 26 -0.14 -0.71 1.55 

Calvert Cliffs 2 PWR PCC202 P 3 21 -0.14 -0.38 1.55 

Catawba 1 PWR FCB101 F 6 20 0.14 0.05 1.93 

Catawba 1 PWR WCB101 W 3 19 -0.27 -0.46 1.55 

Catawba 2 PWR PCB201 P 6 21 0.30 0.26 1.93 

Catawba 2 PWR WCB201 W 3 19 1.75 0.74 1.55 

Comanche Peak 1 PWR PCP101 P 4 19 0.38 -0.15 1.73 

Connecticut Yankee ex-PWR PCTY04 P 3 21 1.02 -0.60 1.55 

Connecticut Yankee ex-PWR PCTY02 P 3 21 0.17 -0.45 1.55 

Crystal River 3 PWR PCR301 P 4 21 1.46 1.03 1.73 
B-13

General Information Type D Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) ri(max1) ri(max2) C1 

Crystal River 3 PWR WCR301 W 4 26 1.12 1.00 1.73 

Crystal River 3 PWR WHSS66 W 4 26 0.71 -0.78 1.73 

Crystal River 3 PWR WHSSCR W 3 26 0.77 0.06 1.55 

Crystal River & Surry 3 & 2 PWR WHSS65 W 3 26 0.23 0.18 1.55 

D.C. Cook 1 PWR PCK101 P 8 21 0.57 0.28 2.05 

D.C. Cook 1 PWR WCK101 W 3 26 -2.30 -3.73 1.55 

D.C. Cook 2 PWR PCK201 P 8 21 2.27 1.68 2.05 

D.C. Cook 2 PWR WCK201 W 4 19 1.47 1.28 1.73 

Davis Besse PWR FDB102 F 4 19 0.98 -0.60 1.73 

Davis Besse PWR WDB101 W 5 26 2.01 0.32 1.84 

Davis Besse PWR PRS101 P 3 21 -0.05 -0.12 1.55 

Davis Besse PWR WRS101 W 3 26 -0.26 -0.36 1.55 

Diablo Canyon 1 PWR PDC103 P 3 21 -0.53 -1.24 1.55 

Diablo Canyon 1 PWR WDC101 W 3 26 1.14 -0.69 1.55 

Diablo Canyon 2 PWR PDC201 P 8 21 0.21 -0.04 2.05 

Diablo Canyon 2 PWR WDC201 W 4 26 0.54 -0.15 1.73 

Dresden 3 BWR WDR302 W 3 26 0.74 -1.02 1.55 

Dresden 2 BWR PDR201 P 5 21 -0.23 -1.56 1.84 

Dresden 3 BWR PDR301 P 6 21 0.49 -0.20 1.93 

Dresden 3 BWR WDR301 W 5 26 1.01 0.43 1.84 

Duane Arnold BWR PDAC01 P 3 21 0.66 0.39 1.55 

Duane Arnold BWR WDAC01 W 3 19 0.14 -0.32 1.55 

Farley 1 PWR PFA101 P 8 21 1.39 1.20 2.05 

Farley 1 PWR WFA101 W 4 26 0.38 -0.46 1.73 

Farley 2 PWR PFA201 P 8 21 1.92 1.22 2.05 

Farley 2 PWR WFA201 W 4 19 -2.12 -2.13 1.73 

FitzPatrick BWR PFTZ01 P 6 21 -0.03 -0.16 1.93 

Fort Calhoun PWR PFC101 P 5 21 0.03 -0.11 1.84 

Fort Calhoun PWR WFC101 W 4 26 0.59 0.32 1.73 

Ginna PWR FGIN02 F 4 19 1.35 -0.34 1.73 

Ginna PWR FGIN01 F 4 19 2.19 1.10 1.73 

Ginna PWR WGIN01 W 4 26 1.17 0.58 1.73 
B-14

General Information Type D Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) ri(max1) ri(max2) C1 

H.B. Robinson 2 PWR WHB201 W 3 26 0.96 0.05 1.55 

Indian Point 2 PWR PIP202 P 3 21 1.26 -0.57 1.55 

Indian Point 2 PWR PIP203 P 3 21 1.81 1.53 1.55 

Indian Point 3 PWR PIP304 P 5 21 1.41 1.11 1.84 

Indian Point 3 PWR WIP301 W 3 26 1.90 1.54 1.55 

Kewaunee PWR FKWE02 F 4 19 -0.08 -0.43 1.73 

Kewaunee PWR FKWE01 F 4 19 -0.04 -0.05 1.73 

Kewaunee PWR WKWE01 W 4 26 1.10 0.74 1.73 

Maine Yankee ex-PWR PMY_01 P 6 21 2.36 1.58 1.93 

Maine Yankee ex-PWR SHSS01 SRM 17 21 1.48 0.96 2.37 

Maine Yankee ex-PWR WMY_01 W 4 26 0.05 -0.12 1.73 

McGuire 1 PWR PMC101 P 8 21 1.98 1.16 2.05 

McGuire 1 PWR WMC101 W 4 26 0.54 -0.68 1.73 

McGuire 2 PWR FMC201 F 8 20 1.52 0.13 2.05 

McGuire 2 PWR WMC201 W 4 19 1.32 0.14 1.73 

Millstone 1 ex-BWR PML101 P 4 21 0.43 0.18 1.73 

Millstone 2 PWR PML201 P 5 21 1.94 1.09 1.84 

Millstone 2 PWR WML201 W 3 26 -0.27 -1.13 1.55 

Nine Mile Point 1 BWR PNM101 P 5 21 0.05 -0.24 1.84 

North Anna 1 PWR FNA101 F 6 20 0.88 -0.65 1.93 

North Anna 1 PWR WNA101 W 3 26 2.07 0.94 1.55 

North Anna 2 PWR FNA201 F 6 20 -0.12 -0.17 1.93 

North Anna 2 PWR WNA201 W 3 26 -0.59 -0.63 1.55 

Oconee 1 PWR POC102 P 6 21 1.53 1.41 1.93 

Oconee 1 PWR SHSS02 SRM 64 21 1.47 1.40 2.83 

Oconee 1 PWR WOC101 W 3 26 0.87 0.31 1.55 

Oconee 2 PWR FOC201 F 5 19 0.94 0.00 1.84 

Oconee 2 PWR WOC201 W 3 26 -0.09 -1.17 1.55 

Oconee 3 PWR FOC301 F 4 19 0.37 0.16 1.73 

Oconee 3 PWR FOC302 F 3 19 2.53 0.98 1.55 

Oconee 3 PWR WOC301 W 4 26 0.89 -1.03 1.73 

Oyster Creek BWR PGG_01 P 4 19 0.23 -0.05 1.73 
B-15

General Information Type D Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) ri(max1) ri(max2) C1 

Oyster Creek BWR PCPR02 P 4 21 0.48 -0.17 1.73 

Oyster Creek BWR PEP2JP P 5 19 0.86 0.12 1.84 

Oyster Creek BWR WGG_01 W 4 19 0.62 -0.32 1.73 

Oyster Creek BWR WML101 W 6 26 0.07 -0.70 1.93 

Oyster Creek BWR WQC102_1 W 4 26 1.14 1.02 1.73 

Oyster Creek BWR WQC201_1 W 4 26 1.16 1.03 1.73 

Oyster Creek BWR WRB_01 W 3 19 2.27 1.87 1.55 

Palisades PWR PPAL01 P 7 21 0.11 -0.48 2 

Palisades PWR WPAL01 W 4 26 0.21 0.07 1.73 

Point Beach 2 PWR FPB202 F 4 20 1.64 1.35 1.73 

Point Beach 1 PWR PPB102 P 4 21 -0.37 -0.52 1.73 

Point Beach 1 PWR PPB101 P 4 21 1.08 1.03 1.73 

Point Beach 1 PWR WPB101 W 4 26 -0.46 -1.58 1.73 

Point Beach 2 PWR FPB201 F 4 19 1.06 0.94 1.73 

Point Beach 2 PWR WPB201 W 4 26 0.00 0.00 1.73 

Prarie Island 1 PWR FPI101 F 8 19 0.77 0.77 2.05 

Prarie Island 1 PWR WPI101 W 4 26 0.89 -0.43 1.73 

Prarie Island 2 PWR FPI201 F 8 20 0.56 0.11 2.05 

Prarie Island 2 PWR WPI201 W 4 26 0.57 -0.47 1.73 

Quad Cities 1 BWR PQC101 P 6 21 0.74 0.60 1.93 

Quad Cities 1 BWR WQC101 W 4 26 0.63 -0.63 1.73 

Quad Cities 2 BWR PQC201 P 4 21 -0.11 -0.38 1.73 

Quad Cities 2 BWR WQC201 W 4 26 1.07 0.81 1.73 

Saint Lucie 1 PWR PSL101 P 5 21 -0.55 -0.72 1.84 

Saint Lucie 1 PWR WSL101 W 3 26 -0.28 -0.68 1.55 

Saint Lucie 2 PWR PSL201 P 3 21 2.02 -0.01 1.55 

Salem 1 PWR PSA103 P 3 21 -1.09 -1.33 1.55 

Salem 1 PWR PSA101 P 3 21 0.91 0.01 1.55 

Salem 2 PWR PSA201 P 8 21 1.58 1.20 2.05 

Salem 2 PWR WSA201 W 4 26 -0.12 -0.24 1.73 

San Onofre 2 PWR PSO201 P 3 21 0.02 -0.10 1.55 

San Onofre 3 PWR PSO301 P 3 19 2.43 2.34 1.55 
B-16

General Information Type D Deviation (

Plant Name Unit Reactor 

Type

Heat Product 

Form

n σ (

oF) ri(max1) ri(max2) C1 

Seabrook 1 PWR PSB101 P 4 19 1.39 1.19 1.73 

Sequoyah 1 PWR FSQ101 F 8 20 2.37 1.73 2.05 

Sequoyah 1 PWR WSQ101 W 4 26 1.39 1.31 1.73 

Sequoyah 2 PWR FSQ201 F 8 20 1.57 1.36 2.05 

Sequoyah 2 PWR WSQ201 W 4 26 3.62 1.44 1.73 

South Texas 1 PWR PST101 P 4 19 0.71 0.59 1.73 

South Texas 2 PWR PST201 P 4 19 0.67 0.39 1.73 

Surry 1 PWR PSU101 P 3 21 0.80 0.02 1.55 

Surry 1 PWR WSU101 W 3 26 1.88 1.58 1.55 

Surry 2 PWR PSU201 P 6 21 0.55 0.47 1.93 

Surry 2 PWR WSU201 W 3 26 0.00 -0.58 1.55 

Three Mile Island 1 PWR PTM101 P 3 21 0.38 -1.29 1.55 

Trojan ex-PWR PTRO01 P 6 21 0.74 0.14 1.93 

Trojan ex-PWR WTRO01 W 3 19 0.77 0.55 1.55 

Turkey Point 3 PWR FTP302 F 3 20 1.05 0.67 1.55 

Turkey Point 3 PWR SASTM SRM 26 21 1.98 1.94 2.53 

Turkey Point 3 PWR WTP301 W 4 26 1.30 0.36 1.73 

Virgil Summer 1 PWR PVS101 P 8 21 0.12 -0.15 2.05 

Virgil Summer 1 PWR WVS101 W 4 19 0.95 0.16 1.73 

Vogtle 1 PWR PVO101 P 6 19 0.70 0.56 1.93 

Vogtle 1 PWR WVO101 W 3 19 0.67 -0.02 1.55 

Vogtle 2 PWR PVO201 P 6 19 -0.17 -0.23 1.93 

Vogtle 2 PWR WVO201 W 3 19 -0.17 -0.49 1.55 

Waterford 3 PWR PWF301 P 3 19 0.53 -0.87 1.55 

Watts Bar 1 PWR FWB101 F 4 20 0.94 0.85 1.73 

Wolf Creek 1 PWR PWC101 P 8 19 1.10 0.88 2.05 

Wolf Creek 1 PWR WWC101 W 4 19 1.20 1.20 1.73 

Zion 1 ex-PWR PZN101 P 8 21 0.43 0.33 2.05 

Zion 1 ex-PWR WZN101 W 5 26 0.31 0.02 1.84 

Zion 2 ex-PWR PZN201 P 6 21 1.20 0.27 1.93 

Zion 2 ex-PWR WZN201 W 3 26 0.66 0.04 1.55 
C-1

APPENDIX C FLAW DEPTH AND DENSITY DISTRIBUTIONS 

CONSIDERING PROBABILITY OF DETECTION AND BIAS 

IN NDE DATA WITH APPLICATIONS

Prepared for the U.S. Nuclear Regulatory Commission under Subcontract 4000099247

with UT-Battelle, LLC (Oak Ridge National Laboratory)

Mohammad Modarres

University of Maryland

October 2011

C-3

TABLE OF CONTENTS 

TABLE OF CONTENTS.............................................................................................. C-3

LIST OF FIGURES...................................................................................................... C-5

LIST OF TABLES ....................................................................................................... C-5

ABBREVIATIONS....................................................................................................... C-7

SYMBOLS AND EXPRESSIONS............................................................................... C-7

C.1 Introduction and Background.......................................................................... C-9

C.2 Probabilistic Approach to Combine Uncertain NDE Flaw Data with

Prior Flaw Distributions.................................................................................. C-11

C.2.1 The Bayesian Framework ................................................................................. C-11

C.2.2 Probability of Detection and Measurement Error............................................... C-13

C.2.2.1 Probability of Detection....................................................................... C-13

C.2.2.2 Measurement (Sizing) Error................................................................ C-14

C.2.3 The Methodology for Updating the NDE Data ................................................... C-15

C.2.3.1 Updating Flaw Depth Distribution Models........................................... C-16

C.2.3.2 Updating the Flaw Density Model ....................................................... C-19

C.3 Application Example....................................................................................... C-21

C.3.1 Description of the NDE Data Used as Evidence to Build the Likelihood

Function ......................................................................................................... C-21

C.3.2 Description of Flaw-Depth and –Density Information Used in VFLAW as

Prior PDFs in this Example ............................................................................... C-23

C.3.3 Detection and Sizing Error Models.................................................................... C-27

C.3.4 Bayesian Updating of the Parameters of the Flaw-Depth Distributions ............. C-28

C.3.4.1 Bayesian Updating of the Parameters of Large-Flaw Depth

Distribution Based on the 3/8t UT Inspection Data ............................. C-29

C.3.4.2 Bayesian Updating of the Parameters of Small Flaw Depth

Distribution Based on the 3/8t UT Inspection Data ......................... C-31

C.3.4.3 Results of Updating Parameters of Flaw Density Distribution

Based on the 3/8t UT Inspection Data................................................ C-33

C.3.5 Updating the 10 CFR 50.61a Tables................................................................. C-38

C.4 References....................................................................................................... C-41

C-5

LIST OF FIGURES

Figure C-1 A simple description of the Bayesian updating process.................................. C-10

Figure C-2 Measurement error distribution ...................................................................... C-15

Figure C-3 Beaver Valley 2 weld map [C 14] ................................................................... C-23

Figure C-4 Flaw depth and flaw density distributions used in VFLAW and their 

corresponding parameter hyper PDFs. .......................................................... C-24

Figure C-5 POD vs. flaw depth. ....................................................................................... C-27

Figure C-6 Measurement error vs. flaw depth.................................................................. C-28

Figure C-7 Bayesian Updating Elements of the Beaver Valley 2 Example....................... C-29

Figure C-8 Prior and posterior distributions of the flaw-depth intensity of parameter λl. ... C-31

Figure C-9 Bayesian prior and posterior PDFs of λs (per unit inch).................................. C-32

Figure C-10 Marginal POD independent of small flaw depth.............................................. C-32

Figure C-11 Prior and posterior flaw density (a) and intensity (b) for large size flaw .......... C-34

Figure C-12 Prior and posterior flaw density (a) and intensity (b) for small size flaws ........ C-35

Figure C-13 Posterior number of flaws in the 3/8t region in various flaw size intervals 

including epistemic uncertainties.................................................................... C-38

Figure C-14 Posterior number of flaws in the Supplement 4 inspection volume in 

various flaw size intervals including epistemic uncertainties........................... C-40

Figure C-15 MATLAB Routine Output................................................................................ C-47

LIST OF TABLES

Table C-1 Summary of Likelihood Functions .................................................................. C-12

Table C-2 Flaw-Depth (a) and Flaw-Density (b) Distributions and Hyper-PDF 

Parameters Used in VFLAW for PVRUF........................................................ C-25

(a) Flaw-depth characteristics (in meters) based on data from PVRUF RPV.. C-25

(b) Flaw-density characteristics based on data from PVRUF RPV ................. C-26

Table C-3 Updated VFLAW Distribution for Small Flaws ................................................ C-33

Table C-4 Summary of the Posterior Parameter PDFs of Flaw Depth and Flaw 

Density to be used in VFLAW and FAVOR Runs for Beaver Valley 2 ............ C-37

Table C-5 Alternate PTS Rule Flaw Table Assessment using Mean Number-of-Flaws 

by Size Interval for Beaver Valley 2 (Assuming a Lower Limit of 0.04" for 

Observed Data Interval)................................................................................. C-39

Table C-6 Alternate PTS Rule Flaw Table Assessment using Mean Number-of-Flaws 

by Size Interval for Beaver Valley 2 (Assuming a Lower Limit of 0.075" for 

Observed Data Interval)................................................................................. C-39

C-7

ABBREVIATIONS

PDF Probability Density Function

CDF Cumulative Density Function

ISI In Service Inspection

NDE Nondestructive Evaluation

POD Probability of Detection

PTS Pressurized Thermal Shock

RPV Reactor Pressure Vessel

SAW Submerged Arc Weld

SMAW Shielded Metal Arc Weld

UT Ultrasonic Test

SYMBOLS AND EXPRESSIONS

a True flaw depth (inches)

A Random variable representing flaw depth

Logarithm of signal response amplitude in flaw detection NDE

a* NDE measured (or observed) flaw depth (inches)

ath Threshold flaw depth for detection below which flaw detection is beyond the 

capability of the NDE technology used

D The event that a flaw is detected

The event that a flaw is not detected

EM Model error of the NDE measurement error, represented by a normal 

distribution with mean of zero and known standard deviation

fa(a* Mε|Φ) PDF of the true flaw depth, given the vector of PDF parameters represented 

in terms of observed flaw depth a* but corrected for the measurement error 

Mε

Conditional PDF of large flaw depth

Conditional PDF of small flaw depth

f(.), g(.), h(.), PDF functions of model parameters, flaw depth, or flaw density

l(.), m(.), x(.), 

g’(.). k(.), γ(.)

g(Mε) PDF of the measurement error (in terms of a*)

L(a|Φ) Likelihood of true flaw depth given the vector of parameters Φ

L(Data|θ) Likelihood of observed NDE data conditioned on (given) the unknown 

parameter θ

Likelihood of observing n* flaws given there are a total of nj true flaws

Mε NDE measurement error (combined random and systematic errors)

m*i Number of flaw depths observed (reported in NDE) in the interval i

n Number of flaw depth intervals (reported in NDE)

n* Number of exact flaw depths observed (reported in NDE)
C-8

Combination of n* observed flaws out of total flaws nj (observed or detected, 

and unobserved or not detected flaws) 

N Mean of the PDF of the number of flaws in volume v

N(0;σ) Normal PDF with mean zero and standard deviation of σ

POD(a) Probability of detection of a flaw of depth a

POD(a* Mε) POD of true flaw depth represented in terms of observed flaw depth a* by 

correcting for the measurement error Mε

Pr(.) Probability

Pr(D) POD independent of flaw depth

Probability of no detection regardless of size

Probability of total flaws nj conditioned on observing n* flaws in NDE

Pr(Φ, ttr) POD independent of flaw size (i.e., Pr(D))

ttr Transition flaw depth which separates large flaw depth from small flaw depth

v Volume of inspected weld

βi Parameter i of the POD model

Δ Weld bead thickness

ε Random error of the model

λ Flaw depth intensity parameter (inch 1) of the exponential distribution 

representing flaw depth distribution, also flaw intensity (flaws/ft3) representing 

Poisson flaw density distribution:

π0(θ) Prior PDF of an unknown parameter θ

π1(θ|Data) Posterior PDF of an unknown parameter θ given observed NDE data

Φ Vector of parameters of the flaw depth PDF

θ An unknown parameter of a model

Θ Vector of parameters of the POD model

ρ Poisson distribution parameter representing the volumetric intensity of flaws 

(flaws per unit volume)

σPOD(a) Standard deviation of PDF of the POD model error vs. flaw depth

γ(.|α1, α2) Gamma PDF with parameters α1 and α2
C-9

C.1 Introduction and Background

In 2010, the NRC amended its regulations to provide alternative screening methods for 

protection against Pressurized Thermal Shock (PTS) events that could affect the Reactor 

Pressure Vessels (RPVs) of the operating Pressurized-Water Reactors (PWRs). The new rule, 

10 CFR 50.61a [C-1], provides a means for determining whether the flaws found through 

In-Service Inspection (ISI) of a particular RPV are consistent with the assumptions regarding the 

number and size of flaws used in the PTS analyses that provided the technical basis for the new 

rule. To address this requirement, 10 CFR 50.61a includes two tables (one table for weld 

material and one table for plate/forging material) that express the maximum flaw density and 

flaw depths that are allowed in the beltline of an RPV.

The new rule relies on flaw characteristics (flaw depth and density) that were simulated and 

used by the probabilistic fracture mechanics computer code FAVOR [C-2] to develop the 

10 CFR 50.61a flaw tables. These flaw characteristics were proposed by Simonen et al. in 

NUREG/CR-6817 [C-3] and are used by the VFLAW code to generate the input flaws for 

FAVOR. The data include distribution functions that represent the initial fabrication flaws in 

some RPVs. The FAVOR computer code fully incorporates these distributions by sampling from 

each using Monte Carlo techniques.

The flaw distributions reported in NUREG/CR-6817 are based on information obtained from 

destructive and very precise techniques used to experimentally detect and size the flaws. 

These tables have been viewed as the permissible limit for distribution of the “true” flaw depths 

and flaw densities. These depth and densities may be contrasted with those “observed” in an 

ISI using Non-Destructive Evaluation (NDE) techniques such as the Ultrasonic Test (UT). The 

NDE results used to assess compliance with the 10 CFR 50.61a tables would be more 

representative of the specific vessel inspected than the flaw distributions in NUREG/CR-6817 

and could be used to support development of vessel-specific flaw-size and -density 

distributions. However, the NDE results are influenced by detection limits, detection errors, and 

sizing and measurement errors. Development of the vessel-specific distribution of the true flaw 

density and depth should account for such uncertainties.

This report describes the development and application of a methodology to account for 

uncertainties in NDE data and to analyze such data for the purpose of developing more realistic 

vessel-specific flaw-depth and -density distributions for comparison to the 10 CFR 50.61a 

screening tables, as well as for use as an input to FAVOR analysis. The methodology 

considers detection probability, flaw-measurement error, and flaw-detection threshold in its 

application. Application of the methodology is demonstrated using the ultrasonic NDE data 

obtained from an ISI of the Beaver Valley 2 RPV.

Flaw distributions developed and reported in NUREG/CR-6817 are based on destructive 

evaluation of two cancelled RPVs supplemented by expert judgment data. In contrast, the 

vessel-specific inspection data come from NDE inspections using, for example, UT methods. 

The variability in both the characteristics of the data (size, range, and number of flaws 

measured) and the UT system performance (probability of detection and measurement/sizing 

errors) highlighted a need for analyzing the inspection results on a vessel-specific or 

data-set-specific basis. For this purpose, traditional methods were inadequate, and therefore a 

new methodology that could accept a very small number of flaws (typical of vessel-specific NDE 

results), including inspection-system flaw-detection reliability, flaw-sizing accuracy 

(measurement error), and flaw-detection threshold, was developed.
C-10

The methodology is demonstrated here through an application using the UT data reported for 

the Beaver Valley 2 RPV [C-13]. The objective was to provide a probabilistic description (in 

terms of the probability density function) of the actual flaw depth and flaw density of the welds 

based on the detected flaws from NDE examinations of this RPV using UT. Because the NDE 

data are uncertain and contain measurement errors, data developed as part of the PTS study 

(the so-called VFLAW data) were specialized to the Beaver Valley 2 RPV and used as the prior 

flaw information. Combination of the prior information and the NDE results of the Beaver 

Valley 2 RPV led to the development of the posterior flaw information, which represents the 

distribution of the true flaw depth and flaw density of the Beaver Valley 2 RPV welds. See 

Figure C-1 for an illustration of the Bayesian updating process. It is important to note that the 

VFLAW data, while representing generic values of flaw characteristics (based on expert 

judgment and on the PVRUF and Shoreham RPVs), may be specialized to a specific RPV, for 

example by using RPV-specific weld length, bead thickness, geometry and other weld 

characteristics of (in this case) Beaver Valley 2. Therefore, the specialized VFLAW data would 

be the most representative information that can be used to describe prior flaw-depth and 

flaw-density distributions and characteristics. If other prior information is available, such 

information may also be used instead of or in addition to the specialized VFLAW data.

Figure C-1 A simple description of the Bayesian updating process. 

In the remainder of this report, the methodology is described first, followed by the application to

the Beaver Valley 2 ISI data. The results are used to compare the Beaver Valley 2 RPV to the 

10 CFR 50.61a screening tables. As such, the VFLAW-based flaw models are updated to more 

realistically represent this RPV.

UT data 

considered as

evidence of flaw

distribution

True flaw 

distributions

(depth & 

density)

Prior data used as 

VFLAW flaw 

distribution 

(depth & density)
C-11

C.2 Probabilistic Approach to Combine Uncertain NDE Flaw Data with Prior

Flaw Distributions

In this section, a Bayesian updating methodology is proposed to combine the observed NDE 

data with the available flaw data and models used as part of the PTS re evaluation effort. First,

the Bayesian framework in general will be discussed, followed by the NDE data uncertainties

(i.e., probability of detection and measurement/sizing error), and finally the developed Bayesian 

updating procedure will be discussed.

C.2.1 The Bayesian Framework

Suppose that background (prior) information is available about a model (e.g., the probability

density functions representing flaw depth and flaw density). If new evidence becomes available,

for example vessel specific NDE data, it is possible to update the prior information (e.g.,

distribution models) in light of the new NDE based evidence. The process of updating prior

distribution models may be formally done through Bayesian inference. Bayesian inference is

conceptually simple and logically consistent. It provides a powerful approach to combine 

observed or measured data with background (prior) information.

In Bayesian inference, the state of knowledge (uncertainty) of a random variable of unknown 

value that is of interest is quantified by assigning a probability distribution or Probability Density

Function (PDF) to its possible values. Bayesian inference provides the mathematical formalism

by which this uncertainty can be updated in light of any new evidence.

In the framework of the Bayesian approach, the parameters of the model of interest (e.g., the

intensity parameter, λ, of an exponential distribution representing flaw depth) are treated as

random variables, the true values of which are unknown. Thus, a PDF can be assigned to

represent the parameter values. In practice, however, some prior information about the 

parameters may be known, including any prior data and subjective judgments regarding the

parameter values that may be available. For example, the intensity parameter, λ, of an

exponential distribution representing the variable flaw depth (e.g., in inch 1) may be known from

related observations and data of similar vessels. If new NDE observations provide limited but

more specific data about a particular RPV, it is possible to update any prior PDF of the flaw

depth intensity parameter by combining the NDE data with the prior PDF. In this case, the prior

knowledge is combined with the specific NDE data to build a posterior PDF that is more

representative of the true intensity parameter and thus the true flaw depth distribution that

accounts for the uncertainties in the observed NDE data.

Let θ be a parameter of interest (for example the flaw intensity parameter). Assume that θ is a 

continuous random variable, such that the prior and posterior PDFs of θ are likewise 

continuous. Also, let L(Data|θ) express how likely is it to observe the data (e.g., the NDE data

measured) in light of given values of parameter θ. Certain values of θ show that the data 

observed are more likely to support the PDF whose parameter is θ. Then, according to

Bayesian inference [C 4], the posterior PDF that represents a properly weighted combination of

the prior PDF and the likelihood of the parameter θ will be: 

Eqn. (C-1) 

( ) ( ) ( )

( ) ( ) ∫

θ

θθθπ

θθπ

=θπ

L Data d

L Data

Data

0

0

1
C-12

The posterior PDF, π1(θ|Data), represents the updated prior PDF of θ, π0(θ), in light of the 

observed data (shown by its likelihood function L(Data|θ)). The denominator of Eqn. (C-1) is 

called the marginal density of the data or the normalization constant. The most difficult part of a 

Bayesian analysis, besides describing the likelihood function, is the computational challenge of 

determining the normalizing constant that often requires multidimensional numerical integration. 

The prior PDF π0(θ) reveals knowledge of parameter θ before data are used. The posterior 

PDF π1(θ|Data) is called posterior because it reflects the PDF of θ after the data are used.

Certain prior PDFs are called “conjugate” [C-4]. This is the class of prior PDFs that yields the 

same functional form for the posterior distribution. For example, if flaw-depth distribution is 

represented by an exponential distribution, a gamma PDF representing the intensity 

parameter, λ, of the exponential distribution is a conjugate distribution. This means that when 

updated by new NDE flaw data, the posterior PDF of λ will also be a gamma distribution. 

Hamada et al. [C-5] present a comprehensive overview of the mathematical steps for updating 

the conjugate distributions used in the Bayesian analyses. In simple problems, the conjugate 

distribution makes posterior PDF calculations simple because it eliminates the complex, 

computationally challenging integrations in Eqn. (C-1). 

For example, consider NDE flaw observations (data). In this case, the likelihood of all such 

data, given a parameter θ of the flaw-depth PDF L(Data| θ), would be expressed as the 

probability of the intersections of the individual flaw measurements; that is, the probability of an 

event consisting of flaw-measurement-1 flaw-measurement-2 

flaw-measurement-3 ... . The likelihood, therefore, would be the product of the probability of 

observing each flaw depth, ai, as shown by Eqn. (C-2). The likelihood function is independent 

of the order of each data point and is given by:

Eqn. (C-2) 

where c is a combinatorial constant that quantifies the number of combinations in which the 

observed NDE data points, ai, could have occurred. The constant c cancels from the numerator 

and denominator of Eqn. (C-1), and therefore is usually not included in the expressions of the 

likelihood function. Table C-1 summarizes the likelihood functions for different types of flaw 

data observations, if the PDF of the variable of interest (flaw depth in this case) is described by 

f(a|θ) with the corresponding Cumulative Density Function (CDF) of . 

Table C-1 Summary of Likelihood Functions 

Type of Observation Likelihood Function Example Description

Exact Flaw Depth f(ai|θ) Exact flaw depth ai is reported

Right Censored Flaw 1-F(aR|θ) Flaw depth exceeds aR

Left Censored Flaw F(aL|θ) Flaw depth is less than aL

Interval Censored F(aR|θ) - F(aL|θ) Flaw depth is between aL and aR

(L Data | =θ ∏ ( ) aLc) i | θ

i

i

∫ θ=θ

a

0

a(F | x(f) | )dx
C-13

Left Truncated f(ai|θ) / [1-F(aC|θ)] Flaw depth is ai where flaw observations 

are not possible below aC

C.2.2 Probability of Detection and Measurement Error

Interpretation of NDE data requires an understanding of the associated uncertainties. For 

example, one inspector may miss a specific flaw found by another. For this reason, the 

reliability of an inspection is customarily expressed in terms of the Probability of Detection 

(POD) of a given flaw size and expressed by curves of POD vs. flaw size. Determining detailed 

POD curves can also be difficult. Flaw detection depends on several factors and it can be 

difficult to produce statistical data to estimate the POD considering variations in material types, 

inspection methods, skill levels, equipment imprecision, and other factors.

Additionally, sizing or measurement errors occur and measurement model uncertainties exist. 

The measurement errors are generally composed of some combination of stochastic (random) 

errors and systematic errors. Random errors are intrinsic to any measurement and are caused 

by instrumentation imprecision and variability, among other sources. Systematic errors are 

biases in NDE measurement resulting in the mean of many separate measurements differing

consistently and appreciably from the true value of the measured flaw. Biases or systematic 

errors are often significant contributors to flaw data uncertainties. For example, in UT 

application to RPVs, there is a general trend toward overestimating the size of small flaws while 

underestimating the size of larger flaws [C-6].

C.2.2.1 Probability of Detection

Formally, the POD can be defined as the probability that the NDE system detects a flaw of 

specific depth a, if it exists, and is denoted by POD(a) [C-6]. POD is generally modeled as a 

function of through-wall extent of the flaw. The POD also depends on other factors such as 

material test equipment, measurement method, and geometry. For example, POD generated 

for a particular material thickness might not be true for the same material with a different 

thickness. The POD should also consider appropriate adjustments for shallow surface flaws 

adjacent to the clad.

Consider a binary random variable D indicating a flaw detected (or indicating a flaw not 

detected). Probability of detection of a flaw of depth ai is:

Eqn. (C-3)

The data from which POD(a) functions are generated can be categorized into two types:

hit/miss and signal-response amplitude. The hit/miss data type shows whether a flaw is

detected or not. This type of data is subjective in nature depending on the operator experience.

In this method, the smallest and largest flaw sizes detected should be identified. Any size below

the smallest size is never detected, whereas a size above the largest size is always detected.

The POD is then calculated as the ratio of the number of successful detections over the total

number of inspections performed for a particular flaw size and is called the averaged POD. 

D

POD i)a( Pr(D | == i)aa
C-14

Eqn. (C-4) 

where a is the flaw depth and N(0;σ(a)) is the random error represented by a normal distribution 

with a constant standard deviation σ or a deviation which may be a function of flaw depth (that 

is, σ(a)). The random error accounts for the POD model error. Model parameters β1 and β2

may be uncertain (epistemic) and would be represented by the bivariate PDF k(Θ), where Θ is 

the vector of the parameters, Θ = {β1, β2}. The PDF function m(σ(a)) may also be used to 

express any epistemic uncertainties by treating σ(a) as a random variable. The parameter ath in 

Eqn. (C-4) represents the threshold (the flaw size below which detection is not possible). 

The other type of POD data represents measurements of the amplitude of signal response 

recorded by the NDE system, such as in a UT system. For signal-response data, much more 

information is supplied in the signal for further analyses than is in the hit/miss data. In the 

signal-response approach, the most important parameters are the inspection threshold (noise 

level) and the decision threshold. All responses less than the inspection threshold are ignored.

In the signal-response approach, it is generally assumed that the logarithm of the 

signal-response amplitude, , is linearly correlated to the logarithm of the flaw depth, a, as 

shown in Eqn. (C-5): 

Eqn. (C-5) 

where ε is the random error and β3 and β4 are the regression parameters. The random error 

can be assumed to have a normal distribution with mean zero and a constant or variable 

standard deviation. Based on this assumption, it can be shown that the POD curve can be 

modeled using a lognormal CDF. The corresponding POD is shown as:

Eqn. (C-6) 

where ath is the decision (detection) threshold signal. The decision threshold is chosen to be a 

bit higher than the inspection threshold in order to minimize the probability of a false call (for 

cases in which the decision threshold is not intentionally chosen to allow a certain probability of 

a false call) in the POD estimates. The â vs. a data can also be converted into hit/miss data by 

using the decision threshold, and an averaged POD can be determined.

C.2.2.2 Measurement (Sizing) Error

Measurement results are always associated with errors of varying magnitudes. Measurement 

error is defined as the difference between the measured and the true flaw depth. Measurement 

error is defined by Eqn. (C-7), where Mε is the measurement error, a* is the measured value of 

flaw depth, and a is the true value of flaw depth:

Mε = a*

 - a Eqn. (C-7) 

The measurement error has two components: systematic error (bias) and random error. 

Random error may be represented by a normal distribution with zero mean and constant 

standard deviation. Systematic error in most cases is a major contribution to flaw 

measurements and cannot be ignored. In its simplest form, the measurement error can be 











 ββ ββ 0 o therwise

logistics a( | )a,, for a> a POD(a | =)a,, 21 th th

21 th

log(ˆ)a 43 log( )a ε+β+β=

POD )a( Pr(aˆ ˆ )a Pr(log(ˆ)a log(aˆ )) th =>= > th

Different forms of POD curves have been used in the literature (see References [C-7], [C-8], and 

[C-9]). The logistic POD model for hit/miss data is a common model and is represented as: 
C-15

represented by a linear function of true size as shown in Eqn. (C-8), where m is the slope and 

c is the intercept of the line representing measurement error, Mε, versus true flaw depth, a. If 

available, PDFs of m and c can be expressed to represent the epistemic uncertainty in these 

parameters. Also, Mε, may be represented as a linear function of measured flaw depth a*

because all data available are in terms of a*

. 

Eqn. (C-8) 

The aleatory random measurement error E'M is shown by the normal distribution NM(0; σ'M) in 

Eqn. (C-8). As such, the total measurement error may be represented as the normal distribution 

g(Mε) = N(m'a*

+c'; σ'M). Figure C-2 shows a conceptual example of the measurement error as a 

function of true flaw size (one can also show Mε vs. a*). According to Eqn. (C-7), the 

relationship between the true flaw depth, a, and measured depth, a*

, is . 

Figure C-2 Measurement error distribution 

If the measurement error’s given flaw depth, a, is Mε, EM describes the PDF of random or

stochastic error. Clearly, Figure C-2 depicts a case in which the standard deviation of the PDF 

of EM is not constant; rather, it is a monotonically increasing line.

C.2.3 The Methodology for Updating the NDE Data

This section discusses the details of the Bayesian updating approach, which combines UT data 

(including their uncertainties) with the prior PDF models of flaw depth and density (used in 

VFLAW to generated FAVOR input) to arrive at posterior distributions of flaw characteristics

*

MMM

* ' '

M

* M *

M

*

MMM

M

and E' ,0(N ' ) of a.vsM

where, a measured depth m, slope c, intercept,

m' ca ' E' 1m

E

1m

c

a

1m

m M

;Ec)Ma(mM or

Eqnonbasedor :)7(.

,0(N ),

M ma Ec

where a, flawtrue depth and E

ε

ε

ε ε

ε

σ=

= = =

++=

+

+

+

+

+ =

++−=

σ=

++=

=

−= Maa ε

*
C-16

C.2.3.1 Updating Flaw Depth Distribution Models

The ultimate objective of this analysis is to describe PDFs of the flaw depth and density 

considering UT measurement of flaws (which contain modeling uncertainty and stochastic 

variability in form of the POD and measurement error). We start with the Bayesian estimation of 

the (large and small) flaw depths, followed by the same estimation for flaw density.

In the Bayesian framework described by Eqn. (C-1), prior information on the flaw depth PDF (for 

example, data and expert elicitation described in NUREG/CR-6817) may be combined with the 

uncertain measurement data from NDE to assess a posterior distribution of the flaw depths. 

Consider the PDF of the flaw depth, a, as f(a | Φ), where Φ is a vector of all the PDF 

parameters.

The data reported in NUREG/CR-6817 show that the small and large flaw depths are 

represented using different distributions. For example, the models proposed and used in 

VFLAW rely on the exponential distribution for large flaw depths but use the multinomial 

distribution to model small flaw depths. The flaw depth that separates the two distributions is 

defined as the transition flaw depth. Therefore, a given PDF may only be true up to a limit from 

which it transitions to another distribution. For the transition flaw depth ttr, the PDF that 

describes the flaw depth should be conditioned on exceeding or falling below the transition limit. 

Therefore:

Eqn. (C-9) 

In VFLAW, for example, ttr for the weld regions was selected as the flaw depth of about the bead 

thickness, Δ, of the corresponding weld. Further, in VFLAW the flaw depth is normalized to the 

dimensionless random variable a/Δ instead of to a. The approach discussed herein applies to 

PDFs of both a and a/Δ, but the respective equations of the approach are only shown in terms 

of the PDF similar to Eqn. (C-9). 

Consider the PDF of NDE measurement error Mε (represented by Eqn. (C-8)) of a measured 

flaw depth a* with stochastic random variable E. The flaw-depth distribution corrected for the 

measurement error, Mε, by assuming that true flaw depth, a, may be represented by correcting 

the measured depth a* using the relationship a = a*

 - Mε [C-10]. As stated earlier in Eqn. (C-8), 

the PDF of Mε will be g(Mε) = N(m'a*

 + c'; σ'M). If there are epistemic uncertainties about 

parameters m' and c', they may be represented by the bivariate PDF x(Ω), where Ω is the vector 

of the parameters m' and c'. The expected distribution of measurement error would be:

Eqn. (C-10) 

While the measurement-error-corrected PDF adjusts the flaw depths to true values, the flaws 

missed, as characterized by the POD, should also be accounted for. That is, for every 

( )

( ) Pr( )ta

a(f | ) af | ta ,

Pr( )ta

a(f | ) af | ta ,

tr

s tr

tr

l tr

<

Φ =<Φ

≥

Φ =≥Φ

= ΩΩ ∫

Ω

g' ε ε d)(x)M(g)M(
C-17

measured flaw a*

, a corresponding probability (including uncertainties) that additional flaw(s) 

may be missed should be accounted for.

If the POD is represented as a mathematical function of the flaw size, a, the vector of 

parameters Θ of the POD function may be associated with a known multivariate PDF k(Θ) in 

order to account for the uncertainties. It is also possible to add a stochastic model error term, 

represented by a normal distribution with the mean zero and the standard deviation σPOD(a). 

For simplicity, it is also possible to assume that the error term is absorbed in the PDF of the 

POD model parameters (i.e., k(Θ)). The marginal POD independent of the random variables Θ 

and σPOD(a) would be:

Eqn. (C-11) 

Marginal POD, independent of flaw depth conditional on Φ (see Eqn. (C-9)) and ttr, is then 

expressed as:

Eqn. (C-12) 

where Pr(D) expresses the probability that a small or large flaw is detected regardless of size, 

which in general is a function of Φ and ttr; that is, POD(Φ, ttr). The probability of not detecting a 

flaw would be Pr(�)=1-Pr(D) ���������������. Let the random variable A represent the true

flaw depth. Then, according to the Bayesian formulation by Celeux et al. [C-11], the probability 

that a detected flaw has a depth in the vicinity of a, inside an interval Δa, may be expressed as:

Eqn. (C-13) 

where D is the event that a flaw is detected. The limit of Eqn. (C-13) as the flaw depth 

interval Δa approaches zero may be found after dividing Eqn. (C-13) by Δa. The left term limit 

represents the likelihood that a detected flaw will have the depth a. Further, by rearranging the 

right side, the PDF of flaw depth independent of detection and POD, given a flaw of depth a, 

may be found:

Eqn. (C-14) 

∫∫

Θσ

= σΘ σΘσΘ

,

POD POD POD

POD

POD )a( POD a( | , a( )) a((m)(k )) dd

∫

∫

∞

=≥Φ= ≥Φ

=<Φ= <Φ

tr

tr

t

l tr l tr

t

0

s tr s tr

Pr )D( POD( , )ta POD a(f)a( | , )ta da

Pr )D( POD( , )ta POD a(f)a( | , )ta da

Pr( )D

1 . Pr(lim D | .)aaAa

a

Pr( aAa a) lim

Pr( a)D

Pr( aaAa Pr(). D | )aaAa a(L | )D lim

a

Pr( aaAa | )D lim

POD )a(

0a

a(f | )t,

0a

0a 0a

tr

         

∆+<<

∆

∆+<<

= ∆

∆+<< ∆+<< == ∆∆+<<

→∆

Φ

→∆

→∆ →∆
C-18

Eqn. (C-15) 

Eqn. (C-15) forms the basis for development of the likelihood function, which would be 

necessary in the Bayesian framework (as discussed in Section C.2.1) to estimate the posterior 

PDF of flaw depth given the observed NDE flaw data and the prior information about the 

characteristics of flaw PDF.

C.2.3.1.1 Likelihood Function of Exact Flaw-Depth Measurements

Suppose that the NDE reports exact flaw depths. Based on Eqn. (C-2), the likelihood function 

of n* flaws of known depth (containing measurement errors) would be 

. It is important to correct for POD and the measurement error and 

parameter uncertainties according to Eqn. (C-10) and to represent flaw depths in terms of the 

measured value using Eqn. (C-7) so that a*

 = Mε + a 2. Therefore, using Eqn. (C-15), the 

likelihood of exact flaw measurements reported may be expressed as [C-10]:

Eqn. (C-16) 

Because NDE data are measured and have associated measurement error and other 

uncertainties, but the POD and measurement error discussed earlier are modeled to be relevant 

to the true flaw depth, a, in Eqn. (C-16) the true flaw depth is replaced with its equivalent (a*

-Mε). 

The expectation of the numerator of Eqn. (C-15), independent of the measurement error, is 

found by multiplying the term by the expected PDF of the measurement error, 

g'(Mε), and integrating this over all values of the measurement error.

C.2.3.1.2 Likelihood Function of Interval Flaw-Depth Measurements

If in addition to or instead of the exact flaw-depth data, interval data are reported (such as the 

number of flaws observed less than a given depth or between an upper and lower limit), the 

likelihood of mi

* flaws reported in the interval i, corrected for the measurement error but 

independent of the error, would be [C-12]:

Eqn. (C-17)

2 Note that if X and Y are two continuous random variables with probability density functions f(x) and g(y), the 

random variable Z = X + Y will have a probability density function h(Z) such that:

POD )t,(

a(f | .)t, POD )a( a(L | )

tr

tr

Φ

Φ =Φ

a ,a ,a , . . . *

3

*

2

*

1

[ ] ∏ ∫ =

ε ε εε

ε

− Φ−

Φ

=Φ

*

*

n

1i M

tr

*

i

*

i n

tr

tr POD(a )M f((a )M | )t, g' Md)M(

POD )t,(

1 (L Allexactmeasureddata | )t,

a(f | .)t, POD )a( Φ tr

*

* i

i

*

1i

m a

a

*

M

* *

tr

tr

*

i POD(a )M f((a )M | ) g' Md)M( da

POD )t,(

1 L(Intervaliconsistingof m me depthsflawasured | )t, 















Φ−−

Φ

=Φ ∫ ∫

− ε

ε ε εε

∫

∞

∞− −= )y(g)yz(f)z(h dy

Using Eqn. (C-14), the corresponding likelihood that a detected flaw is of depth a may be 

expressed as:
C-19

If n such flaw-depth intervals were reported, the corresponding likelihood function using 

Eqn. (C-17) would be:

Eqn. (C-18)

If exact and interval NDE data are both reported, the likelihood function would be a multiple of 

Eqn. (C-16) and Eqn. (C-18). That is:

If in addition to or instead of the exact flaw-depth data, interval data are reported (such as the 

number of flaws observed less than a given depth or between an upper and lower limit), the 

likelihood of mi

* flaws reported in the interval i, corrected for the measurement error but 

independent of the error, would be [C-12]:

If n such flaw-depth intervals were reported, the corresponding likelihood function using 

Eqn. (C-17) would be:

If exact and interval NDE data are both reported, the likelihood function would be a multiple of 

Eqn. (C-16) and Eqn. (C-18). That is:

C.2.3.1.3 Bayesian Updating of Parameters of the Flaw Depth Distribution

Regardless of the form of the data (exact flaw-depth and/or interval data), the Bayesian 

inference of the vector of parameters Φ of the flaw-depth PDF would be obtained (according to 

Eqn. (C-1)) from , where is the posterior 

multivariate PDF of vector Φ, and is the prior multivariate PDF of Φ.

Determination of the posterior requires complex integrations. Further, integration 

of the denominator of the Bayesian inference in Eqn. (C-1) also requires multi-dimensional 

integration that in most cases can only be performed numerically.

It is also critically important to note that Eqn. (C-9) through Eqn. (C-20) are all in terms of the 

actual flaw depth, a, measured in English or metric units. As stated before, it is also possible to 

express the equations in terms of the normalized flaw depth, a/Δ, instead. This is simply done 

by replacing flaw depth, a, with a/Δ in all PDFs, measurement error, and POD equations. 

Clearly the parameters of the equations should be adjusted accordingly.

C.2.3.2 Updating the Flaw Density Model

If flaws are detected with a probability given by Eqn. (C-11) and Eqn. (C-12) as 

Pr(D) = POD(Φ, ttr) (or not detected with a probability of ), the probability that a 

∏ ∫ ∫ =

ε ε εε 















− Φ−

Φ

=Φ

− ε

n

1i

m a

a

*

M

* *

tr

tr

*

* i

i

*

1i

POD(a )M f((a )M | )g' Md)M( da

POD )t,(

1 L(ninterval sof m easureddepths | )t,

L(nInterval MeasuredFlaw Depths | )t , x L(n * Exact MeasuredFlaw Depths | )t ,

L(Mix MeasuredFlaw Depths | =)t ,

tr tr

tr

Φ Φ

Φ

L(nInterval MeasuredFlaw Depths | )t , x L(n * Exact MeasuredFlaw Depths | )t ,

L(Mix MeasuredFlaw Depths | =)t ,

tr tr

tr

Φ Φ

Φ

( | Data (L)t, Data | , )()t 1 Φπ tr ∝ tr 0 ΦπΦ ( | Data) 1 Φπ

)( 0 Φπ

( | Data) 1 Φπ

Pr( 1)D −= Pr( )D
C-20

specific total number of flaws n* observed in a given volume v out of the true number of flaws nj

follows the binomial distribution (see References [C-11] and [C-12]):

Eqn. (C-19) 

where . The best estimate of the true number of flaws would be to assume that 

n*

 represents the mean of Eqn. (C-19). Accordingly, the mean estimate of the true number of 

flaws, N, would be found from:

Eqn. (C-20) 

A more formal way to estimate the number (and thus density) of flaws would be to use the 

Bayesian updating of nj, which allows the estimation of the posterior distribution of nj to describe 

the true number of flaws:

Eqn. (C-21) 

Using Eqn. (C-19) (representing the likelihood of observing n* flaws out of the unknown nj flaws) 

and a Poisson prior flaw density model, the posterior probability distribution of the number of 

flaws would be obtained from:

Eqn. (C-22) 

where ρ is the volumetric flaw intensity and ρv is the expected number of true flaws in the 

inspected volume v. If the mean number of flaws from Eqn. (C-20) is large, the computer 

rounding issues associated with Eqn. (C-22) may be avoided by performing the analysis for a 

smaller volume (for example, 1/100th of the inspected volume) and later prorating nj accordingly.

An alternative approach that is approximate, but simpler than Eqn. (C-19) through Eqn. (C-22), 

would be to update the parameter ρ itself based on the mean number of flaws. For example, if 

the volume of the UT inspection is v, the volumetric flaw intensity ρ of the flaws associated with 

the mean estimated N true flaws from Eqn. (C-20) in this volume would be Assuming 

that the mean occurrence intensity of flaws remains constant over the volume of inspection, the 

[ ] [ ]

[ ] [ ] * j *

* j *

nn

tr

n n

tr *

j

j

*

nn n n

*

j

j

*

POD -1)t,( POD( , )t

n

n

L(n | =)n

or

Pr( -1)D Pr(D)

n

n

L(n | =)n

−

−

Φ Φ 































nn(!n )!

!n

n

n

*

j

*

j

*

j

− =















POD( , )t

n N

tr

*

Φ =

∑

=

nj

jj

*

jj

*

*

j n(L | )n Pr( )n

n(L | )n Pr( )n Pr(n | )n

[ ] [ ]

∑ [ ] [ ] ∞

=

ρ− −

ρ− −

ρ Φ Φ 















ρ Φ Φ 















=

* j

j * j *

j * j *

nn j

v n

nn

tr

n n

tr *

j

j

v n

nn

tr

n n

tr *

j

*

j

] !n

)v(e POD -1)t,( POD( , [)t

n

n

] !n

)v(e POD -1)t,( POD( , [)t

n

n

Pr(n | )n

.

v

N

=ρ
C-21

Poisson distribution may be used to represent the likelihood of N flaws in volume v, given the 

volumetric flaw intensity ρ as shown by Eqn. (C-23): 

Eqn. (C-23) 

where v is the inspection volume and ρ is the flaw intensity (flaws per unit volume) associated 

with the mean estimated number of flaws N.

If prior information about the flaw intensity, ρ, were available, it would be desirable to update the 

flaw intensity by using such prior information. For example, assume that the prior volumetric 

flaw intensity is described by the PDF, π0(ρ). Then, the posterior PDF, π1(ρ|N), can be 

estimated using the likelihood function in Eqn. (C-23) from:

Eqn. (C-24) 

If the prior PDF of the flaw intensity is expressed by the gamma distribution with parameters

, as , the posterior PDF is a conjugate 

distribution described by . The alternative form of the gamma 

distribution used by the MATLAB tool (to be used later in the following example) uses 

parameter β instead of parameter , so that . 

C.3 Application Example

As part of a cooperative effort between the Electric Power Research Institute (EPRI) and the 

NRC to provide guidance on evaluation of PTS, NDE analyses were performed for a PWR RPV

(Beaver Valley 2). In this section, the Beaver Valley 2 NDE data will be described first. Next,

the VFLAW data described in NUREG/CR-6817 will be used as prior information, followed by

the application of the Bayesian updating procedure discussed in Section C.2 to determine 

flaw-depth and flaw-density distributions specific to Beaver Valley 2. The resulting posterior

distribution of the parameters of the flaw depth and flaw density, as described in Section C.2,

will be derived and discussed. The results of flaw-depth and flaw-density PDFs will be used to

compare against the 10 CFR 50.61a flaw tables, and to update the distribution models in 

VFLAW into new flaw distributions that are representative of the Beaver Valley 2 RPV.

C.3.1 Description of the NDE Data Used as Evidence to Build the Likelihood Function

The EPRI report by Spanner [C-13] provides UT-based measured flaw data near the inner

surface (~2.5 inches) of the Beaver Valley 2 RPV, including small flaw sizes. These data, while 

subject to POD and measurement error, provide a more vessel-specific perspective of the

distribution of flaws for Beaver Valley 2 than does the VFLAW distributions used in FAVOR. 

N!

)v( L(N| e=)

N

)v(- ρ ρ ρ

where N(L | N(L) | )

( | L(NN) | )()

j

j

1 0

∏ ρ=ρ

ρπρ∝ρπ

ρα−

−αα

αΓ

ρα =ργ =ααρ 1

22

e

)( )( gamma( | ),

2

1

1

0 21

1 )( =ργ gamma( | α+α+ρ 2j1 )n,v

α1 ), 1

gamma( | 2

1

α

α

=βρ
C-22

1. 19 weld flaws were detected by the UT NDE of Beaver Valley 2 in the first inch (the

inspection volume specified in Supplement 4 to Mandatory Appendix VIII to Section XI of

the ASME Code) of the RPV (~0.616 ft3

), all having a flaw depth less than 0.125".

2. 103 weld flaws were detected and reported by the UT NDE of Beaver Valley 2 in the

first 3/8t (2.953") (the inspection volume specified in Supplement 6 to Mandatory

Appendix VIII to Section XI of the ASME Code) of the RPV were reported, all with flaw

depths less than 0.125", except for one flaw that measured 0.260".

The lower limit of the detected flaw intervals described above is not stated in [C-13], but is 

certainly not zero. Two possible subjective lower limits were assumed, and later the 

sensitivities of the final (posterior) flaw-distribution results to these two choices were assessed. 

The two lower limits are 0.04" and 0.075". 

The NDE data described above provide an incomplete depiction of the true flaws in the Beaver 

Valley 2 RPV because they contain uncertainties associated with the UT technology used to 

detect and size flaws. The associated weld bead thicknesses are not reported. However, the 

weld region of the observed flaws and flaw length is reported. Such results should be corrected 

for detection and sizing capability, particularly for the small flaws. 

The Beaver Valley 2 RPV weld map is shown in Figure C-3 [C-14]. In the absence of the 

Beaver Valley 2 average weld bead thickness as the point of transition between large and small 

depths, it is assumed that all flaws reported are Submerged Arc Welds (SAWs), which form over 

90% of welds in the VFLAW data, with the bead thickness of ∆ = ttr = 0.26". Using the Beaver 

Valley 2 RPV information shown in Figure C-3, the following weld characteristics were 

computed and used to specialize the VFLAW data to represent the prior distributions of flaw 

depth and density for Beaver Valley 2 RPV: 

Total Weld Length = 816.18" 

Total Weld Volume3 = 4.975 ft3

Total Weld Fusion Area = 92 ft2

Weld Volume of 1" = 0.616 ft3

Weld Volume of 3/8t = 1.865 ft3

3 The total volume of reactor vessel weld area according to the weld dimensions shown in Figure C-3 = [1.375 × 

99.45 × 2 × (86.531 - 78.656)] + [2 × 1.375 × 61.68 × (86.531 - 78.656)] + [1.25 × 3.14 × 2 × 86.531 × 

(86.5312 - 78.6562)] = 8,595.29 in3 = 4.974 ft3. 

The observed Beaver Valley 2 NDE data (with detection and sizing uncertainty) are mostly in 

the form of interval-censored data as summarized below [C-13]: 
C-23

Figure C-3 Beaver Valley 2 weld map [C 14] 

C.3.2 Description of Flaw-Depth and –Density Information Used in VFLAW as Prior PDFs

in this Example

Smaller flaws neighboring the inner surface of the RPV that would be subjected to high thermal 

stresses during PTS events are dominant contributors to the risk of vessel failure posed by PTS.

During the PTS re-evaluation effort in the late 1990s and early 2000s, the Marshall distribution 

was updated using the results of destructive tests of the Pressure Vessel Research User Facility

(PVRUF) and Shoreham RPVs [C-2]. These analyses assumed that the flaws were near the 

inner surface of the RPV and included very small flaws of less than 0.125 inches (3 mm) in

through-wall extent. The purpose of the re-evaluation was to provide an up-to-date estimate of

the distribution of weld flaw density and sizes using modern NDE methods of analysis. These

distributions represent the flaw-depth and flaw-density models in VFLAW [C-3].

Because we need prior distributions in the Bayesian inference described earlier, the VFLAW

distributions many be specialized to Beaver Valley 2. This is done by using the corresponding

bead thickness and other vessel characteristics for Beaver Valley 2 to determine the prior

distributions of the flaw depth and flaw density from VFLAW distributions. The prior distributions

fill the gaps in the limited inspected data and uncertainties associated with the NDE results.

Analysis of flaws should consider different vessel regions and welding types. Welding types

include the Submerged Arc Weld (SAW), Shielded Metal Arc Weld (SMAW), and repair weld.

Depending on the known details of fabrication, NUREG/CR-6817 estimated flaw distributions for

each weld type used in a particular region of the vessel. Measured flaw data showed 

vessel-to-vessel variability in both flaw density and depth. To supplement the limited data from

the PVRUF and Shoreham flaw measurements, NUREG/CR-6817 used expert elicitation.
C-24

Distribution functions to characterize the number and sizes of flaws in the various regions of the 

RPVs were then developed based on the measured data and insights from an expert elicitation 

exercise and used in VFLAW.

The prior distributions used in this example updated the PVRUF flaw models described in 

NUREG/CR-6817 and used in VFLAW, including the hyper-distributions that address the 

uncertainties associated with the parameters for the distribution functions describing flaw depth 

and flaw density. For example, the exponential distribution was used to represent the variability 

of large flaw depths. However, the parameter λ of the exponential distribution (i.e., assuming 

f(a) = λe-λa, where a is the flaw depth) was in turn considered to be a random variable and 

described by the gamma distribution. The gamma distribution itself has two parameters, 

α1 and α2, that are given as constants in NUREG/CR-6817. These parameters were updated in 

this example based on the observed data from Beaver Valley 2. The values of the 

hyper-distributions used in VFLAW are shown in Table C-2. Note that the flaw-depth data in 

Table C-2 are in meters, whereas this example calculation is based on inches. The relationship 

between the flaw-depth and flaw-density PDFs and the corresponding hyper-PDFs of their 

parameters are illustrated in Figure C-4. 

Figure C-4 Flaw depth and flaw density distributions used in VFLAW and their 

corresponding parameter hyper PDFs 
C-25

Table C-2 Flaw-Depth (a) and Flaw-Density (b) Distributions and Hyper-PDF Parameters Used in VFLAW 

(a) Flaw-depth characteristics (in meters) based on data from PVRUF RPV

Case Flaw Size

Category

Welding 

Process

Random Variable 

Representing Flaw 

Depth

PDF of Flaw 

Depth

Parameters 

of PDF

Distribution Describing 

Uncertainty of 

Parameters of PDF

1 Small

(a ≤ Δ)

SAW a/Δ Multinomial P1, P2, P3 Dirichlet 

2 Small

(a ≤ Δ)

SMAW a/Δ Multinomial P1, P2, P3 Dirichlet 

3 Small

(a ≤ Δ)

Repair 

Weld

a/Δ Multinomial P1, P2, P3 Dirichlet 

4 Large

(a > Δ)

SAW a/Δ Exponential λ Gamma 

5 Large

(a > Δ)

SMAW a/Δ Exponential λ Gamma 

6 Large

(a > Δ)

Repair 

Weld

a/Δ Exponential λ Gamma 
C-26

(b) Flaw-density characteristics based on data from PVRUF RPV

Case Flaw Size 

Category

Welding 

Process

Random Variable 

Representing Flaw 

Depth

PDF of 

Flaw 

Depth

Parameters 

of PDF

Distribution Describing 

Uncertainty of 

Parameters of PDF

1 Small

(a ≤ Δ)

SAW Flaws per cubic meter Poisson λ Gamma 

2 Small

(a ≤ Δ)

SMAW Flaws per cubic meter Poisson λ Gamma 

3 Small

(a ≤ Δ)

Repair 

Weld

Flaws per cubic meter Poisson λ Gamma 

4 Large

(a > Δ)

SAW Flaws per cubic meter Poisson λ Gamma 

5 Large

(a > Δ)

SMAW Flaws per cubic meter Poisson λ Gamma 

6 Large

(a > Δ)

Repair 

Weld

Flaws per cubic meter Poisson λ Gamma 
C-27

C.3.3 Detection and Sizing Error Models

Analysis of UT-detected performance data reported by EPRI [C-6] was used to identify a POD 

function for the purpose of this example. Currently, EPRI is updating these performance data 

and will supply more appropriate POD models for future consideration; the POD and flaw-sizing 

error functions used here are therefore intended only to illustrate this numerical method. The 

threshold limit of this POD function (Eqn. (C-4)) was taken as 0.00 and the epistemic 

uncertainties associated with the parameters of the model were not considered in this example. 

Accordingly, the following mean POD function based on Eqn. (C-4) was used4

: 

Eqn. (C-25) 

where a is the true, unbiased flaw size. Figure C-5 shows a plot of this POD function.

the normal PDF: . 

4 The model error associated with the logistic distribution was not considered.

63.2100 .0a( 1124) e1

1 POD 1)a( − + −=

Figure C-5 POD vs. flaw depth 

The measurement error was assumed, based on some examples and measurement errors

reported in EPRI report [C-6]. The measurement error is a linear function that oversizes small 

flaws and undersizes large flaws. Figure C-6 depicts a plot of the measurement-error model

used in this example. The model itself can be described as a line with a slope of -0.1905 and

an intercept of 0.0476, with the variability resulting from the model error described by a normal

distribution. That is, Mε = −0.1905a

*

+ 0.0476 + N(0,0.0298) , where N(0, 0.0298) is a normal

distribution with a mean of zero and a constant standard deviation of 0.0298. Note that in this

example we are not accounting for the epistemic uncertainties of the measurement-error model.

However, such uncertainties should be considered when new measurement-error models are 

developed. Equally, as described by Eqn. (C-10), it is possible to represent the above line by

* 2 564.55 .0M( 1905 .0a 0476) g' 13.41e)M( − + −

ε ε =
C-28

Figure C-6 Measurement error vs. flaw depth 

C.3.4 Bayesian Updating of the Parameters of the Flaw-Depth Distributions

In this section, the process of updating the prior data specialized to Beaver Valley 2 with the 

observed NDE data using Bayesian inference will be discussed. Figure C-7 describes the main

elements of the updating process. The observed UT-based flaw data discussed in 

Section C.3.1 is corrected for POD and measurement error. The POD and measurement error

models were discussed in Section C.3.3. In the remainder of this section, development of the

likelihood functions for the two sets of observed flaw data (one for the first one inch and another

for the 3/8t of the inner RPV welds) will be discussed first. Then the Bayesian inference that

combines the observed data with the prior data will be considered. The analysis will be

performed for each of the NDE observed data sets to determine different conclusions.

1. The observed data for the first 3/8t of the RPV welds were used to update the prior

models shown in Table C-2 in order to specialize them for the Beaver Valley 2 RPV.

The updated values can be used for PTS calculations specific to the Beaver Valley 2

RPV using VFLAW and FAVOR.

2. The observed data for the first inch of the vessel were used to estimate the true number

of flaws in the flaw-depth ranges of the 10 CFR 50.61a tables. This information is used

to assess how the estimated number of flaws of a given size in Beaver Valley 2

(estimated based on inspection data, VFLAW distributions, and Bayesian inference)

compares to the number and size of flaws permitted by the 10 CFR 50.61a tables.
C-29

Figure C-7 Bayesian Updating Elements of the Beaver Valley 2 Example 

C.3.4.1 Bayesian Updating of the Parameters of Large-Flaw Depth Distribution 

Based on the 3/8t UT Inspection Data 

According to the prior data used by VFLAW as described in Section C.3.3, small-to-large 

flaw-size transition occurs at flaw depths exceeding the SAW weld bead thickness. According 

to Table C-2, large flaws will follow an exponential distribution, conditional on exceeding the 

transition flaw depth. Thus, the distribution of large-flaw depths corrected for the bias would be:

Eqn. (C-26) 

where λl is the large-flaw depth intensity (per inch) and atr is the transition flaw depth (assumed 

to be 0.26"). To build the likelihood function, the flaws should be represented in terms of the 

measured flaw depths. Because the NDE data reported only one exact flaw depth (n*

 = 1, 

a1

*

 = 0.26) in the large-flaw region (exceeding the transition ttr) for Beaver Valley 2, the likelihood 

function based on Eqn. (C-16) would be:

Eqn. (C-27)

where would be near 1 in this case because the POD(a) reaches unity 

when the flaw depth exceeds 0.2 inch in Eqn. (C-25). Note that, for simplicity, the random 

variable Mε is integrated over the range of -1 to 1 because these are the extreme ranges of the 

( ) )tMa(

1

)ta(

l

tr

l

l tr tr * l tr l e e

Pr( )ta

a(f | ) af | ta , −λ− ε −−λ− λ= λ=

>

λ =>λ

( ) [ ]( ) Π∫ ε

λ

−−

ε ε

ε

 λ



 





+

− λλ

1

1-

-M-a- 260. 5- 64.55 +M( 19050. -a 04760. )

l 63.2100 .0Ma( 1124)

1

1=i

1

l

l

*

data e 13.41e Md

e1

1 1

OD[P ( )]

1 L(a | =) * 2 i

*

il

*

i

∫ λ λ λ

∞

.0 26

- (a- .0 26) POD( l =) POD(a) l e da l
C-30

measurement error. The next step is finding the posterior distribution of λl based on Eqn. (C-1). 

That is:

Eqn. (C-28) 

Using Eqn. (C-27) as the likelihood, the Bayesian updating with the gamma PDF as the prior 

hyper-PDF for λl, (or the alternative form

), from the VFLAW (SAW) information specialized to 

Beaver Valley 2 by using the bead thickness of 0.26" and converted to per unit inch (using the 

SAW data listed in Table 6.6 of NUREG/CR-68175

), the posterior distribution of λl is calculated 

and fitted into another gamma distribution. The posterior gamma PDF representing the Beaver 

Valley 2 RPV would be and plotted and compared to the 

prior PDF in Figure C-8 (see Appendix C-1). The gamma distributions used to describe 

flaw-depth intensity and flaw density in Table C-2 are normalized based on the bead thickness. 

As evident from Table C-2, VFLAW uses normalized flaw-depth distributions (i.e., based on a/Δ 

instead of a). Assuming a bead thickness of 0.26", the normalized gamma prior and posterior 

PDFs for large-flaw-depth intensity for Beaver Valley 2 would be 

and . Note that 

Figure C-8 is not the normalized version. The normalized posterior would be the new 

hyper-distribution that reflects the measured data and can be used in the VFLAW and FAVOR 

runs for Beaver Valley 2 RPV.

From Figure C-8, it is evident that the prior and posterior values are very similar, because only 

one flaw depth data point is reported and used, so the posterior relies primarily on the prior 

information. The impact will, however, affect the density PDF more strongly.

5 Note that to specialize VFLAW flaw-depth distributions for Beaver Valley 2, only PVRUF large-flaw depths reported 

for SAW in Table 6.6 of the NUREG/CR-6817 were used instead of the distributions summarized in Table 1-2 of this 

report.

∫

λ

λλπλ

λπλ λπ

l

ll0l

*

data

l0l

*

* data

l1 data L(a | d)()

L(a | )() ( | =)a

λπ l0 gamma(=)( | 1l α=αλ 2 )4=,2.1

(=)( | = 83330. )4=, λπ l0 gamma l βλ α2

(=)( | .1= 186 )5=, λπ l1 gamma αλ 1l α2

(=)( | .4 615 )4=, λπ l0 gamma 1l α=αλ 2 (=)( | .4= 563 )5=, λπ l1 gamma αλ 1l α2
C-31

Figure C-8 Prior and posterior distributions of the flaw-depth intensity of parameter λl

C.3.4.2 Bayesian Updating of the Parameters of Small Flaw Depth Distribution

Based on the 3/8t UT Inspection Data

Flaw depths smaller than the bead thickness for PVRUF (from Table 6.4 in NUREG/CR-6817) 

were analyzed and appeared to best fit an exponential PDF. That is:

Eqn. (C-29) 

where λs is the flaw depth (per inch) for small flaws. The hyper-distribution of λs was also 

estimated as the gamma distribution that was used as the 

prior PDF for Beaver Valley 2.

The procedure from this point on is the same as that for the large flaws with the exception that 

the NDE data for small flaws were given in the form of a single flaw depth interval, as discussed 

in Section C.3.1. Accordingly, with m = 1 and using Eqn. (C-17), the likelihood function for the 

evidence consisting of 103 detected (observed) flaws, all with a depth of less than 0.125" but 

larger than 0.04" (or 0.075" as sensitivity value), will be:

Eqn. (C-30)

The Bayesian updating for small flaws is the same as Eqn. (C-28) and the likelihood given by 

Eqn. (C-30) results in the posterior distributions of λs as shown in Figure C-9 (see 

Appendix C-1). Also, a plot of the POD(λs) as expressed by equation:

Eqn. (C-31) 

, > 0, a 0>

e1

e f(a | =) .0- 26 s

as

s s

s

λ −

λ λ λ

λ

π (=)( | .2 854, 39) λs0 gamma 1s 2 =α=αλ

( ) 10 .0 125

.0 or075 .0 04

*

1

1

5- 64.55 +M( 19050. -a 04760. )

.0- 26

)Ma(-

s

63.2100 .0Ma( 1124) s

s 13.41e Md da

e1

e

e1

1 1

POD )(

1 L(Data | ) * 2

s

* s

*

































−

λ 



 





+

− λ=λ ∫ ∫−

λ ε

−λ

−−

ε

ε

ε

( ) ∫ λ−

λ−

− −

λ 



 





+

−=λ

26.0

s

s

.0 26 a

a

s s 63.2100 .0a( 1124) e1

e

e1

1 1

0

DP )(O da
C-32

is shown in Figure C-10. Clearly, because small flaws are associated with small POD and 

considerable measurement error, the impact of these would be significant in the posterior 

results shown in Figure C-9. The posterior can be expressed as the gamma PDF 

. The normalized versions of the prior and posterior 

can be expressed by dividing α1 by the bead thickness of 0.26". Note that Figure C-9 does not 

show the normalized versions of the prior and posterior distributions.

The VFLAW data for small flaw depths uses the multinomial distribution, whose parameters are 

described by the Dirichlet PDF. Accordingly, it is possible to find the equivalent Dirichlet PDFs 

that best describe the posterior PDF of λs expressed in form of the gamma distribution.

Figure C-9 Bayesian prior and posterior PDFs of λs (per unit inch)

Figure C-10 Marginal POD independent of small flaw depth 

To update the Dirichlet hyper-distribution that represents uncertainties in the parameters of the

multinomial distribution representing small-flaw-depth PDF used in VFLAW, the posterior PDF

of λs shown in Figure C-9 is used to calculate the number of flaws in each of the ranges

(0" to 0.072", 0.072" to 0.126", and 0.126" to 0.170") used by the multinomial distribution in 

VFLAW. Because the Dirichlet distribution is a conjugate distribution, the posterior number of

flaws is found (see Section C.3.4.3.2 for estimating the number of posterior flaws) by adding the 

posterior mean number of flaws in each flaw-depth bin (see Table C-3). When added to the 

prior number of flaws (see Appendix A of NUREG/CR-6817 for the procedure), the updated 

Dirichlet values are viewed as being more representative of the distributions of true flaws in the 

Beaver Valley 2 RPV and are summarized in Table C-3. 

π (=)( | .1 614, 60) λs1 gamma 1s 2 =α=αλ

0

0.04

0.08

0.12

0.16

0.2

0 10 20 30 40 50 60

Posterior

Prior

PDF

Flaw size intensity (per unit inch)
C-33

Table C-3 Updated VFLAW Distribution for Small Flaws 

A critical observation from this example is that the posterior results of the flaw-depth distribution

in general and small depth distribution in particular are most sensitive to the POD model and 

measurement error model and their associated uncertainties. The lower tail of the POD model, 

in the ranges of small flaw depths (<0.1-in.), expects small probabilities of detection. When a 

flaw of small depth is reported, because of the corresponding small POD, it increases the 

likelihood that there are several flaws not detected for the one detected. This will substantially 

affect the results.

Appendix C-1 describes the MATLAB routine used to solve the integrals in Eqn. (C-29) through 

Eqn. (C-31) to estimate the posterior PDF of small flaws.

C.3.4.3 Results of Updating Parameters of Flaw Density Distribution Based on the 

3/8t UT Inspection Data 

In Section C.2.3.2, two methods were presented to update the flaw densities. One was based 

on a binomial likelihood function (Eqn. (C-19)) and one used the Poisson density and took

advantage of the conjugate properties of the prior gamma PDF used as the prior distribution of

the intensity, ρ, of the Poisson distribution (Eqn. (C-23)). The later method is used to update the

flaw densities for this example. This method is based on the mean values only and is simpler

than the former.

C.3.4.3.1 Posterior Density of Large Flaws

The number of large flaws (size > 0.26 inch), given the single UT-detected flaw, yields the 

posterior flaw depth intensity, λl, which was shown in Figure C-8. The marginal POD 

independent of the flaw size was almost 1 (for any value of posterior λl). Accordingly, using 

Eqn. (C-20), the number of flaws based on the posterior estimates of flaw depth would be 1.

Using the conjugate features of the prior gamma distribution for ρl, the posterior distribution (see 

Appendix A of NUREG/CR-6817) will be:

Eqn. (C-32) 3

1l 2

ll1 1l 2 l

( | .8 5119 )5, ftflaws/ 

( | ()n | .6 6467 )n4,V

=α=αρ

=+=α+=αρ=ρπ

gamma

gamma

Flaw-Depth 

Bins (in)

Normalized 

Flaw-Depth 

Bins (per 

NUREG/

CR-6817) per 

Unit of Bead 

Thickness

Prior U 

(see Table 

C-2)

Prior 

Multinomial 

Parameter Posterior U

Updated 

Mean of

Multinomial 

Parameter

a1 (0 to 0.072) 0.25 (0.0 to 0.4) U1 = 34 P1 = 0.7907 U'1 = 479.75 P'1 = 0.9639

a2 (0.072 to 0.126) 0.55 (0.4 to 0.7) U2 = 8 P2 = 0.1860 U'2 = 9.71 P'2 = 0.0332

a3 (0.126 to 0.17) 0.85 (0.7 to 0.1) U3 = 1 P3 = 0.0233 U'3 = 5.354 P’3 = 0.0029
C-34

Figure C-11 compares prior and posterior distributions of the number of flaws and flaw intensity 

of large flaws for Beaver Valley 2 in a volume of 1.8652 ft3

. Note that VFLAW values are in 

cubic meter. The equivalent prior and posterior distributions in cubic meter are summarized in 

Table C-4. 

(a)

(b) 

Figure C-11 Prior and posterior flaw density (a) and intensity (b) for large size flaw

C.3.4.3.2 Posterior Density of Small Flaws

Similar to the large flaw density, the prior gamma distribution representing the flaw density per

unit volume, ρs, used in the VFLAW was updated based on the 103 UT-detected small flaws in 

the interval of 0.04" to 0.125". This would yield the posterior flaw depth intensity, λs, as was

shown in Figure C-9. The mean value of the flaw depth intensity (i.e., λs = 37.16) estimated by

the posterior shown in Figure C-9 yields a marginal probability of detection independent of flaw

depth of, POD(λs) = 0.0274. 

0 0.5 1 1.5 2 2.5 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Flaw density (per unit cubic feet)

PDF
C-35

Eqn. (C-33) 

Figure C-12 compares prior and posterior distributions of the number of flaws and volumetric 

flaw intensity of small flaws.

(a)

(b) 

Figure C-12 Prior and posterior flaw density (a) and intensity (b) for small size flaws 

Because the posterior flaw density distributions shown in Figure C-11 and Figure C-12 are 

based on the mean values of λ for both large and small flaws, a Monte Carlo simulation was

used to select random realizations of λ from the posterior PDFs of λ for large and small flaws to 

develop the corresponding posterior flaw density PDFs. Figure C-13 shows the results of the 

spread of the number of the flaws of various depths for the Beaver Valley 2 RPV, including the

epistemic uncertainties shown in the form of box plots.

Similar to the flaw-depth distribution, the posterior distribution of flaw density will be dominated 

by the POD and measurement error models and their uncertainties. Specifically, when a large 

number of small flaws are reported during the NDE inspection, the corresponding low POD

value increases the number of expected undetected flaws.

(Table 2.6 SAW PVRUF NUREG/CR - 6817)

()( | .6 6467, 1419 flaws) / ft

( | .8 5119, 1909)

( | ()n | .6 6467 ,V 1419 )n

3

s0 s,1s s,2

pos

s,2

pos

s s,1

s

pos

s,2

pos

ss1 s s,1

−

=α=αρ=ρπ

=α=αρ=

+=α+=αρ=ρπ

gamma

gamma

gamma

The likelihood of observing ns small flaws would be expressed as: 
C-36

Based on the results of this section, Table C-4 summarizes the posterior results to be used for 

Beaver Valley 2 VFLAW and FAVOR runs. The posterior results have been changed to metric 

units in this table, because VFLAW uses metric values.
C-37

Table C-4 Summary of the Posterior Parameter PDFs of Flaw Depth and Flaw Density to be used in VFL

Runs for Beaver Valley 2 

Case Flaw Size 

Category

Welding 

Process

Random Variable 

Representing Flaw 

Depth

PDF of Flaw 

Depth

Parameter

s of PDF

Distribution 

Describing 

Uncertainty 

of 

Parameters 

of PDF

Original

VFLAW

Parameters 

Uncertainty 

Distributio

(Flaw Dept

parameters a

specialized 

Beaver Valle

1 Small

(a ≤ Δ)

SAW Flaws per cubic 

meter

Poisson ρ Gamma α3 = 0.180

α4 = 1419

2 Large

(a > Δ)

SAW Flaws per cubic 

meter

Poisson ρ Gamma α3 = 0.180

α4 = 4

3 Small

(a ≤ Δ)

SAW a/Δ Multinomial P1, P2, P3 Dirichlet U1 = 34

U2 = 8 

U3 = 1 

4 Large

(a > Δ)

SAW a/Δ Exponential λ Gamma α1 = 4.6156

α2 = 4

6 VFLAW combined all SAW and SMAW flaw data to arrive at the gamma distribution with α1 = 21.68 α2 = 52. As 

Section C.3.4.1, this example used only PVRUF SAW data for large flaw depths to build the specialized Beaver 
C-38

Figure C-13 Posterior number of flaws in the 3/8t region in various flaw size intervals 

including epistemic uncertainties

C.3.4.3.3 Sensitivity of the Flaw Density Results to a Lower Bound of 0.075” for the Interval 

Data Observed in the 3/8t Region

Estimations of the posterior PDFs presented in Sections C.3.4.3.1 and C.3.4.3.2 have been 

made by assuming that the observed interval of small flaws was 0.075" to 0.125". To assess 

the sensitivity of this assumption, it is assumed that the detection up to 0.075" is possible and all 

data would be between 0.075" and 0.125". Repeating the calculations in Section C.3.4 

(including subsections) yields the posterior flaw depth and density PDFs that are very similar. 

Therefore, it was concluded that the results are relatively insensitive to choice for the lower 

bound of the data. More discussions of this topic are presented in Section C.3.5.

C.3.5 Updating the 10 CFR 50.61a Tables

The NDE data from the inspection volume specified in Supplement 4 to Mandatory 

Appendix VIII to Section XI of the ASME Code (the first one-inch of the weld) is used as the 

evidence for the Bayesian updating procedure described in the previous sections to obtain the 

flaw depth and density characteristics for Beaver Valley 2. The posterior characteristics are 

used to develop the corresponding 10 CFR50.61a flaw tables (consisting of only 19 

UT-detected flaws in the interval 0.04" to 0.125"). The procedure is the same as the one used 

to update the UT data observed in the 3/8t region as discussed in Section C.3.4.

If the posterior distributions of the flaw density are used to estimate the mean number of flaws in 

the ranges of flaw sizes described in the 10 CFR 50.61a flaw tables, the results should be 

prorated to the number of flaws per 1,000" of weld. Because Beaver Valley 2 has a total weld 

length of 816.18", the prorated mean number of flaws was calculated and compared with the 

allowable number of flaws per length of weld, as shown in Table C-5. If the lower limit of the 

observed data interval is changed from 0.04" to 0.075" to line up with the smallest bin size in the 

10 CFR 50.61a flaw tables, the results summarized in Table C-5 are calculated. In this case, 

the results of the mean number of flaws were also not too sensitive to the choice of the lower 

limit of the interval of NDE data.

0 - 0.075 0.075 - 0.125 0.125 - 0.175 0.175 - 0.225 0.225 - 0.26 10-1

100

101

102

Actual number of flaws

Flaw size intervals (inch)

Max

75%

25%

Min

Median
C-39

To assess the epistemic uncertainties in the POD and measurement error uncertainties, again

for the case of the Supplement 4 inspection volume (the first one inch), a Monte Carlo 

simulation was used to select random realizations of λ from the posterior PDFs of λ for both

large and small flaws to develop the corresponding posterior flaw density PDFs. Repeating this

process will result in the epistemic uncertainty for each flaw depth interval used in Table C-4. 

Figure C-14 shows the results of the number of the flaws of various depth intervals, by

employing box and whisker plots. Epistemic uncertainties are larger (than those shown in 

Figure C-13), because of the smaller evidence, because there were only 19 observed flaws in 

the Supplement 4 inspection volume. 

Table C-5 Alternate PTS Rule Flaw Table Assessment using Mean Number-of-Flaws by 

Size Interval for Beaver Valley 2 (Assuming a Lower Limit of 0.04" for 

Observed Data Interval)

Flaw Depth

(inch)

Observed 

(Detected) 

Number of Flaws 

(Biased)

Posterior Mean

Number of Flaws 

(Unbiased and 

Corrected for 

POD)

Rule’s Limits 

per 1,000" of 

Weld

0.000 < a ≤ 0.075

19

124.98 No limit

0.075 < a ≤ 0.475 38.21 166.70

0.125 < a ≤ 0.475 0 14.13 90.80

0.175 < a ≤ 0.475 0 4.86 22.82

0.225 < a ≤ 0.475 0 1.30 8.66

0.275 < a ≤ 0.475 0 0.21 4.01

0.325 < a ≤ 0.475 0 0.13 3.01

0.375 < a ≤ 0.475 0 0.09 1.49

0.425 < a ≤ 0.475 0 0.04 1.00

Table C-6 Alternate PTS Rule Flaw Table Assessment using Mean Number-of-Flaws by 

Size Interval for Beaver Valley 2 (Assuming a Lower Limit of 0.075" for 

Observed Data Interval)

Flaw Depth

(inch)

Observed 

(Detected) 

Number of Flaws 

(Biased)

Posterior Mean

Number of Flaws 

(Unbiased and 

Corrected for 

POD)

Rule’s Limits 

per 1,000" of 

Weld

0.000 < a ≤ 0.075 0 122.89 No limit

0.075 < a ≤ 0.475 19 39.05 166.70

0.125 < a ≤ 0.475 0 14.69 90.80
C-40

0.175 < a ≤ 0.475 0 5.12 22.82

0.225 < a ≤ 0.475 0 1.38 8.66

0.275 < a ≤ 0.475 0 0.21 4.01

0.325 < a ≤ 0.475 0 0.13 3.01

0.375 < a ≤ 0.475 0 0.08 1.49

0.425 < a ≤ 0.475 0 0.04 1.00

Figure C-14 Posterior number of flaws in the Supplement 4 inspection volume in various 

flaw size intervals including epistemic uncertainties

0 - 0.075 0.075 - 0.125 0.125 - 0.175 0.175 - 0.225 0.225 - 0.26

100

101

102

Actual number of flaws

Flaw size intervals (inch)

Max

75%

25%

Min

Median
C-41

C.4 References

[C-1] U.S. Code of Federal Regulations, Title 10, “Energy,” Chapter I, Section 50.61a,

“Alternate Fracture Toughness Requirements for Protection Against Pressurized 

Thermal Shock Events” (10 CFR 50.61a).

[C-2] Williams, P.T., T.L. Dickson, and S. Yin, “Fracture Analysis of Vessels - Oak Ridge 

FAVOR, v09.1, Computer Code: Theory and Implementation of Algorithms, Methods, 

and Correlations,” ORNL/TM-2010/5, January 2010, Oak Ridge National Laboratory, 

Oak Ridge, TN. 

[C-3] U.S. Nuclear Regulatory Commission (NRC), “A Generalized Procedure for Generating

Flaw-Related Inputs for the FAVOR Code,” NUREG/CR-6817, March 2004, Agencywide 

Documents Access and Management System (ADAMS) Accession No. ML040830499. 

[C-4] Gelman, A., et al., Bayesian Data Analysis, 2nd Ed., Chapman & Hall/CRC, Boca

Raton, FL, July 2003.

[C-5] Hamada, M.S., et al., Bayesian Reliability, Springer Science+Business Media, LLC, New 

York, NY, July 2008.

[C-6] Becker, F.L., “Reactor Pressure Vessel Inspection Reliability Based on Performance 

Demonstrations,” EPRI Report 1007984, June 2004, Electric Power Research Institute,

Palo Alto, CA. 

[C-7] Georgiou, G.A., “Probability of Detection (PoD) Curves: Derivation, Applications and 

Limitations,” Research Report 454, UK Health & Safety Executive, London, UK, 2006.

[C-8] Li, M., and W. Q. Meeker, “A Noise Interference Model for Estimating Probability of 

Detection for Nondestructive Evaluations,” Proceedings of the Review of Progress in 

Quantitative Nondestructive Evaluation, July 20–25, 2008, Chicago, IL, American 

Institute of Physics, College Park, MD, 2009. 

[C-9] U.S. Department of Defense, “Nondestructive Evaluation System Reliability 

Assessment,” MIL-HDBK-1823, April 30, 1999.

[C-10] Chatterjee, K., and M. Modarres, “A Bayesian Probabilistic Approach to Improved Health 

Management of Steam Generator Tubes,” published online by the Prognostics and 

Health Management Society, 2011, available at 

https://www.phmsociety.org/sites/phmsociety.org/files/phm_submission/2011/phmc_11_

012.pdf (accessed July 21, 2014).

[C-11] Celeux, G., et al., “Using Markov Chain Monte Carlo Methods to Solve Full Bayesian 

Modeling of PWR Vessel Flaw Distributions,” Reliability Engineering and System Safety, 

66(3):243–252, December 1999.

[C-12] Chatterjee, K., and M. Modarres, “A Probabilistic Approach for Estimating Defect Size 

and Density Considering Detection Uncertainties and Measurement Errors,” Journal of 

Risk and Reliability, 227(1):28–40, February 2013. 
C-42

[C-13] Spanner, J., “Materials Reliability Program: Reanalysis of Reactor Vessel Examination 

Data from the 1996 Beaver Valley 2 Vessel Examination (MRP-207), RPV Flaw 

Distribution,” EPRI Report 1014548, November 2006, Electric Power Research Institute, 

Palo Alto, CA.

[C-14] NRC, “Probabilistic Fracture Mechanics - Models, Parameters, and Uncertainty 

Treatment Used in FAVOR Version 04.1,” NUREG-1807, June 2007, ADAMS Accession 

No. ML072010411. 
C-43

Appendix C-1: Sample MATLAB Routine

clear

%%***********************************************************************

%%This MATLAB routine estimates posterior values of parameters of flaw- 

%%depth distributions for small and large flaws in RPVs using NDE data,

%%accounting for measurement error, POD, and epistemic uncertainties. The

%%routine solves Equations 16, 17 and 18. The specific data used in this

%%routine are related to the POD of Eqn. 25 and the measurement error 

%%discussed in Section C.3.3 The NDE data of Beaver Valley 2 are used. It

%%also shows the solution to the likelihood functions of Eqn. 27 and Eqn. 30.

%%Finally the routine solves the Bayesian inferences in Eqn. 28 for both

%%small and large flaws.

%%***********************************************************************

% THIS ROUTINE IS FOR DEMONSTRATION OF ONE WAY TO SOLVE THE BAYESIAN

% INFERENCE METHODS DISCUSSED IN THIS REPORT. THE RESULTS MAY BE USED TO

% CROSS-CHECK THE RESULTS IF OTHER VALUES OR OTHER SOLUTION ROUTINES ARE

% USED. THE ROUTINE DOES NOT COVER ALL E ANALYSES PERFORMED AND DISCUSSED

% IN THIS REPORT. FOR EXAMPLE, THE ROUTINE TO ESTIMATE THE FLAW-DENSITY

% DISTRIBUTIONS HAS NOT BEEN PRESENTED (ONLY FLAW-DEPTH MODEL

% DISTRIBUTIONS HAVE BEEN PRESENTED). 

%%***********************************************************************

%%LIMITATIONS

% 1. THIS ROUTINE ASSUMES THE SINGLE PARAMETER EXPONENTIAL DISTRIBUTION

% FOR MODELING DISTRIBUTION OF BOTH SMALL AND LARGE FLAW DEPTHS.

% 2. THE POSTERIOR FOR SMALL FLAWS WILL GO TO INFINITY IF THE RIGHT EXTREME

% OF THE LEFT-CENSORED NDE DATA OR LEFT EXTREME OF INTERVAL DATA FOR

% SMALL FLAWS IS EXTREMELY SMALL (THAT IS, LESS THAN 0.09 INCH). 

% 3. THE POSTERIOR FOR SMALL FLAWS APPROACHES INFINITY FOR LARGE SIGMA; 

% THAT IS, THE RANDOM ERROR FOR THE MEASUREMENT ERROR MODEL (WHEN SIGMA

% EXCEEDS 0.035"). 

%%***********************************************************************

%%ASSUMPTIONS

% 1. THIS ROUTINE ASSUMES LEFT-TRUNCATED SINGLE-PARAMETER EXPONENTIAL

% DISTRIBUTION FOR FLAW DEPTH FOR SMALL FLAWS. 

% 2. THIS ROUTINE ASSUMES RIGHT-TRUNCATED SINGLE-PARAMETER EXPONENTIAL

% DISTRIBUTION FOR LARGE FLAWS. 

% 3. THIS ROUTINE ASSUMES TWO-PARAMETER LOGISTIC DISTRIBUTION EQN. 4 WITH

% A POD THRESHOLD OF ZERO. 

% 4. SIMILARLY TO EQN. 30, INTEGRAL RANGE FOR THE MEASUREMENT IS BETWEEN

% -1 AND 1, WHICH COVERS THE EXTREME RANGES OF THE BIAS AND RANDOM ERRORS. 

%%***********************************************************************

%%NOMENCLATURE:

%m & c are parameters discussed in Eqn. 8; sigma is standard deviation of

%random error associated with the measurement error model of Eqn. 8. 

%beta1 & beta2 are POD function parameters in Eqn. 4; ath is the detection

%threshold of Eqn. 4. 

%atr is the transition flaw depth between small and large flaws discussed

%in Eqn. 9. 

%lambda1 & lambda2 are flaw-depth distribution parameters (i.e., the flaw- 

% depth intensity) for small and large defects respectively. 

%n1 is the total number of censored NDE data for small flaws. 

%are is the right extreme of left-censored or interval of small-flaw- 

%depth NDE data. 

%ale is the left extreme of interval of small-flaw-depth data; ale must
C-44

% be greater than the parameter c of the measurement error model. 

%a1 is a set, representing values of exact small-flaw-depth NDE data

%reported. 

%n2 is the number of exact small-flaw-depth NDE data reported

%n3 is the total number of exact large-flaw-depth NDE data reported

%n4 is the total number of interval or left-censored large-flaw-depth NDE

%data reported

%a2 is set, representing exact values of large-flaw-depth NDE data

%reported

%are_large is the right extreme of the left-censored or interval large- 

%flaw-depth NDE data reported

%ale_large is the left extreme of interval data of large-flaw-depth NDE

%data reported

%%***********************************************************************

%%Measurement error parameters

m=0.84;c=0.04;sigma=0.0298;

%%***********************************************************************

%%POD parameters

ath=0;beta1=63.21;beta2=0.1124;

%%***********************************************************************

%%Transition point for large flaws

atr=0.26;

%%***********************************************************************

%%***********************************************************************

%%NDE data of small flaws

n1=103;are=0.125;ale=c;a1=[0.15];n2=0;

%%***********************************************************************

%%***********************************************************************

%%NDE data of large flaws

a2=[0.26];n3=length(a2);n4=0;ale_large=0.27;are_large=0.3;

%%***********************************************************************

%BAYESIAN INFERENCE FOR ESTIMATING POSTERIOR DISTRIBUTION OF THE PARAMETER

%LAMBDA (FLAW-DEPTH INTENSITY) OF THE SMALL-FLAW-DEPTH EXPONENTIAL PDF

lambda1=linspace(0,60,100);

Norm_const=0;

for i=2:length(lambda1)

Marginal_Pod=@(a)((1-(1+exp(-beta1*beta2))./(1+exp(beta1*(a-beta2-ath)))).*(l

ambda1(i).*exp(-lambda1(i).*a)./(1-exp(-lambda1(i).*atr))));

Likeli_int=@(Ea,a)((1-(1+exp(-beta1*beta2))./(1+exp(beta1*(a-Ea-beta2-ath))))

.*(lambda1(i).*exp(-lambda1(i).*(a-Ea))./(1-exp(-lambda1(i).*atr))).*((1/sqrt

(2*pi*sigma^2)).*exp(-(1/(2*sigma^2)).*((m*Ea+(1-m)*a-c)/m).^2)));

Likeli_exact=@(Ea)((1-(1+exp(-beta1*beta2))./(1+exp(beta1*(a1-Ea-beta2-ath)))

).*(lambda1(i).*exp(-lambda1(i).*(a1-Ea))./(1-exp(-lambda1(i).*atr))).*((1/sq

rt

(2*pi*sigma^2)).*exp(-(1/(2*sigma^2)).*((m*Ea+(1-m)*a1-c)/m).^2)));

Likelihood_exact(i)=((quad(Likeli_exact,-1,1))./(quad(Marginal_Pod,0,atr)))^n

2;

Likelihood_int(i)=((dblquad(Likeli_int,-1,1,ale,are))./(quad(Marginal_Pod,0,a

tr)))^n1;

Prior_small(i)=(gampdf(lambda1(i),39,.3504));

Numerator(i)=Likelihood_int(i).*Likelihood_exact(i).*Prior_small(i);

Norm_const=Norm_const+Numerator(i)*(lambda1(i)-lambda1(i-1));

end

Posterior_small=Numerator/Norm_const;

Mean_Posterior_Small_Flaw_Depth_Intensity=sum(lambda1.*Posterior_small)*0.606

1 

Mean_Posterior_Small_Flaw_Depth=1/Mean_Posterior_Small_Flaw_Depth_Intensity
C-45

POD_of_Posterior_Mean_Small_Flaw_Depth=1-(1+exp(-beta1*beta2))./(1+exp(beta1*

(Mean_Posterior_Small_Flaw_Depth-beta2-ath)))

subplot(211)

plot(lambda1,Posterior_small,lambda1,Prior_small,'-.','LineWidth',2)

xlabel('Flaw Depth intensity (per unit 

inch)','fontsize',12,'fontweight','b','FontName','Times New Roman') 

ylabel('Relative Frequency','fontsize',12,'fontweight','b','FontName','Times 

New Roman') 

title('Posterior and prior flaw depth intensity for small 

flaws','fontsize',14,'fontweight','b','FontName','Times New Roman') 

h = legend('Posterior_small','Prior_small');

set(h,'Interpreter','none') 

set(gca,'FontSize',12,'FontWeight','b','FontName','Times New Roman') 

%%***********************************************************************

%BAYESIAN INFERENCE FOR ESTIMATING POSTERIOR DISTRIBUTION OF THE PARAMETER

%LAMBDA (FLAW-DEPTH INTENSITY) OF THE LARGE-FLAW-DEPTH EXPONENTIAL PDF

lambda2=linspace(0,10,100);

Norm_const1=0;

for i=2:length(lambda2)

Marginal_Pod1=@(a)((1-(1+exp(-beta1*beta2))./(1+exp(beta1*(a-beta2-ath)))).*(

lambda2(i).*exp(-lambda2(i).*(a-atr))));

Likeli_exact1=@(Ea)((1-(1+exp(-beta1*beta2))./(1+exp(beta1*(a2-Ea-beta2-ath))

)).*(lambda2(i).*exp(-lambda2(i).*(a2-Ea-atr))).*((1/sqrt(2*pi*sigma^2)).*exp

(-(1/

(2*sigma^2)).*((m*Ea+(1-m)*a2-c)/m).^2)));

Likelihood_exact1(i)=((quad(Likeli_exact1,-1,1))./(quad(Marginal_Pod1,atr,10)

))^n3;

Likeli_int1=@(Ea,a)((1-(1+exp(-beta1*beta2))./(1+exp(beta1*(a-Ea-beta2-ath)))

).*(lambda2(i).*exp(-lambda2(i).*(a-Ea-atr))).*((1/sqrt(2*pi*sigma^2)).*exp(-

(1/

(2*sigma^2)).*((m*Ea+(1-m)*a-c)/m).^2)));

Likelihood_int1(i)=((dblquad(Likeli_int1,-1,1,ale_large,are_large))./(quad(Ma

rginal_Pod1,atr,10)))^n4;

Prior_large(i)=(gampdf(lambda2(i),4,0.8333));

Numerator1(i)=Likelihood_exact1(i).*Likelihood_int1(i).*Prior_large(i);

Norm_const1=Norm_const1+Numerator1(i)*(lambda2(i)-lambda2(i-1));

end

Posterior_large=Numerator1/Norm_const1;

Posterior_small=Numerator/Norm_const;

Mean_Posterior_Large_Flaw_Depth_Intensity=sum(lambda2.*Posterior_large)*0.101

0 

Mean_Posterior_Large_Flaw_Depth=1/Mean_Posterior_Large_Flaw_Depth_Intensity

POD_of_Posterior_Mean_Large_Flaw_Depth=1-(1+exp(-beta1*beta2))./(1+exp(beta1*

(Mean_Posterior_Large_Flaw_Depth-beta2-ath)))

subplot(212)

f1=plot(lambda2,Posterior_large,lambda2,Prior_large,'-.','LineWidth',2)

xlabel('Flaw depth intensity (per unit 

inch)','fontsize',12,'fontweight','b','FontName','Times New Roman') 

ylabel('Relative Frequency','fontsize',12,'fontweight','b','FontName','Times 

New Roman') 

title('Posterior and prior flaw depth intensity for large 

flaws','fontsize',14,'fontweight','b','FontName','Times New Roman') 

h = legend('Posterior_large','Prior_large');

set(h,'Interpreter','none') 

set(gca,'FontSize',12,'FontWeight','b','FontName','Times New Roman') 

screen_size = get(0, 'ScreenSize');

f1 = figure(1);
C-46

set(f1, 'Position', [0 0 screen_size(3) screen_size(4) ] );

%%***********************************************************************

Output from the above routine is displayed in Figure C-14

(also shown in Figure C-8 and Figure C-9) 

Mean_Posterior_Small_Flaw_Depth_Intensity = 

37.8118

Mean_Posterior_Small_Flaw_Depth = 

0.0264

POD_of_Posterior_Mean_Small_Flaw_Depth = 

0.0035

Mean_Posterior_Large_Flaw_Depth_Intensity = 

5.4042

Mean_Posterior_Large_Flaw_Depth = 

0.1850

POD_of_Posterior_Mean_Large_Flaw_Depth = 

0.9900

f1 = 

230.0087

231.0082

Published with MATLAB® 7.12
C-47

Figure C-15 MATLAB Routine Output 

D-1

APPENDIX D SENSITIVITY STUDY RESULTS ON FLAW 

DISTRIBUTIONS CONSIDERING VFLAW DATA, POD, 

AND MEASUREMENT ERRORS IN NDE DATA

Prepared for the U.S. Nuclear Regulatory Commission under the Subcontract 4000111626 

with UT Battelle, LLC (Oak Ridge National Laboratory)

Mohammad Modarres

University of Maryland

March 2012

D-3

TABLE OF CONTENTS

TABLE OF CONTENTS.............................................................................................. D-3

LIST OF FIGURES...................................................................................................... D-5

LIST OF TABLES ....................................................................................................... D-5

ABBREVIATIONS....................................................................................................... D-7

SYMBOLS AND EXPRESSIONS............................................................................... D-7

D.1 Introduction ....................................................................................................... D-9

D.2 Overview of the Bayesian Approach to Update Flaw-Depth and FlawDensity Distributions ........................................................................................ D-9

D.3 Application to a Base Case Example............................................................. D-10

D.4 Application to Sensitivity Cases.................................................................... D-15

D.5 Discussion and Summary .............................................................................. D-22

D.6 References....................................................................................................... D-23

D-5

LIST OF FIGURES 

Figure D-1 Beaver Valley 2 Weld Map [D-8] .................................................................... D-12

Figure D-2 Flaw-Depth and Flaw-Density Distributions Used in VFLAW and Their 

Corresponding Parameter Hyper-PDFs ......................................................... D-13

LIST OF TABLES

Table D-1 Alternate PTS Rule Flaw Table Assessment Using Mean Number of 

Flaws by Size Interval for Beaver Valley 2 (assuming a Lower Limit of

0.04" vs. 0.075" for Observed Data Interval) .................................................. D-14

Table D-2 Results of Sensitivity Case 1.......................................................................... D-16

Table D-3 Results of Sensitivity Case 2.......................................................................... D-16

Table D-4 Results of Sensitivity Case 3.......................................................................... D-17

Table D-5 Results of Sensitivity Case 4.......................................................................... D-17

Table D-6 Results of Sensitivity Case 5.......................................................................... D-18

Table D-7 Results of Sensitivity Case 6.......................................................................... D-18

Table D-8 Results of Sensitivity Case 7.......................................................................... D-19

Table D-9 Results of Sensitivity Case 8.......................................................................... D-19

Table D-10 Results of Sensitivity Case 9.......................................................................... D-20

Table D-11 Results of Sensitivity Case 10........................................................................ D-20

Table D-12 Results of Sensitivity Case 11........................................................................ D-21

Table D-13 Results of Sensitivity Case 12........................................................................ D-21

D-7

ABBREVIATIONS

PDF Probability Density Function

NDE Nondestructive Evaluation

POD Probability of Detection

RPV Reactor Pressure Vessel

SAW Submerged Arc Weld

UT Ultrasonic Test

SYMBOLS AND EXPRESSIONS

a True flaw depth (inches)

a* NDE measured (or observed) flaw depth (inches)

ath Threshold flaw depth for detection, below which flaw detection is beyond the 

capability of the NDE technology used

D The event that a flaw is detected

The event that a flaw is not detected

EM Model error of the NDE measurement error, represented by a normal 

distribution with a mean of zero and known standard deviation

L(a|Φ) Likelihood of true flaw depth given the vector of parameters Φ

L(Data|θ) Likelihood of observed NDE data conditioned on (given) the unknown 

parameter θ

Likelihood of observing n* flaws given that there are a total of nj true flaws

Mε NDE measurement error (combined random and systematic errors)

n Number of flaw depth intervals (reported in NDE)

"n" ̅ Mean of the PDF of the number of flaws in volume v

n* Number of exact flaw depths observed (reported in NDE)

Combination of n* observed flaws out of total flaws nj (observed or detected, 

and unobserved or not detected flaws) 

POD(a) Probability of detection of a flaw of depth a

Pr(.) Probability

Pr(D) POD independent of flaw depth

Probability of no detection regardless of size

Probability of total flaws nj conditioned on observing n* flaws in NDE

βi Parameter i of the POD model

Δ Weld bead thickness

π0(θ) Prior PDF of an unknown parameter θ

π1(θ|Data) Posterior PDF of an unknown parameter given observed NDE data

Φ Vector of parameters of the flaw depth PDF

θ An unknown parameter of a model

D-9

D.1 Introduction

This report discusses the results of a sensitivity analysis by applying a Bayesian updating

methodology described in Appendix C to account for probability of detection (POD) and

measurement (sizing) error in the data for flaws detected through ultrasonic testing (UT). The

methodology estimates vessel specific flaw depth and density distributions for comparison to the 

10 CFR 50.61a screening tables and updates the VFLAW code’s distributions for further

analysis with the FAVOR code. The sensitivity analysis was performed using assumed 

nondestructive examination (NDE) flaw data. Existing VFLAW distributions for flaw depth and

density, representing welds of the Pressure Vessel Research User Facility (PVRUF) vessel,

were specialized to the Beaver Valley 2 reactor pressure vessel (RPV) welds and assumed to

properly describe prior flaw depth and flaw density distributions and characteristics.

In the remainder of this Appendix, a very brief overview of the methodology is described first,

followed by the results of the sensitivity analysis. The results are compared to the 10 CFR

50.61a screening tables and conclusions are summarized. 

D.2 Overview of the Bayesian Approach to Update Flaw-Depth and FlawDensity Distributions

Finding flaws using NDE requires characterization of associated uncertainties. The reliability of 

an inspection is customarily expressed in terms of the POD of a given flaw size and expressed 

by curves of POD vs. flaw size. Additionally, sizing or measurement errors occur and model 

uncertainties exist. Sizes of UT-detected small flaws in RPVs tend to be overestimated while 

the sizes of large flaws are underestimated [D-1]. 

POD is generally modeled as a function of true flaw depth. Different forms of POD curves have 

been used in the literature (see References [D-2], [D-3], and [D-4]. The logistic POD model for 

hit/miss data is a common model and is represented as: 

Eqn. (D-1) 

Measurement error is defined by Eqn. (D-2), where Mε is the measurement error, a* is the 

measured value of flaw depth, and a is the true value of flaw depth:

Mε = a* - a Eqn. (D-2)

In its simplest form, Mε can be represented by a linear function of true size, as shown in 

Eqn. (D-1), where m is the slope and c is the intercept of the line representing measurement 

error versus true flaw depth:

Eqn. (D-3) 





















ββ ββ

ββ

0 otherwise

for a> a

e+1

e+1 -1 POD(a | =)a,, th (a- )a-

-

21 th 21 th

21

),0(N

M ma Ec

MMM

M

where a, flawtrue depthandE σ=

++=

=

ε
D-10

The likelihood of exact flaw measurements reported may be expressed as a function of POD 

and Mε (see Appendix C). If, in addition to or instead of the exact flaw depth data, intervals of 

flaw depths are reported (such as the number of flaws observed at less than a given depth or 

between an upper and lower limit), the likelihood may also be similarly expressed (see Appendix 

C).

Regardless of the form of the data (exact flaw depth and/or interval data), the Bayesian 

inference of the vector of parameters Φ of the flaw-depth probability density function (PDF) 

would be obtained from the Bayesian inference , where

is the posterior multivariate PDF of vector Φ and is the prior multivariate PDF 

of Φ.

If flaws are detected with a probability Pr(D) (or not detected with a probability of 

), the probability that a specific total number of flaws n* observed in a given 

volume v out of the true number of flaws nj follows the binomial distribution (see 

References [D-5] and [D-6]:

Eqn. (D-4) 

Accordingly, the mean estimate of the true number of flaws would be found from:

Eqn. (D-5) 

The Bayesian updating of nj, which allows the estimation of the posterior distribution of nj to 

describe the true number of flaws, would be:

Eqn. (D-6) 

where the prior Pr(nj) may be expressed by a Poisson distribution with parameter ρ (defined in 

VFLAW).

D.3 Application to a Base Case Example

The EPRI report by Spanner [D-7] provides UT-based measured flaw data near the inner 

surface (~2.5 inches) of the Beaver Valley Unit 2 RPV, including small flaw sizes. These data, 

while subject to POD and measurement error, provide a more vessel-specific perspective of the 

distribution of flaws for weld metals in the Beaver Valley 2 RPV than do the VFLAW distributions 

used in FAVOR.

The observed Beaver Valley 2 NDE data (with detection and sizing uncertainty) are mostly in 

the form of interval data as summarized below [D-7]:

19 weld flaws were detected by the UT NDE of Beaver Valley 2 in the first inch (ASME 

Code, Section XI, Mandatory Appendix VIII, Supplement 4 inspection volume) of the 

( | Data (L) Data | )() 1 ∝Φπ 0 ΦπΦ

( |Data) 1 Φπ )(0 Φπ

Pr( 1)D −= Pr( )D

[ ] [ ] * j * nn n n

*

j

j

* Pr( -1)D Pr(D)

n

n

L(n | =)n −

















n

POD )D(

n n

*

=

∑

=

nj

jj

*

jj

*

*

j n(L | )n Pr( )n

n(L | )n Pr( )n Pr(n | )n
D-11

RPV (these data are assumed normalized to 1,000" of weld length), all having a flaw 

depth less than 0.125". 7

The lower limit of the detected flaw intervals described above was not stated in [D-7], but is not 

zero. Two possible subjective lower limits were assumed, and later the sensitivities of the final 

(posterior) flaw distributions to these two choices were assessed. The two lower limits selected 

were 0.04" and 0.075". 

The associated weld bead thicknesses are not reported in [D-7]. However, the weld region of 

the observed flaws and flaw length is reported. Such results must be corrected for detection 

and sizing capability, particularly for the small flaws. The Beaver Valley 2 RPV weld map is 

shown in Figure D-1 [D-8]. In the absence of the Beaver Valley average weld bead thickness 

as the point of transition between large and small depths, it was assumed that all flaws reported 

are in submerged arc welds (SAWs), which form over 90% of welds in the VFLAW data, with the 

bead thickness of ∆ = 0.26". Using the Beaver Valley 2 RPV information shown in Figure D-1, 

the VFLAW data were specialized to represent the prior distributions of flaw depth and density 

for Beaver Valley 2 RPV.

Total Weld Length = 816.18"

Total Weld Volume = 4.975 ft3

Total Weld Fusion Area = 92 ft2

Weld Volume of 1" = 0.616 ft3

Weld Volume of 3/8t = 1.865 ft3

7 In Appendix C, the same analysis is performed, except that the analysis did not assume that the data were 

normalized to 1,000" of linear length of weld. Instead, it assumed that the data came from 816.18" of weld, which 

is the actual length of weld in the Beaver Valley 2 RPV.
D-12

Figure D-1 Beaver Valley 2 Weld Map [D-8] 

The relationship between the flaw depth and flaw density PDFs and the corresponding prior

hyper-PDFs of their parameters are illustrated in Figure D-2. 
D-13

Figure D-2 Flaw-Depth and Flaw-Density Distributions Used in VFLAW and Their 

Corresponding Parameter Hyper-PDFs

Analysis of UT-detected performance data reported by the Electric Power Research Institute 

(EPRI) [D-7] was used to identify a POD function for the purpose of this example. The threshold 

limit of this POD function was taken as 0.00, and the epistemic uncertainties associated with the 

parameters of the model were not considered in this study. Accordingly, the following mean 

POD function was used:

Eqn. (D-7) 

The measurement error was assumed based on some examples and measurement errors 

reported in Reference [D-7]. After combination of Eqn. (D-2) and Eqn. (D-3), the measurement 

error (a linear function that oversizes small flaws and undersizes large flaws) is:

Eqn. (D-8)

where N(0, 0.0298) is a normal distribution with a mean of zero and a constant standard 

deviation of 0.0298. The observed data for the first inch of the vessel were used to estimate the 

true number of flaws in the flaw-depth ranges of the Alternate PTS Rule flaw tables. This 

information was used to assess how the estimated number of flaws of a given size in Beaver 

Valley 2 (estimated based on inspection data, VFLAW distributions, and Bayesian inference) 

63.2100 .0a( 1124) e1

1 POD 1)a( − + −=

.0M 1905 .0a 0476 .0,0(N 0298) *

ε −= ++
D-14

compares to the number and size of flaws permitted by the Alternate PTS Rule flaw tables. The

posterior characteristics were used to develop the corresponding Alternate PTS Rule flaw

tables.

If the lower limit of the observed data interval is changed from 0.04" to 0.075" to line up with the 

smallest bin size in the Alternate PTS Rule flaw tables, the results summarized in Table D-1 are 

calculated. In this case, the results of the mean number of flaws show no sensitivity to the 

choice of the lower limit of the interval of NDE data. Given this flaw observation, true estimated 

numbers of flaws in all bins were below the Alternate PTS Rule flaw limits. 

Table D-1 Alternate PTS Rule Flaw Table Assessment Using Mean Number of Flaws by 

Size Interval for Beaver Valley 2 (assuming a Lower Limit of 0.04" vs. 0.075" 

for Observed Data Interval)

Flaw Depth

(in)

Base Case 1 Base Case 2

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

Number of 

Flaws 

(Biased 

with Lower 

Detection 

Limit of 

0.04")

Posterior 

Mean 

Number of 

Flaws 

(Unbiased 

and 

Corrected 

for POD)

Observed 

(Detected) 

Number of 

Flaws 

(Biased with 

Lower 

Detection 

Limit of 

0.075")

Posterior 

Mean 

Number of 

Flaws 

(Unbiased 

and 

Corrected for 

POD)

1 0.000 < a ≤ 0.075

19

111.41 0 109.09 No limit

2 0.075 < a ≤ 0.475 25.73 19 27.02 166.70

3 0.125 < a ≤ 0.475 0 8.46 0 8.98 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 2.88 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 0.79 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.29 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.14 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.09 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.05 1.00
D-15

D.4 Application to Sensitivity Cases

In order to examine the effects of changes in the number of flaws observed through NDE, as 

well as the significance of the POD and the VFLAW prior distributions, twelve sensitivity cases 

were identified and examined. Methods and tools discussed in Sections D.2 and D.3 were used 

to carry out these sensitivity cases. The sensitivity cases examined were as follows:

1. No flaws detected, with consideration of the VFLAW prior distributions, POD, and

measurement error.

2. 70% of the Alternate PTS Rule’s allowed flaws in Bins 2 and 3 are detected, with

consideration of the VFLAW prior distributions, POD, and measurement error.

3. 110% of the Alternate PTS Rule’s allowed flaws in Bin 3 are detected, with consideration

of the VFLAW prior distributions, POD, and measurement error.

4. No flaws detected, with no consideration of VFLAW priors (i.e., non-informative priors)

and POD, but with consideration of flaw measurement error only (i.e., no POD or

VFLAW prior).

5. 70% of the Alternate PTS Rule’s allowed flaws in Bins 2 and 3 are detected, with no

consideration of VFLAW priors and POD, but with consideration of flaw measurement

error only.

6. 110% of the Alternate PTS Rule’s allowed flaws in Bin 3 are detected, with no

consideration of VFLAW priors and no consideration of POD, but with consideration of

flaw measurement error only.

7. No flaws detected, no consideration of VFLAW priors, but with consideration of POD and

flaw measurement error.

8. 70% of the Alternate PTS Rule’s allowed flaws in Bins 2 and 3 are detected, with no

consideration of VFLAW priors, but with consideration of POD and flaw measurement

error.

9. 110% of the Alternate PTS Rule’s allowed flaws in Bin 3 are detected, with no

consideration of VFLAW priors, but with consideration of POD and flaw measurement

error.

10. No flaws detected, no consideration of POD, but with consideration of VFLAW priors and

flaw measurement error.

11. 70% of the Alternate PTS Rule’s allowed flaws in Bins 2 and 3 are detected, with no

consideration of POD, but with consideration of VFLAW priors and flaw measurement

error.

12. 110% of the Alternate PTS Rule’s allowed flaws in Bin 3 are detected, with no

consideration of POD, but with consideration of VFLAW priors and flaw measurement

error.

The results of the sensitivity studies are listed in Table D-2 through Table D-13. 
D-16

Table D-2 Results of Sensitivity Case 1 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 1

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 80.13 No limit

2 0.075 < a ≤ 0.475 25.73 0 40.76 166.70

3 0.125 < a ≤ 0.475 0 8.46 0 18.79 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 7.81 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 2.71 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.29 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.14 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.09 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.05 1.00

Table D-3 Results of Sensitivity Case 2 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 2

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit 

of 0.04")

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 306.12 No limit

2 0.075 < a ≤ 0.475 25.73 116.69 34.16 166.70

3 0.125 < a ≤ 0.475 0 8.46 63.56 7.71 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 1.69 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 0.44 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.29 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.14 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.09 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.04 1.00
D-17

Table D-4 Results of Sensitivity Case 3 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 3

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 155.03 No limit

2 0.075 < a ≤ 0.475 25.73 0 41.33 166.70

3 0.125 < a ≤ 0.475 0 8.46 99.88 15.21 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 4.51 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 1.21 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.29 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.14 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.09 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.05 1.00

Table D-5 Results of Sensitivity Case 4 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 4

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 0.00 No limit

2 0.075 < a ≤ 0.475 25.73 0 0.00 166.70

3 0.125 < a ≤ 0.475 0 8.46 0 0.00 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 0.00 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 0.00 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.00 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.00 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.00 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.00 1.00
D-18

Table D-6 Results of Sensitivity Case 5 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 5

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Lower 

Detection 

Limit of 0.04")

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 56.47 No limit

2 0.075 < a ≤ 0.475 25.73 116.69 60.22 166.70

3 0.125 < a ≤ 0.475 0 8.46 63.56 36.13 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 18.67 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 5.98 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.00 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.00 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.00 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.00 1.00

Table D-7 Results of Sensitivity Case 6 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 6

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 32.85 No limit

2 0.075 < a ≤ 0.475 25.73 0 67.03 166.70

3 0.125 < a ≤ 0.475 0 8.46 99.88 47.02 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 27.19 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 11.17 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.00 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.00 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.00 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.00 1.00
D-19

Table D-8 Results of Sensitivity Case 7 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 7

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 0.00 No limit

2 0.075 < a ≤ 0.475 25.73 0 0.00 166.70

3 0.125 < a ≤ 0.475 0 8.46 0 0.00 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 0.00 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 0.00 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.00 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.00 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.00 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.00 1.00

Table D-9 Results of Sensitivity Case 8 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 8

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 5131.91 No limit

2 0.075 < a ≤ 0.475 25.73 116.69 263.80 166.70

3 0.125 < a ≤ 0.475 0 8.46 63.56 35.54 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 4.88 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 0.39 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.00 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.00 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.00 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.00 1.00
D-20

Table D-10 Results of Sensitivity Case 9 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 9

Alternate

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 1233.10 No limit

2 0.075 < a ≤ 0.475 25.73 0 202.01 166.70

3 0.125 < a ≤ 0.475 0 8.46 99.88 54.12 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 13.13 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 1.95 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.00 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.00 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.00 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.00 1.00

Table D-11 Results of Sensitivity Case 10 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 10

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 79.14 No limit

2 0.075 < a ≤ 0.475 25.73 0 41.18 166.70

3 0.125 < a ≤ 0.475 0 8.46 0 19.09 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 7.93 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 2.42 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.29 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.14 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.09 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.05 1.00
D-21

Table D-12 Results of Sensitivity Case 11 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 11

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 73.49 No limit

2 0.075 < a ≤ 0.475 25.73 116.69 57.04 166.70

3 0.125 < a ≤ 0.475 0 8.46 63.56 31.09 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 14.66 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 4.81 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.29 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.14 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.09 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.05 1.00

Table D-13 Results of Sensitivity Case 12 

Flaw Depth

(in)

Base Case 1 Sensitivity Case 12

Alternate 

PTS Rule 

Limit (per 

1,000" of 

Weld)

Bin No.

Observed 

(Detected) 

No. of Flaws 

(Biased with 

Detection 

Limit of 0.04") 

Posterior 

Mean 

No. of Flaws 

(Unbiased 

and 

Corrected 

for POD)

Assumed No. 

of Detected 

Flaws

(with Bias)

Posterior 

Mean 

No. of Flaws 

(Unbiased)

1 0.000 < a ≤ 0.075

19

111.41 0 63.04 No limit

2 0.075 < a ≤ 0.475 25.73 0 66.84 166.70

3 0.125 < a ≤ 0.475 0 8.46 99.88 39.42 90.80

4 0.175 < a ≤ 0.475 0 2.98 0 20.55 22.82

5 0.225 < a ≤ 0.475 0 0.79 0 7.21 8.66

6 0.275 < a ≤ 0.475 0 0.29 0 0.29 4.01

7 0.325 < a ≤ 0.475 0 0.14 0 0.14 3.01

8 0.375 < a ≤ 0.475 0 0.09 0 0.09 1.49

9 0.425 < a ≤ 0.475 0 0.05 0 0.05 1.00
D-22

D.5 Discussion and Summary

In this study, analysis of a base case of UT detected weld flaw data involving measurement 

(sizing) error for Beaver Valley 2 was performed. The base case was evaluated for interval flaw 

depths detected in the inspection volume specified in Supplement 4 to Mandatory Appendix VIII 

to Section XI of the ASME Code. Detected flaw depth intervals were analyzed assuming lower 

UT detection limits of 0.04" and 0.075". Subsequently, twelve sensitivity cases were assessed 

based on variations in the assumed detected flaw depth data (in the form of intervals), choices 

of considering VFLAW flaw depth and flaw densities as prior information (as opposed to no prior 

information), and choices of considering the POD (as opposed to perfect detection; i.e., no 

POD) were evaluated and compared to the base case as well as the Alternate PTS Rule flaw 

table limits. No sensitivities to the choice of the lower UT detection limit on the observed data 

were found.

The results obtained from the twelve sensitivity cases were consistent and showed that small 

overpopulations of flaws in Bins 2 and 3 of the Alternate PTS Rule flaw tables resulting from 

possible oversizing of small flaws would be shifted to Bins 1 and 2 after accounting for the 

measurement error in the Bayesian inference. When POD is considered, the effect of the 

missed small flaws was clearly seen in Bins 1 and 2 with an additional number of flaws in the 

posterior estimates as compared to the observed flaws.

The effects of the consideration and choice of the prior distributions of flaw density and depth 

were significant. When no prior information was used to describe the flaw density and flaw 

depth distributions, POD and measurement error were also sensitive and significantly amplified 

the number of flaws in Bins 1 and 2. However, when prior VFLAW PDFs were used, the 

posteriors were significantly moderated by the existence of the prior PDFs, and the POD and 

measurement errors played less significant roles.

If the approach documented in this appendix is used to reassess actual NDE flaws, it would be 

advisable to use informative or semi informative prior estimates of the flaw depth and density 

distributions.
D-23

D.6 References

[D-1] Becker, F.L., “Reactor Pressure Vessel Inspection Reliability Based on Performance 

Demonstrations,” EPRI Report 1007984, June 22, 2004, Electric Power Research 

Institute, Palo Alto, CA. 

[D-2] Georgiou, G.A., “Probability of Detection (PoD) Curves: Derivation, Applications and 

Limitations,” Research Report 454, UK Health & Safety Executive, London, UK, 2006.

[D-3] Li, M., and W. Q. Meeker, “A Noise Interference Model for Estimating Probability of 

Detection for Nondestructive Evaluations,” Proceedings of the Review of Progress in 

Quantitative Nondestructive Evaluation, July 20–25, 2008, Chicago, IL, American 

Institute of Physics, College Park, MD, 2009. 

[D-4] U.S. Department of Defense, “Nondestructive Evaluation System Reliability

Assessment,” MIL-HDBK-1823, April 30, 1999.

[D-5] Celeux, G., et al., “Using Markov Chain Monte Carlo Methods to Solve Full Bayesian 

Modeling of PWR Vessel Flaw Distributions,” Reliability Engineering and System Safety, 

66(3):243–252, December 1999.

[D-6] Chatterjee, K., and M. Modarres, “A Probabilistic Approach for Estimating Defect Size 

and Density Considering Detection Uncertainties and Measurement Errors,” Journal of 

Risk and Reliability, 227(1):28–40, February 2013. 

[D-7] Spanner, J., “Materials Reliability Program: Reanalysis of Reactor Vessel Examination 

Data from the 1996 Beaver Valley 2 Vessel Examination (MRP-207), RPV Flaw 

Distribution,” EPRI Report 1014548, November 2006, Electric Power Research Institute, 

Palo Alto, CA.

[D-8] U.S. Nuclear Regulatory Commission, “Probabilistic Fracture Mechanics - Models, 

Parameters, and Uncertainty Treatment Used in FAVOR Version 04.1,” NUREG-1807, 

June 2007, Agencywide Documents Access and Management System (ADAMS) 

Accession No. ML072010411. 

NUREG-2163

G. Stevens, M. Kirk, M. Modarres

Office of Nuclear Regulatory Research, U. S. Nuclear Regulatory Commission, Washington, D.C. 20555-0001 

University Of Maryland Clark School of Engineering College Park, MD 20742-7531

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, D.C. 20555-0001 

During plant operation, the of reactor pressure vessel (RPVs) is exposed to neutron radiation, resulting in 

embrittlement of the vessel steel in the area of the RPV adjacent to the core. If an embrittled RPV had a 

flaw of critical size and if certain severe system transients occurred, the flaw could rapidly propagate through 

the vessel that could challenge the integrity of the RPV. The severe transients of concern, known as 

pressurized thermal shock (PTS), are characterized by a rapid cooling of the internal RPV surface in 

combination with repressurization of the RPV. Advances in understanding material behavior, the ability to 

realistically model plant systems and operational characteristics, and the ability to better evaluate PTS 

transients to estimate loads on vessel walls led the U.S. Nuclear Regulatory Commission (NRC) to develop 

a risk informed revision of the existing PTS Rule in Title 10 of the Code of Federal Regulations (10 CFR) 

50.61a, “Alternate Fracture Toughness Requirements for Protection against Pressurized Thermal Shock 

Events.” This report explains the basis for the requirements that establish the entry conditions to permit the 

use of 10 CFR 50.61a and describes methods that licensees can use to meet the requirements of 10 CFR 

50.61a.

Pressurized thermal shock (PTS), 10CFR50.61a, 10CFR50.61, reactor pressure

vessel embrittlement, pressurized water reactor

September 2018

Technical

Technical Basis for Regulatory Guidance on the Alternate Pressurized 

Thermal Shock Rule

Final



NUREG-2163

Final

Technical Basis for Regulatory Guidance on the Alternate Pressurized Thermal Shock Rule September 2018