NUREG/CR-5587

SAIC-92/1137

Approaches for Age-Dependent

Probabilistic Safety Assessments

With Emphasis on Prioritization

and Sensitivity Studies

Prepared by

W. E. Vesely

Science Applications International Corporation

Prepared for

U.S. Nuclear Regulatory Commission
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NUREG/CR-5587

SAIC-92/1137

RG, R1, R9

Approaches for Age-Dependent

Probabilistic Safety Assessments

With Emphasis on Prioritization

and Sensitivity Studies

Manuscript Completed: May 1992

Date Published: August 1992

Prepared by

W. E. Vesely

Science Applications International Corporation

655 Metro Place South, Suite 745

Dublin, OH 43017

Prepared for

Division of Engineering

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555

NRC FIN L1072
ABSTRACT

Approaches are described for incorporating component aging reliability models into a

probabilistic safety assessment (PSA), or probabilistic risk assessment (PRA), of a

nuclear power plant. These approaches and procedures are described from a technical

standpoint and are not to be interpreted as having any regulatory implications.

Component aging failure rate models and test and maintenance aging control models are

presented for utilization. Different approaches for carrying out the aging evaluations are

given. Demonstrations are given involving prioritizing aging contributors, evaluating

maintenance effectiveness, carrying out time dependent evaluations, and carrying out

uncertainty and sensitivity analyses of aging effects.

lii
TABLE OF CONTENTS

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

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

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

EXECUTIVE SUMMARY ....................................................... xv

ACKNOWLEDGEMENT...................................................................................... xxvii

1. THE AGE-DEPENDENT PSA VERSUS THE STANDARD PSA ............. 1

1.0 Introduction..................................................... 1

1.1 The Difference in the Treatment of Component Failures ............... 4

1.2 The Difference in the Treatment of Test, Maintenance,

and Repair....................................................................................... 6

1.3 Results Obtainable from an APSA ............................................... 9

1.4 Issues Associated with an APSA .............................................. 15

2. COMPONENT RELIABILITY MODELS USED IN AN

AGE-DEPENDENT PSA .................................................. 17

2.0 Introduction. ........ ,......... 17

2.1 Definition of Aging for Reliability and Risk Applications ................ 17

2.2 Aging Failure Rate Models .............................................. 21

2.3 Failure Rate Aging Effects Versus Overall Time Trends .................. 24

2.4 Age Dependent and Tume Dependent Component Reliability

Results...........................................................I................................... 28

2.5 Modeling the Aging Control of a Test, Maintenance, or

Repair Activity .............................................. 31

2.6 The Good as New Restoration Model and The Good as Old

Restoration Model .33

2.7 More Complex Maintenance and Restoration Models .37

2.8 Summary of Models and Data Needed to Quantify Component

Reliability and Unavailability Effects of A gng .42

v
TABLE OF CONTENTS CONTINUED

3. APPROACHES FOR TRANSFORMING A PSA INTO AN AGEDEPENDENT PSA .............. . ............................. 45

3.0 Introduction ................................................ 45

3.1 Successive Stepwise Evaluations Using a Standard PSA ................ 46

3.2 Substitution of Aging Models Into a PSA ........................................ 50

3.3 The Risk Importance Approach for Evaluating

Aging Effects ............................................... 52

4. APPLICATIONS OF AN AGE-DEPENDENT PSA ................................. 58

4.0 Introduction ............................................... 58

4.1 Questions To Be Answered in Setting Up an APSA Application ..... 59

4.2 Impact of Available Component Aging Failure Rate Data .............. 59

4.3 Impact of Available Test and Maintenance Information .................. 63

4.4 Impact oEPSA Information Which is Available .............................. 64

4.5 Impact of Results Which Are of Most Interest .................................. 66

5. PRIORITIZATIONS OF AGING CONTRIBUTORS ................................. 67

5.0 Introduction ....... 67

5.1 Application of the Risk Importance Aging Approach ....................... 68

5.2 Selection of Aging Failure Rate Models and Data ........................... 70

5.3 Selection of Test and Models........................................................... 73

5.4 Selection of the Formulas for the Component Aging Impacts .......... 75

5.5 Detailed Prioritizations of and Component Contributors .................. 79

5.6 Grouped Components Prioritizations ............................................... 88

Vi
TABLE OF CONTENTS CONTINUED

6. IDENTIFICATION OF RISK-DIRECTED AGING MANAGEMENT 94

STRATEGIES............................................................................................

6.0 Introduction .94

6.1 Risk-Directed Aging Management Strategies .94

7. TIME DEPENDENT AGING EVALUATIONS ....................................... 104

7.0 Introduction ............................................. 104

7.1 Basic Time Dependent Equations ............................................. 105

7.2 Time Dependent Equations-for a Linear Aging Failure Rate ............. 106

7.3 Applications of the Time Dependent, Linear Aging Failure Rate

Equations..................................................................................... 108

8. SENSITIVITY AND UNCERTAINTY EVALUATIONS .......................... 111

8.0 Introduction . ............................................. l 

8.1 Uncertainty Analysis of Data Used in an APSA .............................. 111

8.2 Sensitivity Studies of the Effects of Different Aging Rates ............. 115

8.3 Sensitivity Studies of the Effects of Different Test and

Replacement/Repair Policies ............................................. 119

9. CONSIDERATIONS IN USING A PSA TO EVALUATE THE RISK

EFFECTS FROM AGING OF PASSIVE COMPONENTS ........................ 124

9.0 Introduction .................................................. 124

vu
TABLE OF CONTENTS CONTINUED

9.1 The Role and Use of PSA to Evaluate the Reliability of Passive 124

Components and Their Risk Impacts.

9.2 Aging Component Reliability Models Required for PSA Aging 126

Evaluations......................................................................................

9.3 The Crack Growth Phenomenon . .127

9.4 The Corrosion Phenomenon . .128

9.5 Stochastic Analysis as a Complement to Deterministic Crack 128

Growth Analysis.............................................................................

10. SUMMARY AND CONCLUSIONS ........................ 130

REFERENCES ........................................................ ............................................... 131

APPENDIX: GENERAL FORMULAS FOR AGING COMPONENT

UNRELIABILITIES AND UNAVAILBILITIES ............................................... 132

viii
LIST OF FIGURES

FIGURE 1.

FIGURE 2.

FIGURE 3.

FIGURE 4.

FIGURE 5.

FIGURE 6.

FIGURE 7.

FIGURE 8.

FIGURE 9.

FIGURE 10.

BASIC STEPS IN A PSA................................................................

THE BATHTUB CURVE OF FAILURE RATE VERSUS AGE....

INCREASE IN CORE DAMAGE FREQUENCY FROM AGING

FOR DIFFERENT TEST AND MAINTENANCE PROGRAMS...

TIME DEPENDENT CORE DAMAGE FREQUENCY

INCREASE DUE TO AGING........................................................

SENSITIVITY ANALYSIS EVALUATING THE AGING

CONTROL OF A GIVEN TEST AND MAINTENANCE

PROGRAM.....................................................................................

QUESTIONS TO BE ANSWERED IN SETTING UP AN

EVALUATION......................................................................

CORE DAMAGE FREQUENCY INCREASE DUE TO AGING:

MINIMAL MAINTENANCE VERSUS RISK-DIRECTED

CONTROL.....................................................................................

RELATIVE CORE DAMAGE FREQUENCY INCREASE DUE

TO AGING: MINMAAL MAINTENANCE VERSUS

RISK-DIRECTED CONTROL.......................................................

TOM DEPENDENT CORE DAMAGE FREQUENCY

INCREASE AC DUE TO AGING................................................

UNCERTAINTY ANALYSIS OF AGING EFFECTS: PLANT A

2

5

11

13

14

60

102

102

109

114

ix
LIST OF FIGURES CONTINUED

FIGURE 11.

FIGURE 12.

FIGURE 13.

CORE DAMAGE FREQUENCY INCREASE FOR A

PLAUSIBLE RANGE OF AGING REPLACEMENT AT

FAILURE: MONTHLY TESTING ............................................. 120

CORE DAMAGE FREQUENCY INCREASE FOR A

PLAUSIBLE RANGE OF AGING: REPLACEMENT AT

FAILURE: TWO DIFFERENT TEST INTERVALS ...................... 121

CORE DAMAGE FREQUENCY INCREASE FOR A

PLAUSIBLE RANGE OF AGING: REPLACEMENT AT

FAILURE VERSUS REPAIR AT FAILURE: MONTHLY

TESTING....................................................................................... 122

x
LIST OF TABLES

TABLE 1.

TABLE 2.

TABLE 3.

TABLE 4.

TABLE 5.

TABLE 6.

TABLE 7.

TABLE 8.

TABLE 9.

TABLE 10.

TABLE 1 1.

THE DIFFERENCES IN COMPONENT RELIABILITY

TREATMENTS FOR A PSA AND AN APSA.............................

PRIORITIZED COMPONENT AGING CONTRIBUTORS.........

ISSUES ASSOCIATED WITH AN APSA....................................

QUESTIONS AND ALTERNATIVE ANSWERS TO

EVALUATE THE AGING RELIABILiTY EFFECTS OF AN

ACTI ITY ...................................................................................

THE SUCCESSIVE STEPWISE APPROACH FOR PSA

AGING EVALUATIONS.............................................................

THE SUBSTITUTION APPROACH FOR PSA AGING

EVALUATIONS..........................................................................

THE RISK IMPORTANCE APPROACH FOR PSA AGING

EVALUATIONS..........................................................................

TIRGALEX AGING RATES USED FOR ACTIVE

COMPONENTS ................................................ ...........................

LOW SENSITIVITY AGING RATES USED FOR

DOMNINANT CONTRIBUTORS................................................

HIGH SENSUVY AGING RATES USED FOR

DOMNINANT CONTRIBUTORS ...............................................

TIRGALEX SURVEILLANCE TEST EF ICIENCIES ...............

8

10

16

34

49

53

57

72

74

74

76

xi
LIST OF TABLES CONTINUED

TABLE 12A.

TABLE 12B.

TABLE 13A:

TABLE 13B:

TABLE 14A:

TABLE 14B:

CORE DAMAGE FREQUENCY INCREASE FROM ACTIVE

COMPONENTS PLANT A: BASE CASE, SINGLE

CONTRIBUTIONS.......................................................................

CORE DAMAGE FREQUENCY INCREASE FROM ACTIVE

COMPONENTS PLANT A: BASE CASE, DOUBLE

CONTRIBUTIONS......................................................................

CORE DAMAGE FREQUENCY INCREASE FROM ACTIVE

COMPONENTS PLANT A: UPPER BOUND CASE,

SINGLE CONTRIBUTIONS........................................................

CORE DAMAGE FREQUENCY INCREASE FROM ACTIVE

COMPONENTS PLANT A: UPPER BOUND CASE,

DOUBLE CONTRIBUTIONS......................................................

CORE DAMAGE FREQUENCY INCREASE FROM ACTIVE

COMPONENTS PLANT A: LOWER BOUND

CASE, SINGLE CONTRIBUTIONS............................................

CORE DAMAGE FREQUENCY INCREASE FROM ACTIVE

COMPONENTS PLANT A: LOWER BOUND CASE,

DOUBLE CONTRIBUTIONS......................................................

80

81

82

83

84

85

TABLE 15. COMPONENT IDENTIFIERS ..................... - . 87

TABLE 16.

TABLE 17.

COMPONENTS PRIORITIZED BY ORDER OF MAGNITUDE

CONTRIBUTION: BASE CASE.................................................

COMPONENTS PRIORITIZED BY ORDER OF MAGNITUDE

CONTRIBUTION: UPPER BOUND CASE...............................

89

90

xli
I U.S. NUCLEAR REGULATORY.

PACKING SLIP

COMMISSI ON DATE: 08/25/93

USNRC

Jo VORA

217B NLS

ORDER NUMB: A65617-00006

ORDER TYPE: 2

DOCUMENT NO.

NUREGCR5587,

TOTAL DOCUMENTS ORDERED

TOTAL DOCUMENTS ENCLOSED

QTY a COST TOTAL COST COMMENTS

-5

5

5
LIST OF TABLES CONTINUED

TABLE 18. COMPONENTS PRIORITIZED BY ORDER OF MAGNITUDE

CONTRIBUTION: LOWER BOUND CASE.............................

TABLE 19. RELATIVE ORDERING OF THE COMPONENT

CONTRIBUTORS: COMBINATION OF THE THREE CASES.

TABLE 20. ABSOLUTE ORDERING OF THE COMPONENT

CONTRIBUTORS: COMBINATION OF THE CASES...............

TABLE 21A. CORE DAMAGE FREQUENCY INCREASE FROM ACTIVE

COMPONENTS PLANT A: BASE CASE, SINGLE

CONTRIBUTIONS......................................................................

TABLE 21B. CORE DAMAGE FREQUENCY INCREASE FROM ACTIVE

COMPONENTS FOR PLANT A: BASE CASE, DOUBLE

CON BUTIO NS .....................................................................

TABLE 22A. CORE DAMAGE FREQUENCY INCREASE FROM AGING

ACTIVE COMPONENTS PLANT A: FIRST

RISK-DIRECTED STRATEGY, SINGLE CONTRIBUTIONS....

TABLE 22B. CORE DAMAGE FREQUENCY INCREASE FROM AGING

ACTIVE COMPONENTS PLANT A: FIRST

RISK-DIRECTED STRATEGY, DOUBLE CONTRIBUTIONS..

TABLE 23A. CORE DAMAGE FREQUENCY INCREASE FROM AGING

ACTIVE COMPONENTS PLANT A: SECOND

RISK-DIRECTED STRATEGY, SINGLE CONTRIBUTIONS...

TABLE 23B. CORE DAMAGE FREQUENCY INCREASE FROM AGING

ACTIVE COMPONENTS PLANT A: SECOND

RISK-DIRECTED STRATEGY, DOUBLE CONTRIBUTIONS..

91

92

93

95

96

98

99

100

101

TABLE 24. RELATIVE AGING FAILURE RATE CATEGORIES................ 118

xiii
EXECUTIVE SUMMARY

Overview

Explicit consideration of the risk effects of aging has been an important feature of the

Nuclear Plant Aging Research (NPAR) program being conducted by the Office of

Research of the Nuclear Regulatory Commission. By explicitly considering the risk

effects of aging, aging contributors can be prioritized according to their risk importance.

The aging contributors include active and passive components which are susceptible to

aging and include the aging mechanisms and stressors which can cause component aging.

By prioritizing aging contributors according to their risk effects, aging research and

aging activities can thereby be focused on the risk important areas.

In addition to risk prioritizing the aging contributors, explicit consideration of the risk

effects of aging allows aging management schemes to be explicitly evaluated for their

risk effectiveness in controlling aging. Scheduled maintenance, corrective maintenance,

operational testing, and condition monitoring can all be evaluated for their risk

effectiveness in specific situations. Risk effective combinations of activities and risk

effective schedules can thereby be identified. Furthermore, by focusing on the risk

importance contributors, the risk effective aging management strategies can be made cost

effective.

Finally, explicit consideration of the risk effects of aging allows component failure data

to be evaluated for aging effects and associated risk implications. Aging of single

components and simultaneous aging of multiple components exhibited in data can be

evaluated for their risk effects. Because the risk effects of aging are not necessarily

additive, the risk effects of aging of a single component can be insignificant but the same

aging exhibited by several components can be extremely risk significant. The risk

significant aging effects exhibited in data are of high priority and their causes need to be

evaluated to assure that research programs and aging management programs focus on

these causes.

xv
Age-Dependent Probabilistic Safety Assessments

Because of the usefulness and importance of explicitly considering risk effects of aging,

the NPAR program supported the development of a methodology for age-dependent

probabilistic risk assessments (PRAs) and age dependent probabilistic safety assessments

(PSAs). This report describes the procedures which have been developed for

transforming a PRA or a PSA to an age-dependent evaluation. A probabilistic risk

assessment, or PRA for short, has become a standard approach for modeling and

quantifying accidents and their consequences which can occur at a nuclear power plant.

A probabilistic safety assessment, or PSA for short, is a PRA which focuses on accidents

leading to core damage and which quantifies the core damage frequency, but does not

extend the evaluations to quantify the associated consequences, such as the expected

manrem released. The age-dependent approaches which have been developed to date in

the NPAR program have focused on age-dependent PSAs, however the general

approaches are also applicable to age-dependent PRAs.

There are three basic differences between a standard PSA and an age-dependent PSA, or

an APSA as we will term the age-dependent PSA. These three differences, which also

apply to a PRA, are listed below:

1. An APSA explicitly models aging effects in component failure rates, which generally

cause the failure rates to increase with age, while a standard PSA assumes component

failure rates are constant.

2. An APSA explicitly models the effects of test and maintenances in controlling the

aging of components while a standard PSA does not.

3. An APSA explicitly calculates the aging effects and age dependence on the core

damage frequency and system unavailabilities, while a standard PSA does not and

instead calculates constant values for the core damage frequency and system

unavailabilidies.

The Uses of Age-Dependent PSAs

Because an age dependent PSA, or APSA, explicitly models and evaluates aging effects

on the core damage frequency and system unavailabilities, an APSA can be used in

xvi
various ways to evaluate the risk effects of aging.' Three of the principal uses are listed

below:

1. Aging effects on passive and active components can be explicitly prioritized with

regard to their resulting impacts on core damage frequency and risk. Aging control

activities can thus focus on the risk important aging contributors.

2. The risk effectiveness of given aging management programs, including specific test

and maintenance strategies, can be explicitly evaluated and risk effective strategies can

be identified.

3. Failure data and other experience data at a plant can be input to an APSA to monitor

aging effects on risk to provide feedback to the aging management program being

conducted at the plant.

Issues Associated with Age-Dependent PSAs

The issues associated with an APSA generally involve a lack of data to accurately

determine the aging component failure rates and a lack of test and maintenance aging

control information. At the present time, age dependent component failure rates and test

and maintenance aging control parameters are indeed very sparse. Because of the present

lack of data, the work in the NPAR program has focused on developing approaches

using APSAs which do not necessarily require accurate data. The emphasis of the work

has consequently been on prioritization of aging contributors and sensitivity studies of

aging effects and of aging management program effectiveness which do not necessarily

require precise data or information. This report describes the specific procedures which

have been developed for carrying out APSA evaluations with this emphasis.

Approaches for Age-Dependent PSAs

An earlier NUREG, NUREG/CR-5510 (1), was published in June 1990 and described the

basic methodology that was developed in NPAR for age dependent PSAs or APSAs.

However, detailed procedures for utilizing APSAs for specific evaluations were not

"Risk" is used in a general context here and includes the core damage ferquency, as well as public

health risks.

xvii
covered. This report describes these detailed approaches, and specific evaluations that

can be carried out using presently available information. The chapters of the report are

summarized below:

1. The Age-Dependent PSA Versus the Standard PSA

The differences between an APSA and a standard PSA, which were summarized in the

previous discussions, are described in some detail in this first chapter. The table on the

next page highlights these differences.

2. Component Reliability Models Used in an Age-Dependent PSA

This chapter describes specific aging component failure rate models and specific test and

maintenance aging control models which can be used in an APSA. The aging failure rate

models which are described cover the spectrum of aging behaviors which are likely to be

exhibited by nuclear plant components and include the Weibull failure rate model, the

linear failure rate model, and the exponential failure rate modeL The test and

maintenance models which are presented cover the spectrum of aging renewal activities

which can occur at a plant and include corrective maintenance models, preventive

maintenance models, and piecepart maintenance models. 1

3. Approaches for Transforming a PSA into an Age-Dependent PSA

This chapter describes three approaches that can be used to incorporate aging evaluations

into a standard PSA to transform it to an APSA. Procedures for each approach are given

along with the strengths and limitations of the approach. One of the approaches is the

approach described in NUREG/CR-5510, which provides detailed aging contributor

prioritizations, including multiple component aging effects. In this prioritization

approach, appropriate risk importance coefficients are extracted from the standard PSA

and are combined with component aging models. Hence, the approach is efficient since

existing PSAs can be directly used with minimal requantification required.

4. Applications of an Age-Dependent PSA

This chapter describes the different applications of an APSA and the questions that need

to be addressed in setting up any application. The figure on page xvi presents the

specific questions that need to be addressed to determine the specific aging models and

XVIII
THE DIFFERENCES BETWEEN A STANDARD PSA AND AN AGE

DEPENDENT PSA (AN APSA)

I

PSA APSA

Component Failure Constant Age-Dependent

Rates Failure Rates Failure Rates

Surveillance Tests Only Affects Component Effects on Component Age

. ~~Up or Down Status Also Modeled

Maintenances Only Component Effects on Component

Downtimes Considered Age Also Modeled

Repairs Does Not Affect Age Effects on Component Age

Also Modeled

Risks Results Calculated Do Not Explicitly Explicitly Accounts

Account for Aging for Aging Effects

Prioritizations of Based on Constant Risk Aging Contributors

Contributions Contributions Explicitly Identified

Maintenance Maintenance Downtimes Benefit of Maintenance in

Effectiveness Evaluations Only Explicitly Evaluated Controlling Aging Also

:______ _ for Risk Effects Evaluated

xix
QUESTIONS TO BE ANSWERED IN SETTING UP AN

APSA EVALUATION

Available aging failure rate data?

. - ~~~~~~~~~~~~~~~~~~~~~i 

plant

specific

I I

generic

I

Available test and maintenance information?

subjective data

I

detailed

information

I I

minimal

information

I

Available PSA information?

event trees and

fault trees

I

truncated

minimal

I n cut sets

Results of most interest?

bottom line

numbers

I I

pnoritizaton

and sensitivies

xx
approaches that are most effectively used. As shown in the figure, the four questions that

need to be asked involve the component aging failure rate data which is available, the test

and maintenance information which is available, the standard PSA information which is

available, and the aging results which are of most interest The specific aging models

and approaches which are most effective for each possible answer to the questions are

defined. What is identified from these descriptions is the aging models which are

available for a given application, and the applications which can be carried out, when

there is little to detailed aging data and information.

5. Prioritization ofAging Contributors

This chapter demonstrates the use of an APSA to prioritize aging contributions with

regard to their risk impacts. This application is important since it can provide a basis for

focusing aging management activities. Those aging contributors which have significant

risk impacts are most important and need priority attention. Prioritization procedures are

described along with interpretation of the results. The tables on the next page illustrate a

prioritization which is obtained as a part of a demonstration using a plant specific PSA.

The components in the plant are prioritized in terms of the average increase in core

damage frequency AC which is caused by component aging between replacements of the

components. The average increase AC applies to each year, and the new core damage

frequency for any year is CO + AC where CO is the baseline PSA core damage frequency.

Every component in the PSA is prioritized for its aging contribution to core damage

fiequency and every interaction of aging components is also prioritized for the

interaction contribution.

The two tables on the next page show the top 90% individual component aging

contributors and the top 90% two-component aging interactions for given aging data.

The tables rank the contributors, beginning with the highest aging contributor to the core

damage frequency (cdf). In the top table, the component name as used in the standard

PSA is given along with the importance of the component (I) as calculated from the

standard PSA. The component unavailability q and the increase in component

unavailability Aq due to aging are then given. The aging contribution to the core damage

frequency AC is given in the last column and is the increase in core damage frequency

(above the PSA value) caused by aging of the component The aging contribution AC is

simply the product of the importance I of the contributor and the aging effect on the

contributor Aq which is extremely useful for applications. The table below is similar

xxi
TABLE 1. DOMINANT SINGLE COMPONENT AGING CONTRIBUTORS FOR A SPECIFIC BWR

(ACTIVE COMPONENTS ONLY)

Component Component Aging

Rank Component ID importance I Unavailability Factor AC

q Aq Y/yr)

I ESW-AOV-CC-CCP 9.70E0S 1.OE-03 2.9EO1 2.8E-0S

2 EHV-AOV-CC-CCP 6.34E-0S .OE-03 2.9B-O1 t.8E-OS

3 ESW-AOV-CC-0241B 3.68E-0 1.OE-03 2.9E-01 I.IE-OS

4 ESW-AOV-CC-0241C 3.68E-05 1.OE-03 2.9E-01 1.1E-05

5 EHV-SRV-CC-RV2 2.53E4OS 3.OE-04 2.9E-01 7.OE-06

6 EHV-SRV-CC-RV3 2.5 3E-05 3.OE-04 2.9E-01 7.OE-06

7 DCP-BAT-LP.CCF -2.16E-04 1.08E-03 1.9E-02 4.1E-06

8 Ha-MOV-CC-MV14 SA2E-06 3.OE-03 2.6E-01 1.4E-06

9 HCI-MOV-CC-MV19 5.42E-06 3.OE-03 2.6E01 IAE-06

10 ACP-DGN-FR-EDGC 2.09E-0 1.6E02 3.3E-OQ 7.OE-07

AC = Core damage frequency increase due to aging

TABLE L DOMINANT DOUBLE COMPONENT AGING INTERACTIONS FOR A SPECIFIC BWR

(ACTIVE COMPONENTS ONLY)

Joint Aging Aging

Rank Component ID Component ID Imponance I Factor Factor AC

_ _ql Aq2 O

I ESW-AOV-CC-0241B ESW-AOV-CC-0241C 134E-03 2.9E-01 2.9E-01 1.I-04

2 ACP-DWN-LP-EDGB ESW-AOV-CC-424IC 8.50E-04 3.3E2- 2.9E-01 8.1E-06

3 ACP-DGN-LP-EDGC ESW-AOV-CC-0241B 8.50E-04 3.3E-02 2.9E-01 8. IE-06

4 ACP-DON-LP-EDGC EHV-SRV-CC-RV2 7.69E-04 3.3E-02 2.9E-01 7.1E-06

5 ACP-DGN-LP-EDGB EHV-SRV-CC-RV3 7.69E-04 3.3E-2 2.9E-01 7.1E-06

6 ACP-DGN-FR-EDGC ESW-AOV-CC-0241B 4.79E-04 3.3E-02 2.9E-01 4.6E-06

7 ACP-DGN-FR-EDWB ESW-AOV-CC-0241C 4.79E-04 3.3E-02 2.9E-01 4.6E-06

8 ACP-DWN-FR-EDWC EHV-SRV-CC-RV2 4AOE-04 3.3E-02 2.9E-01 4.12-06

9 ACP-DGN-FR-EDGB EHV-SRV-CC-RV3S 4.40E-04 3.3E-02 2.9E-01 4.1E-06

10 ACP-DGN-FR-EDGB ACP-DGN-FR-EDGC S.34E-04 3.3E-02 3.3E-02 5.9E-07

AC = Core damage frequency increase due to aging

xxii
except the importance I is the joint importance of the two contributors from the PSA.

The aging contribution AC represents the additional core damage frequency increase

from the simultaneous aging of the components. AC is the product of the joint

importance I and the two aging effects on the components ( Aql and Aq2).

As demonstrated in the tables, it has generally been found that relatively few aging

contributors dominate, even though many components may be aging. The importance of

the contributor (I) as given by the PSA and the aging effect in the contributor (Aq) must

both be properly taken into consideration to obtain the aging contribution to the core

damage frequency. The procedures presented do this proper evaluation. Furthermore,

the aging interactions from the simultaneous aging of multiple components must be

considered since these interactions are nonlinear and are often the dominate aging

contributions, being often larger than the single component aging contributions.

Prioritization of aging contributors does not necessarily require precise data and can be a

powerful tool to focus aging management activities.

6. Identification of Risk-Directed Aging Management Strategies

Once aging contributions are prioritized, aging management programs can be directed to

the dominant risk contributors. This chapter illustrates how risk-directed aging

management strategies can be defined and can be evaluated. The aging contributors

prioritized in the previous chapter are used to define two alternative risk-directed

maintenance and replacement programs. By carrying out more frequent maintenances

and replacements on the 24 dominant components, it is shown that the aging effects on

core damage frequency are basically controlled so as to be less than the baseline core

damage frequency.

7. Time dependent Aging Evaluations

This chapter describes how detailed time dependent aging results can be obtained from

the PSA using the models and approaches given in the previous chapters. Detailed time

plots are obtained showing the progression of aging impacts on the core damage

frequency and system unavailabilities. The time dependent results show when in a

plant's lifetime aging effects will become significant from a risk standpoint and when

actions need to be taken. Examples are given for a specific plant showing aging effects

having significant impacts on the core damage frequency at a plant age of 15 years

Xxiii
because of insufficient maintenances and replacements on the risk dominant components.

Once the contributors are identified the aging impacts are controllable.

8. Sensitivity and Uncertainty Evaluations

Another important use of an APSA is for sensitivity and uncertainty evaluations of the

risk effects of aging. Even where aging data are sparse, appropriate sensitivity and

uncertainty evaluations can provide useful information on aging sensitivities and on the

risk effectiveness of aging management programs. In this chapter, procedures are

demonstrated for carrying out sensitivity and uncertainty analyses to evaluate plant

sensitivities to aging, to evaluate capabilities of aging management programs, and to

identify aging management strategies which effectively control risks from aging over a

spectrum of plausible aging behaviors.

The figure on the next page illustrates a sensitivity study that is demonstrated to evaluate

two policies: repair at failure versus replace at failure. Under a repair policy, when a

component fails then minimal repairs are made; aged pieceparts are not replaced but are

again made operational. For a replacement policy aged pieceparts are replaced with new

parts at failure. The y-axis (AC) is the average increase in core Oamage frequency over

40 years due to aging, where AC is the increase above the standard PSA core damage

frequency value. The average increase AC again applies to each year. The x-axis is the

plausible range of aging exhibited by the components, expressed as a relative percentage

increase per year in the component failure rate due to aging.

For the sensitivity study, all components were assumed to have the same relative aging.

The same surveillance test intervals were assumed for both policies. The figure shows

that the replacement policy controls the core damage frequency increase due to aging for

a wide range of plausible aging behaviors. The repair policy does not control the risk

effects due to aging, even for relatively small aging behaviors. From the prioritization of

aging contributors, which can be carried out in parallel, the dominant aging contributors

can be identified and replacements only carried out on the important contributors. Thus,

an effective aging management policy can be identified which does not necessarily entail

major costs. Similar sensitivity studies can be carried out for other proposed aging

management programs or maintenance programs.

xxiv
CORE DAMAGE FREQUENCY INCREASE: REPLACEMENT VERSUS REPAIR AT FAILUIRE

1.OE-02

AC 1.OE-03 ........ .

1.OE-04 .....

1.OE-046....____________

1 .O -0 E 7 . . . ... . .. .. I .. . . .. .. .I . .. .. . . . .. .. .. . . . ... . . . . ... . . . . I.. .. . . . ... . ... . 0%................% ....... 50%.........................100%I......... .... . Relative....... Aging...... Rate.... (%..................in...Failure.......Rate....Per Year)... ...
9. Considerations in Using a PSA to Evaluate the Risk Effectsfrom Aging of Passive

Components

Finally, this chapter discusses special considerations, beyond those already discussed, for

evaluating the risk effects from aging of passive components. The discussions focus on

more detailed analyses which can be done to estimate passive component aging failure

rates from basic phenomenological models covering crack growth and corrosion. It is

planned that this subject will be covered in greater depth in a subsequent report

Conclusions

The report which has been developed presents detailed models and systematic procedures

for incorporating aging evaluations into a probabilistic safety assessment (PSA) to

explicitly evaluate the risk effects due to aging. The approaches can also be applied to a

probabilistic risk assessment (PRA). The resulting age-dependent PSA (or age

dependent PRA) will allow a spectrum of important applications to be carried out,

including prioritization of aging contributors according to their risk importance,

evaluation of the risk effectiveness of existing aging management programs, and

identification of risk effective aging management policies. Even when aging data are

sparse, applications can be carried out to identify the potentially dominant aging

contributors, the risk sensitive maintenance practices, and the robust programs which can

be carried out to control aging impacts over ranges of plausible aging behaviors that can

exist.

xxvi
ACKNOWLEDGEMENTS

Acknowledgement is given to G.H. Weidenhamer, the NRC project monitor, for

providing competent and practical direction to the work and to LP. Vora of the NRC for

his ideas and inspirational guidance. Acknowledgement is given to P. Kafka,

GeselIschaft fur Reactorsicherheit (GRS) mbh, for his discussions with the author on the

reliability treatments of passive components. Finally, acknowledgement is given to S.M.

Scalzo for her invaluable assistance in preparing this report.

xxvii
1. THE AGE-DEPENDENT PSA VERSUS THE STANDARD PSA

1.0 Introduction

This report describes procedures for explicitly incorporating component aging

evaluations into a probabilistic safety assessment of a nuclear power plant. A

probabilistic safety assessment, or PSA as it is termed, is a probabilistic model of

accidents which can occur at a nuclear plant which can lead to core damage. A PSA

focuses on the evaluation of the core damage frequency as opposed to a probabilistic risk

assessment (PRA) which also evaluates the resulting consequences and health risks from

a core damage event.

Figure 1 is an overview of the basic steps in a PSA. A set of initiating events is first

identified which require safety system responses. For each initiating event, an event tree

is constructed to define the sequences of system responses (success or failure) which can

occur for the given initiating event. The consequence of each sequence in the event tree,

in terms of whether a core damage occurs or not, is determined from plant response

considerations.

For each defined system failure in the event tree, a fault tree is constructed to identify the

basic component failures which can cause the system failure. The fault tree is used to

quantify the system failure probability using component reliability models and

component data. Human errors, test contributions, and maintenance contributions are

included as causes of components being down, in addition to failure causes. The system

fault trees are incorporated into the event trees to identify the component contributors to

the accidents and to quantify the accident sequence frequencies using component data.

The frequencies of the individual accident sequences leading to core damage are finally

summed to provided the core damage frequency. Additional details for carrying out a

PSA or PRA are given in References 1-3, including specific models and formulas which

are used, along with associated computer programs.

In standard PSA evaluations, aging of components is not explicitly included in the

component failure models which are used to quantify the system failure probabilities and

the core damage frequency. When the effect of component aging is to be specifically

evaluated then the standard PSA component failure models need to be modified. Aging

of components can significantly increase the component failure probabilities and can

1
Safety Functions

IE IE

.....................> ..............

Identify and Categorize

Initiating Events (IE's) Develop Functional

Event Trees ..................................................................................................................................................................

IE 61

>..............> ................

Develop System Develop System

Event Trees Fault Trees ................................................................................. .................................................................................................................. ........................................

Importance

'...................{ CDF

Integrate Fault Trees Determine Core Damage

into Event Trees Frequency and Contibutors

FIGURE 1. BASIC STEPS IN A PSA
significantly increase the core damage frequency, if the aging is not effectively

controlled by tests and maintenances. The next section, Section 1.1, briefly describes the

differences in component failure treatments which are needed when aging is to be

explicitly evaluated using the PSA. This area is described in further detail in Chapter 2.

Standard PSAs also do not explicitly model the effectiveness of tests and maintenances in

controlling aging effects. When the effect of aging is to be explicitly evaluated by the

PSA then the standard PSA models for test and maintenance need to be modified to

explicitly consider their effectiveness in controlling and mitigating aging effects. Section

1.2 briefly describes the differences in test and maintenance treatments that are needed to

evaluate the aging control of test and maintenance activities. Detailed treatments are

again provided in Chapter 2.

When aging effects are explicitly included in the PSA by using component aging failure

models and test and maintenance aging control models then the PSA is transformed to an

age-dependent PSA. As an abbreviation for an age-dependent PSA we shall use the term

"APSA" where the first "A" denotes "Age-Dependent". The results which are obtainable

from an APSA and the applications of an APSA are highlighted in Section 1.3. Finally,

as the last part of Chapter 1, special modeling and evaluation issues associated with an

APSA are highlighted in Section 1.4. Chapter 1 thus provides an overview of the

differences between a PSA and an APSA.

Chapter 2 describes the detailed component models and test and maintenance models

which can be used in an APSA. The focus of Chapter 2 is on modeling the reliability

effects of aging of active components, such as pumps, valves and circuit breakers. The

aging failure rate models in Chapter 2 can also be applied to passive components,

however the aging failure rates may need to be determined using techniques different

from those used for active components. Chapter 3 describes procedures for actually

transforming a PSA to an APSA. Chapter 4 describes different applications of an APSA

and their requirements. Chapter 5 presents example applications of an APSA focused on

prioritizations of aging contributors. Chapter 6 demonstrates how APSA evaluations

can be used toidentify risk-effective aging management strategies. Chapter 7 describes

how time-dependent applications can be carried out using an APSA. Chapter 8

demonstrates how aging sensitivity and uncertainty evaluations can be carried out.

Finally, because the previous chapters focus on active components, Chapter 9 discusses

3
specific considerations for incorporating passive components and their aging impacts into

a PSA. It is planned that a separate report will be issued on the treatment of passive

components in risk evaluations of aging.

1.1 The Difference in the Treatment of Component Failures

The component failure rate is the basic data used in a PSA to determine the failure

probability and the unavailability of a component. Basically, the component failure rate

is the probability of a component failure per unit time given no previous failure. A

standard PSA assumes the component failure rate is constant and is the same value for all

component ages. When aging is explicitly considered then the change in component

failure rate as a function of component age must be considered. An APSA allows the

component failure rate to be a function of age and to change as the component age

increases. The effect of allowing the component failure rate to be age-dependent can

cause significant impacts on the calculated system unavailabilities and the core damage

frequency.

From reliability theory (see References (4-6)) when age dependence is considered then

the component failure rate generally follows a bathtub curve as shown in Figure 2. At an

early component age the failure rate decreases with age as design, manufacturing, and

installation failures are corrected when they are found. This decreasing failure rate

behavior is termed the bum-in period of the failure rate curve. After bum-in, the failure

rate remains constant reflecting steady state failure behavior. This flat portion of the

bathtub is the constant failure rate period of the failure rate curve. Finally, after the

steady state period, the failure rate increases with age, reflecting wear-out and aging

behavior. This is the aging period of the failure rate. The lengths of the bum-in, steady

state, and aging periods of the bath tub curve can vary for different components and for

different operating environments.

A standard PSA assumes a constant failure rate and hence focuses on the steady state

portion of the failure rate curve. An APSA, in addition to the steady state behavior, also

includes the increasing failure rate portion of the failure rate curve and thus can account

4
Bathtub Failure Rate

)(w)

Burn-in Steady State Aging

Agew

FIGURE 2. THE BATHTUB CURVE OF FAILURE RATE VERSUS

AGE

5
for the transition from a constant failure rate to an increasing failure rate.* Chapter 2

presents specific models which can be used to explicitly include aging in the component

failure rate. These models are standard models which are used in the reliability field.

When an APSA explicitly models the increasing component failure rate with age then as

indicated, significant impacts can occur in the calculated risk results. If the test and

maintenance practices do not control the component aging then the component failure

probability and component unavailability can significantly increase with component age

because of the increasing failure rate. This in turn can cause the system unavailability to

increase with age. When the system unavailability increases with age then the core

damage frequency can increase with age. Besides causing unavailabilities to increase,

the increasing component failure rates can cause the accident initiating event frequency

to increase with age, which can also cause the core damage frequency to increase with

age. Whether the increases occur or not, and the sizes of the increases, depends on the

aging control of the test and maintenance practices. The sizes of the unavailability

effects and the size of the core damage frequency effect are explicitly calculated in an

APSA.

1.2 The Difference in the Treatment of Test. Maintenance, and Repair

Since a standard PSA does not explicitly consider the age of the component, the effects

of testing, maintenance, and repair in controlling aging are not evaluated in a PSA. Also,

since a PSA assumes a constant component failure rate which never changes, the effect

of a test, maintenance, or repair activity on the component failure rate is not considered.

The effect of a test and maintenance in controlling the aging of a component is a special

focus of an APSA. The control of aging is evaluated by determining the change in

component age which results from a test or maintenance activity. The effect of a test or

maintenance on the age of the component is important since the component failure rate

depends on the component age. Hence as the component age is modified through testing

and maintenance, the component failure rate is accordingly modified. The failure rate

modifications which occur change the component unavailability and the component

*The burn-in period of the failure rate can also be included, and can be important when there can be

initial design or manufacturing defects in a new component which is used to replace an aged component.

When the component undergoes qualification testing or burn-in testing, as generally carried out for

nuclear plant components, then the burn-in period is generally removed.

6
failure probability which in turn change the system unavailability and the core damage

frequency.

Detailed models for the effects of testing, maintenance, or repair on the component age

are used in an APSA. If the component is replaced with a new component then the age

of the component is set back to the age of a new component. If aged pieceparts are not

replaced then the age of the component is not affected and remains the same. Partial

maintenances which only replace specific pieceparts, but not the entire component, will

cause the age of the component to be set back to a partially restored value. A

preventative maintenance, such as lubricating bearings, will not change the age of the

component since piece parts are not replaced, but will slow the aging process of the

component.

Because of the detailed testing and maintenance models which can be used, an APSA can

comprehensively evaluate the effectiveness of a testing and maintenance program in

controlling component aging and its resulting impacts on system unavailabilities and on

the core damage frequency. Not only is the interval important at which the test or

maintenance is performed, but the specific action which is performed is important.

Chapter 2 describes models which are used in an APSA to model the aging control of

different types of test, maintenance and repair activities. Even when minimal

information exists, these models can be useful for evaluating maintenance sensitivities.

It is important to note that because a standard PSA does not model the removal of aging

effects by maintenance, it can not explicitly model any benefits from maintenance. Only

the negative downtime contribution while maintenance is being performed is explicitly

modeled in a PSA. Thus, only the negative effect due to maintenance is explicitly

modeled. An APSA models both the benefits and negative effects of maintenance.

These effects determine the unavailabilities and core damage frequency which result.

Specific formulas for calculating the unavailabilities, and specific approaches to

determine the core damage frequency are given in the subsequent chapters. Table 1

summarizes the differences in test and maintenance treatments and in component failure

treatments, which are together classified as differences in component reliability

treatments, for a PSA and an APSA.

7
TABLE 1. THE DIFFERENCES IN COMPONENT RELIABILITY

TREATMENTS FOR A PSA AND AN APSA

PSA APSA

Failure Rate Model Constant failure Age dependent or time

rates are used. dependent failure rates are

also used.

Test Model A test only determines A test can affect

whether component is up component age and failure

or down. rate as well as determining

whether component is up

or down.

Maintenance Only downtime for Effects of maintenance in

maintenance is considered. correcting degradations

and aging are modeled, as

well as inefficiencies and

downtime.

Repair Model Repair does not affect the After repair, the age and

age or failure rate of failure rate of component

component. are modified with

appropriate models.

8
1.3 Results Obtainable from an APSA

As for a PSA, the core damage frequency, accident sequence frequencies, and safety

system unavailabilities are obtainable from an APSA. For an APSA, however, these

results now explicitly include the contributions from aging and explicitly quantify the

effectiveness of given test and maintenance programs in controlling aging effects.

An APSA can produce detailed prioritizations of the aging contributors. This is perhaps

one of the most important uses of an APSA since it allows one to focus on the dominant

aging contributors for aging control, for data collection and monitoring, and for

additional analyses. Table 2, for example, ranks the top 95% individual aging

component contributors for a given APSA evaluation. Each line entry gives the rank

(column 1), the specific component (column 2), the risk importance of the component

(column 3), the component unavailbility (column 4), the increase in component

unavailability due to aging (column 5), and the core damage frequency contribution from

the component aging (column 6). As can be seen, for this application the top 95%

contributors consists of only 10 components, and hence relatively few components

contribute to the aging impacts on the core damage frequency, a1lowing one to

effectively focus aging analyses and aging control. Details of prioritization evaluations

of aging contributors are given in Chapter 5. Chapter 6 describes how the prioritized

contributors can be used to identify risk-effective, and cost-effective, aging management

programs.

An APSA can calculate the core damage frequency and system unavailabilities as a

function of plant age to explicitly show the dynamic, time dependent aging effects. The

core damage frequency and system unavailabilities averaged over time periods or

averaged over the plant age can also be obtained to show average aging effects. The

increases in the core damage frequency or system unavailabilities due to aging as

compared to the no aging case can furthermore be obtained to highlight aging increases.

Figure 3, taken from NUREG/CR-5510 (7), shows the average increase in core damage

frequency AC that results from aging at a plant when different test and maintenance

programs are carried out. The average increase AC applies to each year and the overall

core damage frequency for any year is CO + AC, where CO is the baseline core damage

frequency from the PSA. The specific test and maintenance programs are not of concern

.9
TABLE 2. PRIORHTIZED COMPONENT AGING CONTRIBUTORS

Component Component Aging

Rank Component ID Importance I Unavailabity Factor AC

q Aq (/-V)

1 ESW-AOV-CC-CCF 9.70E-05 1.OE-03 2.9E-01 2.8E-05

2 EHV-AOV-CC-CCP 6.34E-05 1.OE-03 2.9E-01 1.8E-05

3 ESW-AOV-CC-0241B 3.68E-05 1.0E-03 2.9E-01 1.IE-05

4 ESW-AOV-CC-0241C 3.68E-05 1.0E-03 2.9E-01 l.IE-05

5 EHV-SRV-CC-RV2 2.53E-05 3.0E-04 2.9E-01 7.OE-06

6 EHV-SRV-CC-RV3 2.53E-05 3.QE-04 2.9E-01 7.0E-06

7 DCP-BAT-LF-CCF 2.16E-04 1.08E-03 1.9E-02 4.lE-06

8 HCI-MOV-CC-MV14 5.42E-06 3.0E-03 2.6E-01 1.4E-06

9 HCI-MOV-CC-MV19 5A2E-06 3.0E-03 2.6E-01 1.4E-06

10 ACP-DGN-FR-EDGC 2.09E-05 1.6E-02 3.3E-02 7.0E-07

AC = Core damage frequency increase due to aging

10
FIGURE 3. INCREASE IN CORE DAMAGE FREQUENCY FROM AGING FOR DIFFERENT

TEST AND MAINTENANCE PROGRAMS

Plant A

1 .OE-O1

1 .OE-02

1.OE-03 0 Ac

(eyr)

1.OE-04

1 .OE-05

0

o~ ~~~~~~~~~~~~ :

Baseline

_ Core Melt

Frequeny

(per yr)

L=72

1.OE-061

- - - - 1. 0 1- 0 7l ~

L=1 8 T=1 L=72 T=1- L=18 L=72 T=6

-

Program Characterization

L = Overhaul interval (in months) for all components

T = Surveillance interval (in months) for all components (if intermediate surveillance is performed)
here. Test and maintenance modeling is discussed in Chapter 2. The different points for

a test and maintenance program represent different possible component aging failure

rates. The results indicate the significant differences that different test and maintenance

programs can have in controlling-aging effects.

Figure 4 illustrates the type of time dependent results which are also obtainable from an

APSA. The figure shows the time dependent core damage frequency increase due to

aging for given component aging failure rates and for a given test and maintenance

program. The sudden drops in the core damage frequency in Figure 4 occur when major

components are replaced in the test and maintenance program. Such time dependent

results can show when in a plant's life, aging effects become significant and whether

components are being replaced or being overhauled frequently enough. The core damage

frequency becomes so high in Figure 4 because key components are not replaced

frequently enough, allowing aging effects to build up to relatively high levels. Chapter 7

describes the application of time dependent aging evaluations.

Sensitivity and uncertainty analyses can also be carried out using an APSA to evaluate

the core damage frequency sensitivities and uncertainties associated with aging effects.

Figure 5 shows the results of a sensitivity analysis which evaluates the aging control of a

given test and maintenance program. For the sensitivity analysis, the component aging

failure rates are systematically increased to account for plausible aging which can occur.

The baseline core damage frequency for the plant is 3x1I5 per year. As can be

observed, the aging control of this particular test and maintenance program is effective

over a plausible range of aging behaviors, limiting the aging increases to be no larger

than the baseline core damage frequency. Chapter 8 provides further details.

In this report we focus on the use of an APSA for prioritizing aging contributors and for

carrying out sensitivity and uncertainty analyses of aging effects. The models and

approaches which are presented however, can also be used to obtain average core damage

frequency results due to aging or time dependent core damage frequency results due to

aging.

12
FIGURE 4. TIME DEPENDENT CORE DAMAGE FREQUENCY INCREASE DUE TO AGING

AC

(per)

0 100 200 300 400

Plant Age (Months)

500
FIGURE 5. SENSITIVITY ANALYSIS EVALUATING THE AGING CONTROL OF A GIVEN

TEST AND MAINTENANCE PROGRAM

MONTHLY TEST

REPLACEMENT AT FAILURE

3.5E-05

AC3.OE-05., /

AC

(Per Year)

1 . E 0 . . . . .. . . . .. . . . .. . . .. . . .. . . . . . . . .. . . .. . . . .. . . . .. . . . .. . . .. . . . .. . . . .. . . . .. . . .

1 . E 0 . . . .. . . .. . . .. . . ... . .. . . .. . . .. . . .. . . . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . .... . .

5.OE-06 _... . ...

O.OE+00 l I I

0% 25% 50% 75% 100%

Aging Rate (o Change in Failure Rate)
1.4 Issues Associated with an APSA

An APSA requires more data and more extended models than a PSA and hence there are

special issues associated with using an APSA. With regard to data, the basic issue is the

present, general sparseness of failure histories for components and for structures.

Because of this sparseness of failure data, aging failure rates which are estimated from

the raw data will generally have large associated uncertainties. In addition to the

imprecision in failure rate values, the shape of the aging failure rate curve will often not

be known. When'there is no plant specific data available, generic data or expert opinions

will need to be used, which will also generally have large uncertainties. These

uncertainties need to be taken into account in using an APSA for a given application.

The most thorough way of treating these uncertainties is to carry out sensitivity studies or

uncertainty analyses using different aging failure rates. Chapter 8 will illustrate how

such studies can be carried out. Even with little precise aging failure rate data, useful

information can be obtained from an APSA regarding important aging contributors and

sensitivities to aging effects, as will be discussed in the subsequent chapters.

At present, there can also be a lack of information on detailed characteristics of specific

tests and maintenances incontrolling aging to allow their precise modeling in an APSA.

Where information is lacking, approximate models may be used to approximate or bound

the effects of the test or maintenance in controlling aging. Examples of approximate or

bounding models are the "good as old" and "good as new" models as termed in reliability

literature. These models are presented in subsequent chapters. More precise test and

maintenance models are also presented, which allow more detailed analyses to be carried

out if data is available, or which allow sensitivity analyses to be carried out. By using

these models, the aging control of given test and maintenance practices can also be

bounded or can be accurately evaluated where information is available. Perhaps as

importantly, the sensitivity of risks to aging effects under given test and maintenance

practices can be evaluated. The risk important tests and maintenances can thereby be

determined to focus further evaluations and program improvements. The subsequent

chapters describe the bases for these applications, as well as for other applications. Table

3 summarizes the issues which are associated with an APSA.

'15
TABLE 3. ISSUES ASSOCIATED WITH AN APSA

Data Bases Little time-history information exists to estimate age

dependent or time dependent failure rates. Uncertainty and

sensitivity studies need to account for this lack of data.

Failure Rate Models Different failure rate models can cause significant

differences in the calculated results in an APSA.

Sensitivity studies can investigate these effects.

Test and Differences in the test and maintenance models can cause

Maintenance Models significant differences in APSA results. Bounding models

and sensitivity studies can help address this issue.

Results Results from an APSA can be uncertain. Relative results

and more qualitative results can be focused on to address

this issue. Sensitivity and uncertainty analyses can also

identify the meaningful conclusions and interpretations.

16
2. COMPONENT RELIABILITY MODELS USED IN AN AGE-DEPENDENT

PSA

2.0 Introduction

As described in the previous chapter, what makes an age-dependent PSA, or APSA,

different from a standard PSA is the component failure models and the test and

maintenance models, which together comprise the component reliability models which

are used.

This section describes the component failure models and test and maintenance models

which can be used for an APSA. These models are necessary to explicitly evaluate aging

effects and their impacts on system unavailabilities and the core damage frequency. To

begin the chapter, the definition of aging for reliability and risk applications is presented.

The difference between the component age and running time is then discussed. With

these basic concepts defined, the modeling of the aging component failure rate is

described, and specific aging failure rate models which can be used in an APSA are

given. Features of these models and ways these models can be applied are described.

Models are then presented for quantifying the effects of testing and maintenance with

regard to controlling aging. Specific models are presented which can be applied to

surveillance tests, corrective maintenances, preventative maintenances, and repairs.

These models quantify the different effects a specific activity has on the component age

and its associated aging failure rate. Models for maintenance and repair of component

pieceparts are also included. Complete aging control, partial aging control, and

inefficiencies in aging control are included in these models.

2.1 Definition of Aging for Reliability and Risk Applications

The definition of aging for reliability and risk applications is directly tied to the behavior

of the component failure rate. From basic reliability theory (References 4-6) the

definition of the component failure rate at a given time is:

The component failure rate at a given = The probability of component failure (1)

time t per unit time at time t given no

previous failure of the component

17
The failure rate of a component at time t is thus basically the rate of failure at time t

when the component has not previously failed. The failure rate always applies to a given

failure mode (e.g., fail to open, fail to close, etc.) and different failure modes will have

different failure rates.

The standard symbol used for the component failure rate is (t). Thus,

X(t) = The component failure rate at a given time t, (2)

For aging evaluations, it is also necessary to express the component failure rate as a

function of the component age. Let w denote the component age. Then,

(w) = The component failure rate at a given (3)

component age w.

The definition of X(w) now is in terms of the component age:

U(w) = The probability per unit age that the (4)

component fails at age w given no

previous failure of the component.

The failure rate at age w is thus the rate of failure at the given age when the component

has not previously failed. The failure rate as a function of age can be a different shape

and form than the failure rate expressed as a function of time if time and age are not the

same.

The component failure rate at a given time can be related to the component failure rate at

a given age. To relate time t and age w, the age of a component at a given time needs to

be known. This relationship can be expressed as w = w(t). Then the failure rate as a

function of the age can be translated to a failure rate expressed as a function of time.

This failure rate relationship can be expressed as X(t)dt = X(w(t))dw(t), where X(t) is the

failure rate function versus time and X(w) is the failure rate function versus age, i.e., X(t)

18
is given by Equation (2) and X(w) by Equation (3), which are generally different

functions.*

For usual applications, a point in given time t is simply the component age w plus some

constant c (which is the component installation time). For this usual case, t = w + c and

t) = X(w(t)) which is what we will assume for our applications.

For reliability and risk applications the definition of aging is directly related to the failure

rate as a function of age X(w). For reliability and risk applications, a component (or

structure) is defined to be aging if the failure rate as a function of component age is

increasing:

Aging occurs in the component if the failure rate X4w) as afunction of component age is

increasing.

It is important to note that the definition of aging is related to the failure rate as a

function of age and not as a function of time. The failure rate as a function of age may

be increasing, i.e. may be aging, while the failure rate as a function of time may not. For

aging to occur, the failure rate X(w) does not need to continuously increase with age.

There can be periods in which there is no aging, i.e., in which ;(W) does not increase

with age w. Periods in which the failure rate X(w) is increasing, are aging periods. The

figures below indicate different types of aging which can occur with different types of

age dependent failure rates X(w).

Monotonic Aging

Aw(w 

-- -- Aging Perod--- w

*For simpler notation, the two different functions, L(w) and A(t), are not shown with different symbols.

Which failure rate is being referenced, i.e., versus time or age, will be clear from the discussions.

19
Threshold Aging

/.

wo Aging Period w

Bathtb Aging

Aging Period 

Irregular Aging

Aging Period

20
All the above failure rates exhibit some period or periods of aging. In general, aging

periods at the end of the component age are of most interest and concern because of the

large reliability and risk effects which can result if the aging continues unchecked.

However, aging in any period can cause significant reliability and risk problems.

2.2 Aging Failure Rate Models

Various parametric models exist which can be used to model component failure rate

aging behavior for reliability and risk applications. The models most often used for

aging are the linear aging failure rate model, the Weibull aging failure rate model, and

the exponential aging failure rate model. These models can represent increasingly more

severe failure rate increases with age. Thresholds can be incorporated in any of these

models to represent aging beginning at some nonzero age w.. In general all the standard

parametric models apply to aging periods occurring at the end of the component age with

a possible initial threshold. To model aging periods occurring at earlier ages followed by

some periods of nonaging, the models can be extended by reinitializing the age variable

w or by defining a variable which is a nonlinear function of the age. Equations and

representative graphs for the linear model, Weibull model, and exponential model are

given below for aging occurring after some arbitrary threshold age w0. Subsequent

chapters will discuss how these failure rate models are applied in an APSA.

Linear Aging Failure Rate Model

)(w) X .; w< W. (5)

(w) t + a(w-w.); w w (6)

= initial constant failure rate (7)

a = constant aging rate (8)

w. = threshold age after which the failure rate increases (9)

21
Unear Aging Failure Rate

W0 

Weibull Aging Failure Rate Model

X(W) =ko w < o (10)

A(W)=A°[w ];w>w0 (11)

where

ko = initial constant failure rate (12)

b = Weibull shape parameter (13)

w = threshold age after which the failure rate increases (14)

Other equivalent forms also exist for the Weibull model but the general property is that

the failure rate increases as some power b of the age.

22
Welbuff Aging Failure Rate

b I

bal

b<l

vho w

Exponential Aging Failure Rate Model

X(w) X.0 :w<wO

t(w) = X exp (c(w-wO)): w > wo

= initial constant failure rate

c = exponential scale parameter

and

w. = threshold age after which the failure rate increases

(15)

(16)

(17)

(18)

(19)

23
Exponential Aging Faikire Rate

)()

wO w

2.3 Failure Rate Aging Effects Versus Overall Time Trends

There is sometimes a confusion between failure rate aging effects and an overall time

trend in the component failure behavior. One may, for example, observe no time trends

in the failure behavior as recorded in data and erroneously conclude that there is no

component failure rate aging effects. It is important to understand the difference

between failure rate aging effects and overall time trends in the failure behavior to

properly model aging effects in an APSA.

The overall component failure behavior as a function of time is generally described by

the failure frequency and to understand the difference between failure rate aging effects

and an overall time trend in the failure behavior one must first understand the definition

of the failure frequency:

The component failure frequency = The expected number of component (20)

at time t failures at time t per unit time

Note that the failure frequency is the rate of failure at a given time regardless of whether

the component previously failed or not. The component failure rate as previously

defined by Equations (1) and (4) is the rate of failure from only first failures. The failure

frequency as defined by Equation (20) is the rate of failure from first, second, third, etc.

failures.

24
The failure frequency is sometimes given the symbol f(t):

f(t) = the failure frequency at time t. (21)

The failure frequency can be estimated from failure histories by counting the number of

failures which occur in given intervals of time and dividing by the time intervals.

The component failure rate versus age X(w) can show aging effects while the failure

frequency f(t) versus time may show no overall trends or aging effects. This is because

the failure frequency generally incorporates the effects of test and maintenance and does

not account for any change in component age if the component is replaced or renewed.

The component failure rate versus age on the other hand gives the failure rate behavior

between maintenances and replacements. When a new component is installed the age

starts over but the time doesn't. These differences are important to understand since

confusion on age versus time can result in statements being made that components are

not aging when indeed they are. This confusion can furthermore result in incorrect data

analysis and incorrect aging modeling being carried out.

To more fully understand the difference between failure rate aging effects and overall

time trends in the failure frequency one also needs to consider the impacts of component

renewals. In reliability terms,

A renewal is a restoration of the component age (22)

back to zero, i.e., w = 0.

Also,

At a renewal the failure rate is set back to its original value at age w = 0 and (23)

the aging behavior is restarted.

For reliability applications a renewal is defined in terms of its effect on the failure mode

associated with the component failure rate. If a given piecepart of the component (e.g., a

valve actuator) is the principal contributor to the failure mode and the part is replaced

with a new part, then the component age for that failure mode is effectively reset to zero.

If several parts of the component contribute to the failure rate for a given failure mode

then all the parts will need to be replaced with new parts to reset the failure rate age back

to zero. The figure below illustrates the failure rate behavior between renewals.

25
Falkire Rate Behavior Versus Time

ti t

2 nM t t3 4

1 A times of renewa

Note that what is plotted is the failure rate versus time. The failure frequency f(t) versus

time follows the same behavior and incorporates the effects of the renewals. As a

function of time there is no overall trend since the failure behavior is cyclic. The

component age repeats at each renewal cycle. The relationship of the component age w

with time t is shown below.

Component Age Versus nme

c

0

n

n

a

g

5

tI .J 3A4-*iTSl d HemnA

2 Time 

The failure rate versus age behavior is the behavior in the first renewal cycle which is

then repeated for each renewal cycle. The failure rate versus age behavior for each

renewal cycle is illustrated below.

26
Failure Rate Behavior Versus Age

Age w W-t,

This difference between the failure rate behavior versus age and the failure frequency

behavior versus time, or failure rate behavior versus time, is quite important The failure

frequency behavior versus time and the failure rate versus time show no overall time

trend since the behavior is cyclic. The failure rate versus age increases with age and

shows strong aging behavior.

Sometimes, failure data is analyzed and the failure frequency verss time or failure rate

versus time is obtained. This is then mistakenly interpreted as being the failure rate

behavior versus age. The failure frequency or failure rate versus time may show no

overall trend with time. This is then mistakenly interpreted as the failure rate versus age

showing no aging effects. However, when the failure rate is correctly determined versus

age, then aging effects may be observed. Various data analysis techniques which are

used to analyze data for aging effects actually analyze for overall time trends in the

failure frequency. It is extremely important that the proper data analysis be carried out to

differentiate aging behaviors versus age and overall trend behaviors versus time. Failure

rates versus age are required for an APSA when test and maintenance effects on the age

are explicitly modeled. This will be further amplified in subsequent sections.

Instead of complete component replacements or renewals, partial renewals can also take

place at a maintenance or repair where the failure rate age is not reset to zero but to some

lower but nonzero value. This can correspond to replacement of only specific pieceparts

or replacement of a part, not with a new part but with a rebuilt part. The figure below

27
illustrates the effects of partial renewal on the component. As can be seen, an overall

time trend in the failure frequency now can be seen.

Faiure Rate Behmaic Versus Time:

Between Paral Renewals

ti t2 nm*t t

3 to

2.4 Age Dependent and Time Dependent Component Reliability Results

Age dependent component failure rates are used in an APSA to calculate component

reliability results. The component reliability results are then used to calculate the time

dependent system unavailabilities and the time dependent core damage frequency. The

time dependent system unavailabilities and core damage frequency are calculated with

regard to the plant age which serves as the reference time. Because they are used to

calculate the system unavailabilities and core damage frequency it is important to

understand the component reliability results which are calculated in an APSA.

The component reliability results calculated in an APSA can include the age dependent

component unreliability, the time dependent component unreliability, the age dependent

component unavailability, and the time dependent component unavailability. These basic

quantities define the age-dependent and time-dependent reliability and availability

behavior of the component. Which characteristics are calculated for a particular APSA

depends upon the calculational approach used in the APSA as will be discussed in

Chapters 3.

The age dependent component unreliability is the probability of component failure by a

given age:

28
The age dependent component - The probability that the component (24)

unreliability at age w will fail before age w

The age dependent reliability is one minus the age dependent unreliability and is the

probability that the component will not fail before age w. The symbol sometimes used

for the age dependent unreliability is U(w). Thus,

U(w) The age dependent component unreliability. (25)

From standard reliability theory (References 4-6),

U(w)=l-exp-J(w')dw3 (26)

where X(w') is the age dependent failure rate.

The time dependent unreliability is similar to the age dependent unreliability but is

defined as a function of time:

U(t) = The time dependent unreliability (27)

= The probability that the component will fail (28)

before time t

- 1exp (dt' (29)

where now X(t') is the time dependent failure rate at time t'. As was indicated, the

function X(t') is generally different than the function (w'). These failure rate functions

will only be the same if the time origin (t=O) is the same as the age origin (w=O) and

there is no test, maintenance or replacement activity which acts to set back the

component age.

29
In addition to the component unreliability (or component reliability) the other basic

component characteristic is the component unavailability. The age dependent

unavailability is the probability that the component is down at a given age:

The age dependent component = The probability that the component is (30)

unavailability at age w down at age w.

The symbol sometimes used for the age dependent component unavailability is Q(w).

Thus,

Q(w) = The component unavailability at age w. (31)

The age dependent availability is one minus the unavailability and is the probability that

the component is up at a given age. The time dependent unavailability is the probability

that the component is down at a given time:

The time dependent component = The probability that the component is (32)

unavailability at time t down at time t.

The symbol often used for the time dependent component unavailability is Q(t):

Q(t) = The time dependent component unavailability. (33)

The time dependent availability is one minus the time dependent unavailability and is the

probability that the component is up at a given time.

For an APSA the time dependent component unreliability and time dependent component

unavailability need to be calculated to obtain the time dependent system unavailabilities

and time dependent core damage frequency where the reference time is again the plant

age. The plant age is not generally the same as the component age since maintenances on

the component and component replacements can reset the component age. The time

dependent component unreliabilities and unavailabilities are determined from the age

dependent component unreliabilities and unavailabilities by tracking the component age

with time in the APSA.

30
The specific formulas for the above component reliability characteristics depend upon the

specific aging failure rate model and the specific models used for testing, inspection,

maintenance, and repair. Specific testing, inspection, maintenance, and repair models,

and formula implications, are given in the next section. A summary of the formulas for

the component unreliabilities and unavailabilities is also given in the appendix. These

specific formulas can be used to transform the PSA into an APSA. The next chapter,

Chapter 3, describes the approaches which can be used to actually transform the PSA to

an APSA.

2.5 Modeling the Aging Control of a Test. Maintenance, or Repair Activity

When modeling the aging control of a specific test, maintenance, or repair activity for an

APSA the following three questions need to be asked for the given activity:

1. What is the effect of the activity on the operational state of the component?

2. What is the effect of the activity on the age of component?

3. What is the effect of the activity on the aging of the component?

The answers to these questions determine the appropriate aging control model to be used

for the test, maintenance, or repair activity. For many applications, the activity is

performed on a component piecepart instead of the whole component, and the above

questions then apply to the specific piecepart. We consider each of these questions in

further detail.

1. What is the effect of the activity on the operational state of the

component?

For the usual modeling in a PSA which also applies to an APSA, the component can

either be up or down, i.e. can be available or unavailable. Hence for an APSA there is

one of two possible answers:

a. The activity changes the state of the component,

or

31
b. The activity does not change the state of the component.

Testing and maintenance activities which bring the component down for the test or

maintenance must have an associated downtime for the activity. The component is

usually assumed to be in an up state after the activity. If inefficiencies are considered

then there is a probability that the activity will leave the component in a down state due

to testing or maintenance equipment failures, procedure problems, or human errors. The

probability then needs to be assigned for each of these possibilities. If the component is

modeled to have more than two states, as for Markov models, then the state or possible

states after the activity needs to be defined with their associated probabilities. For the

applications discussed here, it will generally be assumed that the component is modeled

as having two states, an up state or down state.

2. What is the effect of the activity on the age of the component?

This is a question regarding the renewal effect of the activity with regard to the age of

the component. The renewal effect is with regard to the failure mode of the component

identified in the PSA (and APSA). There is one of three possible answers to this

question:

a. The activity does not renew the component and hence does not change the age

of the component with regard to the failure mode being considered,

b. The activity completely renews the component and sets the age back to zero

for the failure mode being considered,

or

c. The activity partially renews the component and sets the age to some

intermediate value for the failure mode being considered.

These three answers can be shortened to:

a. No renewal,

b. Complete renewal,

or

c. Partial renewal.

32
For a partial renewal answer, the degree of renewal and the new age after the activity

need to be modeled. For a partial renewal, if possible inefficiencies are also modeled,

then the age after the activity can be larger than the age before the activity. The

proceeding sections describe specific maintenance models which can be used to

determine the effect of an activity on the age of the component.

3. What is the effect ofthe acdvity on the aging of the component?

This is different than the previous question and addresses the effect of the activity on the

aging rate of the component after the activity. For example, a preventative maintenance

consisting of lubricating a pump does not generally renew the pump but slows down the

wearing processes on the pump and hence slows down the aging rate of the pump.

There are two possible answers to this question:

a. There is no change in the aging, i.e., no change in the form of the aging

failure rate,

or

b. There is a change in the aging failure rate and the change needs to be defined.

Specific models for determining the effect of an activity on the aging are also described

in the following sections.

Table 4 summarizes the above questions and alternative answers which determine the

appropriate aging control model to be used for the test, maintenance, or repair activity.

In fact, it can be argued that the questions in Table 4 need to be answered to assess the

aging control of any test, maintenance, or repair activity, regardless of whether an ASPA

is done or not. The models which are presented in the following sections progress from

simpler models to more complex models in addressing each of these questions.

2.6 The Good as New Restoration Model and The Good as Old Restoration Model

The two most straightforward models which can be used to quantify the aging control of

a test, maintenance, or repair activity are the good as new restoration model and the good

as old restoration model. These models are described below in terms of the answers they

33
TABLE 4. QUESTIONS AND ALTERNATIVE ANSWERS TO

EVALUATE THE AGING RELIABILITY EFFECTS OF AN

ACTIVITY

QUESTIONS ALTERNATIVE ANSWERS

What is the effect of the activity on the Changes the state of the component.

operational state? Does not change the state of the component.

What is the effect of the activity on the No effect on the age(age remains the same).

component age? Completely renews the component (age set

back to zero).

Partially renews the component (age

determined by a model).

What is the effect of the activity on the No change in aging rate (same aging failure

component aging? rate used).

Aging rate modified (new aging failure rate

determined by a model).

34
give to the questions regarding the effect of the activity on the operational state of the

component, the age of the component, and the aging of the component.

The Good as New Restoration Model

The good as new restoration model provides the following answers with regard to 1) the

operational state of the component after the activity, 2) the effect on the age of the

component, and 3) the effect of the activity on the aging of the component:

1. The component is in an up state after the activity,

2. The activity renews the age back to zero (to "as good as new"),

and

3. There is no change in the aging behavior after the activity (the same aging

failure rate applies with the age reset to zero).

The good as new restoration model is used to model an activity which replaces or

completely renews the component (or component piecepart if pieceparts are being

modeled). If a component piecepart is the dominant contributor to the component failure

mode being considered then renewal of the piecepart will basically result in renewal of

the component. The good as new restoration model or good as new model for short, is

thus used to model a maintenance or repair activity which replaces or effectively

overhauls the component or the dominant contributing component piecepart. Relatively

simple equations for the component unreliability and unavailability result when the good

as new model is used.

The Good as Old Restoraion Model

The good as old restoration model is the other straightforward model which can be used

to model a testing, inspection, maintenance, or repair activity. The good as old

restoration model is the model opposite to the good as new restoration model with regard

to renewal. The good as old model provides the following answers to the three questions

regarding 1) the component state 2) the age effect, and 3) the aging effect:

1. The component is in an up state after the activity,

35
2. The age remains the same after the activity (no renewal) and there is no age

setback,

and

3. There is no change in the aging behavior after the activity; the same aging

failure rate applies with the same age after the activity as before the activity.

The good as old restoration model, or good as old model for short, is used to model an

activity which assures that the component is in an operational state (up state) but does

minimal repairs on the component if the component is not functionally failed. Thus,

there is no removal of degradations or no major renewal of the component and the age of

the component basically remains the same. When applied to a component piecepart, then

the piecepart is not renewed or significantly refurbished. The good as old model is used

to model a surveillance test or inspection activity which does not involve major

maintenance or repair actions. If a failure or severe degraded state is detected which

requires correction then the repair activity can be separately modeled as a good as new

activity using the good as new model. Thus, routine surveillance testing and inspection

can be modeled as being as good as old activities and when failure or severe degradation

occurs then the repair or corrective activity can be modeled as being a good as new

activity. The good as old model again produces relatively simple equations for the

component unreliability and unavailability.

To utilize the formulas for the good as new restoration model or the good as old

restoration model one must determine whether the aging control of a given test,

maintenance, or replacement is best described as being good as new or as being good as

old. The good as old model can be used to provide an upper bound and the good as new

model a lower bound for the effect of the activity. Combinations of the good as old and

good as new models can be used for different activities carried out at a plant. For

example, as was indicated, a surveillance test carried out to assure a component is

operational can be modeled as having minimal aging control unless the component is

found failed. The surveillance test can thus be modeled as being as good as old with the

repair of a failure being modeled as good as new. The surveillance test interval can be

used as the good as old restoration interval and the good as new restoration interval can

be taken to be the mean time to failure. If scheduled replacements or overhauls are in

addition carried out then these activities can separately be modeled. Thus, the good as

new and good as old models can provide flexibility in modeling the aging control of

testing and maintenance activities.

36
2.7 More Complex Maintenance and Restoration Models

The good as new and good as old models are useful for providing a first order evaluation

of the aging control of a test or maintenance activity. They can also provide bounds on

the aging control effects. More complex maintenance and restoration models involve

modeling the testing or maintenance activity to not be good as old or as good as new, but

somewhere between. More complex models can also involve modeling inefficiencies

associated with a test or maintenance. These more complex models can be applied when

detailed test and maintenance data is available. These more complex models can also be

useful for sensitivity studies to determine the sensitivity to the details of the test or

maintenance activity. For example, a useful analysis is to use the good as old and good

as new models to identify the risk important test and maintenances and then to carry out

more detailed sensitivity analyses on the risk important tests and maintenances. The

more complex models which will be covered are:

1) Modeling the effect of tests or maintenances on individual pieceparts of the

component,

2) Modeling the effect of tests or maintenances which only cover specific failure

causes or mechanisms,

3) Modeling explicitly the age setback which results from a maintenance or

repair activity,

4) Modeling the aging control of preventative maintenances in reducing the

aging rate,

and

5) Modeling inefficiencies associated with a test or maintenance activity.

These more detailed models are discussed in the subsequent sections.

Modeling Tests or Maintenances on Individual Pieceparts

When modeling tests or maintenances on individual pieceparts, the component is

subdivided into its pieceparts and each piecepart is treated as a separate component.

Each piecepart can then be evaluated using the good as old or good as new model or

37
more complex models. For example, a valve can be divided into the valve driver (the

actuator, motor etc.), the valve interior (valve disk, etc.), and the valve exterior body. A

surveillance test which only tests a given piecepart can be modeled as being good as old

and an overhaul or repair of the piecepart can be modeled as being good as new, the

models now being applied to the specific piecepart.

The actual modeling involves replacing the component failure rate by the sum of its

piecepart failure rate contributions (e.g., in fault tree terminology replacing the

component by an "or gate" of its piecepart contributions).' The failure rate for each

piecepart then needs to be determined and the appropriate test and maintenance model for

each piecepart needs to be determined. When the good as old model is used for a

surveillance test and the good as new model is used for repairs the information required

is the appropriate test interval on the piecepart and the mean time to failure for the

piecepart. The test and maintenance procedures and historical data are used to identify

the specific pieceparts which are tested or maintained and the test and maintenance

frequency and characteristics. To prevent the models from becoming overly large, only

the major components can be expanded into their pieceparts. For components which

have one piecepart as the major contributor to the failure mode, the component may be

treated as being equivalent to the piecepart.

Modeling Tests or Maintenances on Specific Failure Causes

If a test or maintenance only covers specific failure causes or failure mechanisms then

the activity can be modeled as only controlling a portion of the component failure rate.

The portion or fraction of the failure rate which is controlled is determined based on the

fraction of total failure contributions which is covered by the test or maintenance. This

fractional restoration modeling is similar to the previous piecepart modeling except

instead of pieceparts being identified, the fraction of failure causes or mechanisms which

is controlled is modeled.

To apply the fractional restoration approach, the total component aging failure rate is

multiplied by the fraction of failure contributions which is controlled by a given test or

maintenance. This fractional failure rate contribution (the total failure rate times the

*The piecepart contributions can more accurately be modeled as being competing cause contributions,

however the difference from the summation of the contributions, which ignores the interactions is

generally insignificant

38
fraction) can then be assigned to be good as new after the given failure causes or

mechanisms are corrected. Surveillance tests which only detect this fraction of failure

contributions can be assigned to be as good as old for the fractional contribution. The

failure rate can be divided into different fractional contributions and each separately

tracked. Failure causes or mechanisms not detectable are treated as not being testable or

maintainable.

Explicitly Modeling Age Setback

A partial restoration of a component can be explicitly modeled as a partial age setback,

where the component age is setback to a given value. In modeling age setback, the age

reduction after a given repair or maintenance activity is explicitly determined. For the

good as old model, there is no age setback i.e., the age reduction is zero after the activity,

but the component is assured to be an up state. For the good as new model, there is a

complete age setback, i.e., the age reduction is equal to the age of the equipment before

the activity, resulting in as good as new equipment For a repair or maintenance activity

modeled as having an intermediate age setback, the value of age setback needs to be

estimated. For a given age setback of Aw after an activity the age of the component is

reduced from w to wI where

W = w -Aw (34)

where w is the component age before the activity. The aging component failure rate then

begins at wI after the activity for the calculation of the component unreliability and

component unavailability.

To calculate the component unreliability or component unavailability versus time, the

component age versus time needs to be tracked, accounting for age setbacks by repairs

and maintenances. The formulas in the appendix can be used to calculate the

unreliability and unavailability with appropriate setback of the age using Equation (34).

With regard to applications, the more difficult question is the appropriate age setback

value to assign to a given repair or maintenance activity. Little work has been done in

this area. Sensitivity studies can be performed by varying Aw to determine the

sensitivity to the degree of restoration. Data analyses can also be carried out to estimate

the age setbacks associated with different types of maintenances by constructing

appropriate likelihood functions with the age setback the parameter to be estimated.

39
Modeling the Effects of Preventative Maintenances in Reducing the Aging Rate

Preventative maintenances may not restore an aged part, but instead may slow the aging

process of the component. Preventative maintenances which involve lubrication or

cleaning are of this type and can be modeled as reducing the aging rate of the equipment.

Before the preventative maintenance the aging rate has a value say of a and after the

maintenance, the aging rate is reduced to a, where

a = a - Aa (35)

and where Aa is the aging rate reduction due to the preventative maintenance.

To determine the aging control of a preventative maintenance the aging rate reduction

needs to be related to the component failure rate change. If the linear aging failure rate

model is used (Equations (5)-(9)) then the aging rate reduction Aa can be directly

interpreted as the change in the linear aging rate a. The new linear aging rate after the

preventative maintenance is then al. Preventative maintenances may be more generally

carried out to control continually increasing rates of aging. To determine the aging

control on aging rates which increase with time, nonlinear failure rate models are

required.

For a nonlinear aging failure rate model, the aging rate a is more generally defined to be

the rate of increase in the failure rate with age:

a = d (36)

dw

where the right hand side of Equation (36) is the derivative of the failure rate with age.

The aging rate a is thus generally a function of the age w, i.e., a = a(w) and can increase

with age.

From the above relationships, a change in the aging rate can be related to the change in

the failure rate, which is what is required for application in an APSA. If Aa is modeled

for a preventative maintenance activity, then the new aging rate can be determined from

Equation (35), and Equation (36) can be used to determine the failure rate after the

preventative maintenance. With the failure rate after the activity determined, the

40
component unreliability and unavailability can then be calculated using the equations in

the appendix.

For example, for the Weibull failure rate model (Equations (10)-(14)) the failure rate

derivative is

dA 2b b-i

dw- wb (37)

Equating the derivative to the new aging rate a, after the preventative maintenance gives

the component age w, after the preventative maintenance,

Aob b-i (38)

wo

or

1w (39) P A1 b J39

The new age w, can then be used for the Weibull failure rate to calculate the unreliability

and unavailability of the component. The more difficult task is to estimate the aging rate

change Aot for a given preventative maintenance activity. Perhaps the best use of the

model is to carry out sensitivity analysis to determine the importance of preventative

maintenance actions. This preventative maintenance model can also be used to analyze

maintenance data to estimate the aging rate reductions for given preventative

maintenances using appropriate likelihood functions with Aa as the unknown parameter

to be estimated.

Modeling Test and Maintenance Inefficiencies

Finally, sometimes a test or maintenance may be inefficient in detecting or correcting a

degradation or failure. One of the most straightforward ways to model a test or

maintenance inefficiency is to increase the test interval or replacement interval to be an

"effective" interval. The use of an effective interval models the inefficiency as being

associated with a constant probability per activity of not detecting or correcting the

41
degradation or failure. Let eT be the test efficiency which is defined to be the probability

of detecting a failure at a test. Let T be the actual test interval and T. be the effective test

interval which is the expected test interval at which the failure is detected. Then using

standard probability relationships*,

T Te = (40)

eT

Similarly if eL is the probability of a restoration activity effectively restoring the

component, L the actual restoration interval, and L8 the effective restoration interval,

then

Le =-. (41)

eL

The effective intervals can then be used in the formulas for the component unavailability

in place of the actual intervals. Sensitivity studies can be performed by varying er or eL

to determine the risk impact of inefficiencies. Those tests or maintenances which are

most sensitive are those where the efficiencies need to be the highest.

Maintenance and repair inefficiencies can also be modeled using the partial restoration

model or age setback model previously given. Instead of assuming good as new

restorations these partial restoration models can be used to model partial restorations

associated with the maintenance or repair. Sensitivity studies can be performed to

evaluate the impacts of partial restorations instead of complete restorations.

2.8 Summary of Models and Data Needed to Ouantifv Component Reliability and

Unavailability Effects of Aging

The previous sections described the failure models and test and maintenance models

which can be used to quantify the reliability and unavailability of a given aging

component. The data required for these models were also discussed. It is useful to

*For a detection probability of er per test the average number of tests before detection is 1/&r based on

the standard geometric probability distribution. For an interval of T between tests, the average interval to

detection is then T/CT.

42
- - -

summarize these modeling and data needs since this encompasses what is needed to

transform a PSA into an APSA.

In summary, for each component for which aging effects are to be explicitly quantified

an aging reliability model is needed. This consists of:

1. A model of the age-dependent failure rate for the component. Commonly used

age-dependent failure rate models are:,

The linear failure rate model,

The Weibull failure rate model,

or

The exponential failure rate model.

The formulas for the above failure rate models were given in Section 2.2. For a given

age-dependent failure rate model the parameters of the model must be estimated from

failure rate data or from engineering information. Instead of the age dependent failure

rate, a model of the overall time trend in the failure rate or in the failure frequency can be

used to show overall trends due to aging. However, an overall time trend model cannot

be used with different test and maintenance models since the overall time trend has the

test and maintenance effects already incorporated and the aging failure rate is not

separated out as a function of age.

In addition to the age-dependent failure rate model when the aging control effects of test

and maintenance practices are also to be explicitly evaluated then appropriate test and

maintenance models are required. Specifically,

2. A model of the age control of each test, maintenance, or repair performed on the

component or component piecepart is required. The most straightforward models

are

The good as old restoration model,

and

The good as new restoration model.

43
More complex models can also be used, including piecepart models, fractional

restoration models, age setback models, and preventative maintenance models.

Inefficiencies in an activity can also be modeled. For a given test or maintenance model,

the parameters in the model need to be determined from the procedures and from

historical data if available. For the good as old or good as new model the only required

input data is the interval at which the activity is performed. Sections 2.6 and 2.7

described the different test and maintenance models. The appendix gives formulas for

calculating the component reliability characteristics using the aging failure rate model

and the appropriate test and maintenance models. These reliability characteristics are

then used to transform the PSA to an APSA. The next chapter, Chapter 3, describes the

approaches which can be used for this transformation process.

44
3. APPROACHES FOR TRANSFORMING A PSA INTO AN AGEDEPENDENT PSA

3.0 Introduction

There are different approaches that can be used for transforming a PSA to an agedependent PSA, or an APSA. We describe three basic approaches. The first approach

involves carrying out a standard PSA evaluation a number of times with different

component failure rates used in each evaluation. The different component failure rates

which are used are stepwise approximations to time dependent component failure rates.

This approach is straightforward, but the age of each component cannot be separately

tracked. Hence, the effect of testing, maintenance, or repair on the age of the component

or on the aging rate cannot be explicitly modeled.

The second approach for transforming a PSA into an APSA is to substitute age

dependent component models into the PSA quantification formulas. The fundamental

PSA formulas for the core damage frequency in terms of the component failure

probabilities and component unavailabilities are still used. However, the quantification

formulas for the component failure probabilities and componentyunavailabilities are

changed from the usual, steady state formulas to those which explicitly incorporate

aging. This approach efficiently calculates the core damage frequency and system

unavailabilities as a function of plant age. However, the aging contributors are not

resolved in detail and die calculations can be time consuming if sensitivity studies are

performed.

The third approach for transforming a PSA to an APSA is to calculate appropriate risk

importance coefficients from the standard PSA and to combine these with calculated

component aging effects using separate component aging models. This approach is

effective for resolving in detail aging contributors, including all the aging interactions.

The approach also allows sensitivity studies to be efficiently carried out. However, the

approach can be time-consuming calculationwise. Formal uncertainty analyses can also

be time consuming.

The following sections describe each of the above approaches. The features of each

approach are further described. Each approach is described in sufficient detail to allow

implementation of the approach for specific applications.

45
3.1 Successive Stepwise Evaluations Using a Standard PSA

The approach of successively quantifying a standard PSA to approximate aging effects is

straightforward. The time dependent failure rate of a component is approximated by a

series of stepwise constant failure rates as shown below.

Approximation of a Time Dependent Failure Rate by a Stepwise

Constant Faihre Rate

F

a

u

r

R

t

to t2 Time t t4

For a time interval with a given approximate constant failure rate, the component can

thus be treated as in a standard PSA which assumes the component has a constant failure

rate. For multiple components which have time dependent failure rates, the time

dependent failure rate of each component is approximated by a series of constant failure

rates using the same set of time intervals for each component. A standard PSA

evaluation (computer run) is then made for each time interval using the associated

constant failure rate for each component. The results from the quantifications for

different intervals then serve as a stepwise approximation of the time dependent core

damage frequency as illustrated below.

Core Damage Frequency at Different Tis Points

Core Damage Frequenc

tI t 2 Tm t3 t4

46
The advantage of the successive stepwise approach is that standard PSA models and

standard.PSA computer codes can be used. Care must be taken in selecting the width of

the time intervals, though this is a numerical accuracy problem which can be addressed

by using finer time intervals.

The basic disadvantage of using the stepwise, approximate approach is that individual

component ages cannot be explicitly tracked since a common time must be used for all

components. Thus, the effects of test, maintenance, or repair on the age of the

component and on the aging rate cannot be explicitly modeled. When a component is

replaced, repaired or maintained, the failure rate value after the activity is the same as the

failure rate value before the activity. This is because of the constant failure rate

assumption used in the PSA run.

The implications of using the same failure rate before and after an activity depend upon

the type of component failure rate function which is used as the basis for the histogram

approximations. When overall time trend failure rates (or failure frequencies) are used as

the basis for the histogram approximations, then the effects of testing, maintenances, and

repair are already factored into the failure rates. The effects of testing, maintenance, and

repair thus cannot be separated out and be explicitly modeled. Different testing,

maintenance, and repair programs consequently cannot be evaluated because of the builtin effects of the testing, maintenance, and repair program under which the time,

dependent failure rates were collected. The PSA results then provide a best-estimate,

stepwise approximation of the time dependent core damage frequency and system

unavailabilities under the given testing, maintenance, and repair programs built into the

failure rates.

If age dependent component failure rates are instead used as the basis for the histograms,

where test, maintenance, and repair effects have been removed, then the PSA runs

generally will provide a conservative, upper bound evaluation of the aging impacts. All

the component ages are equated to a common running time in using the common set of

time intervals for the histogram approximations. Thus, it is assumed that components are

never overhauled or replaced with new components. Because of the constant failure rate

assumption, surveillance tests, maintenances, repairs, and replacements are thus all

effectively modeled as being good as old. No component is ever replaced with a new

component and no degradation is ever removed from a component, causing a renewal of

the component. Because of the good as old assumption for all activities, the stepwise

47
approximation approach in this case generally provides a conservative, upper bound

evaluation of the age-dependent core damage frequency and system unavailability.

Thus, it is important to know whether the basic component failure rate functions which

are used are time trends and incorporate the effects of testing, maintenance, and repair or

whether they are age dependent failure rates which separate out the effects of testing,

maintenance, and repair. This was the basic aging failure rate issue that was discussed in

Section 2.3 and is important for the proper understanding and application, not only for

the approximate stepwise PSA approach, but for the other approaches for carrying out an

APSA as well. It is an issue since as was indicated in Section 2.3, failure rate data bases

may not clearly differentiate as to whether the failure rates are overall trends or are age

dependent with the test and maintenance effects removed. Compounding the problem,

data analyses may calculate overall time dependent failure rates and erroneously call

them age dependent.

One final point involves the PSA minimal cut sets. * A truncated list of minimal cut sets

which have been evaluated as being the most important is among the standard results

provided by the PSA. A list of minimal cut sets is used not only in the successive

stepwise approach, but in all approaches to quantify the aging effects. Truncation of the

minimal cut sets by the PSA can lead to underestimating of the aging effects because

minimal cut sets which were unimportant in the original PSA can become important

when aging is considered. This can particularly be the case for minimal cut sets which

contain components which are simultaneously aging. The simultaneous aging will cause

a multiplicative increase in the minimal cut set contribution to the core damage

fiequency. To check on the effect of additional minimal cut sets being considered, the

minimal cut sets can be expanded to include the multiple components which are aging

and the evaluations carried out again using the expanded set. If this checking is not done

then it should be made clear as to what contributions are included and which are not.

This applies to all the approaches. A summary of the basic features of the stepwise

approach is given in Table 5.

*A minimal cut set is a standard PSA term and is a smallest combination of component failures with an

initiating event that will cause a core damage event

48
TABLE 5. THE SUCCESSIVE STEPWISE APPROACH

FOR PSA AGING EVALUATIONS

Basic Procedure: Approximate the time-dependent component failure rate by a series of

constant stepwise failure rates in given time intervals. Use the same time intervals for all

components. For a given time interval select the appropriate constant failure rate for

each component and quantify the PSA as usual. Repeat for each time interval of interest.

Advantages: Standard PSA models and software can be used with no modifications

required.

Disadvantages: Because of the constant failure rate assumption in the PSA, the age of

the component and the aging rate are never modified. Thus, different test, maintenance,

and repair programs which affect the aging or aging rate cannot be evaluated.

Special Points: If overall, time dependent (time trend) failure rates or failure

frequencies are used for the histogram fittings then the effects of tests, maintenances, and

repairs are built into the failure rates. The PSA results then give a best estimate, stepwise

approximation to the core damage frequency for the aging data and given test,

maintenance, and repair programs built into the failure rates. If age-dependent failure

rates are used with the test, maintenance, and repair effects removed then all tests,

maintenances, and repairs are effectively treated as good as old because of the constant

failure rate assumption. This will generally give conservative, upper bound core damage

frequency results within the histogram approximations. Truncation of the minimal cut

sets, can lead to underestimation of the aging effects if omitted minimal cut sets become

significant because of aging effects.

49
3.2 Substitution of Agingf Models Into a PSA

A second approach for transforming a PSA into an APSA is to substitute aging models

into the PSA component quantification formulas. Instead of calculating component

unavailabilities and component unreliabilities using standard PSA constant failure rate

models, appropriate component aging reliability equations are substituted to calculate

age-dependent component unavailabilities and unreliabilities. The same fault tree and

event tree models in the PSA are

used. However, different values are calculated for the component unavailabilities and

unreliabilities using appropriate component quantification formulas as given in the

appendix. The component unavailabilities and unreliabilities need to be calculated for

each of the times of interest to obtain the time dependent core damage frequency. If

average aging effects are of interest, then averages are calculated over appropriate time

intervals.

To understand the substitution ofthe component aging models into the PSA, consider the

standard PSA formula for the core damage frequency C in terms of the component

contributors:

N (2

C = Ii q qi2.qimi (42)

i=1

where

Ii- = the initiating event frequency for a given (43)

accident

and

qil qi2.qim, = the product of component unavailabilides *

in the ith minimal cut set (a combination of (44)

component failures causing a core damage

event if the initiating event occurs)

* A component unreliability is used instead of a component unavailability when the failure mode is

failure to rn, instead of failure to start.

50
The minimal cut sets can vary in size, and to be general there are assumed to be mj

components in the ith minimal cut set. Also, to be general it is assumed that N minimal

cut sets are obtainable from the original PSA. The unavailabilities can also include

human error contributions. The same general formula as Equation (42) also applies for

system unavailabilities, expected health consequences, and other results calculated by the

PSA.

Equation (42) is dependent only upon the basic logic structure of the PSA and doesn't

depend on any specific quantitative models used for the initiating event frequencies and

component unavailabilities. In standard PSA evaluations, constant failure rate models

are used to calculate values for Ii and c4 2*- qjn.. For age-dependent evaluations,

age-dependent models are instead used to calculate these values at different time points

or plant ages. The calculations need to be repeated for each time point of interest,

however the same basic PSA formula, Equation (42), is used with only different numbers

substituted forIi andqi q(*-- qii..

In substituting age-dependent models for the component unavailabilities and

unreliabilities (or initiating event frequencies) the following poihts need to be considered

for implementations:

1. Truncation of minimal cut sets can again cause certain aging contributors to be

omitted. A truncated minimal cut set contribution can become particularly

important if multiple components in the minimal cut set are aging, multiplying

the contribution of the minimal cut set. The truncation effect can be investigated

by expanding the minimal cut sets to include those omitted minimal cut sets

containing aging components.

2. If different test and maintenance policies are to be evaluated, then age-dependent

component failure rates need to be used which separate out the effects of tests,

maintenances, and repairs. Appropriate test, maintenance, and repair models of

age control, such as those given in Chapter 2, should be used to calculate the

component unavailabilities.

51
3. If time dependent (time trend) failure rates or failure frequencies with built in

test, maintenance, and repair effects are used then different test, maintenance, and

repair practices cannot be evaluated. Good as old restoration models should then

be used in the component quantifications to maintain the time dependent

behaviors in the failure rates.

The advantage of the substitution technique is its straightforwardness. Standard PSA

models and minimal cut sets are used with the quantification formulas modified for the

component unavailabilities and unreliabilities (or initiating event frequencies). Separate

computer subroutines or modules can be developed to calculate the age dependent

component unavailabilities and unreliabilities which can then be used in the standard

minimal cut set expressions for the core damage frequency and system unavailabilities.

Sensitivity and uncertainty analyses can also be incorporated into the quantifications.

The disadvantage of the substitution technique is its limited resolution of aging

contributors. The final core damage frequency and system unavailabilities are

determined but the aging contributors are not delineated. The minimal cut set

contributions give the total contributions from component combinations, but the aging

effects are not separated out. How much a component's aging contributes to the core

damage frequency and how much component aging interactions contribute are not

identified. Also, the calculations at different time points can be tedious if many

sensitivity calculations are carried out, although efficient calculational algorithms can be

constructed to help address this problem. Table 6 summarizes the features of the

approach for substituting aging models into a PSA.

3.3 The Risk Importance Approach for Evaluating Aging Effects

The third approach for transforming a PSA into an APSA is the risk importance approach

whose methodology is described in NUREG/CR-5510(7). Appropriate risk importances

are calculated from the standard PSA and are then combined with component aging

models to give the core damage frequency increase due to aging. Other risk importances

can also be calculated from the PSA to give the increase in any risk result due to aging,

such as increases in system unavailability due to aging. Even though the approach is

described in NUREG/CR-5510, it is summarized here in context of its use for

transforming a PSA into an APSA.

52
TABLE 6. THE SUBSTITUTION APPROACH FOR PSA AGING

EVALUATIONS

Basic Procedure: Use aging models to calculate the component unavailabilities (or

unreliabilities) at a given time point (or given plant age) for the aging components.

Alternatively, use the aging models to calculate average increases in unavailability due to

aging. Substitute the component unavailability values into the PSA minimal cut set

equations to obtain the age-dependent core damage frequency. Repeat at different time

points for time dependent evaluations.

Advantages: The standard PSA logic models and minimal cut sets can be used with

only the quantification formulas modified for the component unavailabilities,

unreliabilities and initiating event frequencies. Separate subroutines can be set up to

calculate the age-dependent unavailabilities, unreliabilities, and initiating event

frequencies to replace the standard PSA quantifications. Different test and maintenance

programs can be evaluated for their risk effectiveness if appropriate age dependent

failure rates are used.

Disadvantages: The aging effects are not delineated and hence prioritization of the

aging effects can not be readily carried out. The calculations can be tedious and time

consuming if different aging calculations are performed such as for sensitivity

evaluations

Special Points: Age-dependent component failure rates should be used which separate

out the test and maintenance effects if different test and maintenance programs are to be

evaluated. If time dependent failure rates or failure frequencies are used which

incorporate test and maintenance effects then good as old restoration models should be

used to maintain the time dependent failure rates or failure frequencies. Truncation of

the minimal cut sets can lead to underestimation of the aging effects and can be expanded

to determine the impacts. The contributors included and those onitted should be

described.

53
Let AC be the increase in the core damage frequency due to aging, i.e. the difference

between the core damage frequency with aging and without aging. Then AC can be

expressed as a sum of contributions,

AC= SjAq + S Aqj qj Aqj (45)

i j>i

+ YSjk Aqi qj qk ... k>j>i

+I S12..n AqlAq2 ... Aqn

n

where

Aqi = the increase in the unavailability of (46)

component i due to aging (the difference

between the unavailability with and without

aging)

and where Si, SiQ,... S12...a are appropriate risk importance coefficients determined from

the standard PSA. NUREG/CR-5510 describes how to calculate the risk importance

coefficients and provides algorithms which can be used for implementations. The last

term on the right hand side is the contribution from the largest size minimal cut sets

obtainable from the PSA (without truncation). The total core damage frequency C with

aging can be obtained by adding AC to the core damage frequency without aging

calculated in the PSA C., i.e., C = C. + AC Similar expressions can be written for the

aging increase in any other risk result.

Equation (45) is an exact expression and gives a detailed breakdown of all the aging

contributions to the core damage frequency increase due to aging. Each Aqi is the

difference between the unavailability q calculated with aging and the unavailability q.

calculated without aging in the PSA, Aq = q - q0. The unavailability increase Ach can be

time dependent (or age dependent) or can be an average aging effect over given time

periods or replacement intervals.

54
With regard to the detailed breakdown of contributions, the first term on the right hand

side of Equation (45) gives the sum of the contributions from individual component

aging effects:

Si Aci = the core damage frequency contribution (47)

from the aging of component .

The second term gives the sum of the two component interaction contributions from two

components simultaneously aging:

Sij A4 Aqj - the core damage frequency contribution (48)

from the simultaneous aging of components

i andj.

The higher order interaction contributions for three components simultaneously aging,

etc. are given by the succeeding terms on the right hand side of Equation (45) up to the

maximum interaction contribution, which is the size of the largest minimal cut set

modeled in the PSA.

Besides breaking down the core damage frequency impact due to aging into the detailed

individual and interaction aging contributions, each contribution in Equation (45) shows

the risk importance factor and the aging effect. For an individual component

contribution Si A, Si is the standard PSA core damage frequency importance of the

component and Ac4 is the aging effect. Similarly, for an interaction contribution, the first

factor is the core damage frequency importance of the interaction and the second factor,

the product of Aq%'s, is the aging effect. For example, for the two component interaction

contribution SjAqAqj, Sq is the risk importance of the contribution and AqiAqj is the

aging interaction effect. Thus, one can determine how much of each core damage

frequency contribution is due to the core damage frequency importance of the

components and how much is due to the aging of the components. The core damage

frequency importances of the components are determined from the basic PSA and

reflects the basic design and operation of the plant. The aging effects Aq, depend upon

the component aging failure rates and the aging control of the test and maintenance

programs.

55
In applications, the contributions to AC are often truncated to only consider second or

third order interactions, i.e. the terms on the right hand side of Equation (45) are

truncated at the second or third summation. As indicated, NUREG/CR-5510 gives

algorithms for calculating the risk importance coefficients SiSij, etc. The aging effects

Aq are calculated using appropriate aging reliability models as has been previously

described. If the aging control of test and maintenance programs are to be explicitly

evaluated for their risk effectiveness, then again age-dependent component failure rates

which separate out the effects of testing, maintenance, and repair should be used.

Appropriate formulas for Aq% are given in the appendix.

The disadvantage of the above aging-risk importance approach is that the risk importance

coefficients Si, Sij, etc. can be tedious to calculate, particularly if many terms are

determined for the contributions to AC Efficient algorithms for determining the risk

importance coefficients focused on those components which are aging can help address

this problem. Uncertainty and sensitivity evaluations can also be tedious if uncertainties

and sensitivities in the risk importance coefficients are included. Equations and

algorithms for the risk importance coefficients given in NUREG/CR-5510 can be used to

obtain the uncertainties and sensitivities in terms of basic component data uncertainties.

The advantage of the aging risk importance approach is that it provides a detailed

breakdown of all the aging contributions to the core damage frequency increase due to

aging. How much of the contribution is due to the risk importance of the contributor and

how much is due to the aging effect is also given. Pioritization of the aging contributors

and of test and maintenance activities thus can be effectively carried out using the

approach. From an implementation standpoint, because the aging evaluations Aqi are

separated from the PSA risk importances S., Si etc., the PSA needs to be solved only

once to determine the risk importances, regardless of the number of aging evaluations

carried out using different aging rates, test and maintenance models, etc. Because the

focus of this report is on aging prioritizations and sensitivity studies, the risk importance

aging approach will be principally used in the applications to be discussed. Table 7

summarizes the features of the risk importance aging approach.

56
TABLE 7. THE RISK IMPORTANCE APPROACH FOR PSA AGING

EVALUATIONS

Basic Procedure: Use the standard PSA to calculate the risk importance coefficients (S.,

Sq, etc.) for each component and combination of components which are aging. Multiply

the coefficients by the increases in unavailability (Aq, Aqj, etc.) due to aging and add to

obtain the total core damage frequency change (AC). Recalculate the unavailability

increases for the time points or ages of interest for time dependent evaluations.

Advantages: The detailed aging contributions are identified and prioritized. The risk

importance factor and the aging effect factor for each contribution is identified. The risk

importance coefficients need only be calculated once for different aging evaluations

which are carried out.

Disadvantages: Calculation of the risk importance coefficients can be time consuming

if many higher order coefficients are calculated. Including uncertainties and sensitivities

in the risk importance coefficients can be tedious.

Special Points: Age-dependent component failure rates which separate out test,

maintenance, and repair effects should again be used if the aging control of test and

maintenance programs are to be explicitly evaluated. If the summation of terms for AC

is truncated at some term then the effects of the truncation can be examined by

calculating additional terms. The truncation limit should be documented as part of the

results.

57
4. APPLICATIONS OF AN AGE-DEPENDENT PSA

4.0 Itrmoduction

An age-dependent PSA, which we have called an APSA, can be used for various

applications. A particular application of an APSA can be classified according to the

principal focus of the analysis, which can be:

Evaluation of the core damage fiequency with aging effects incorporated,

Evaluation of test and maintenance effectiveness in controlling aging impacts,

Prioritization of aging contributors to the core damage frequency,

or

Evaluation of the sensitivities and uncertainties in risks due to aging effects.

When the focus is on evaluation of the core damage frequency with aging effects

incorporated then the emphasis is on determining the bottom line number for the core

damage frequency and system unavailabilities with aging effects explicitly modeled.

When the focus is on evaluation of test and maintenance effectiveness in controlling

aging effects then the emphasis is on evaluating the effectiveness of test and maintenance

programs in controlling the risk impacts of aging under specified aging behaviors.

Different test and maintenance strategies may be investigated and different plausible

aging failure rates may be used. When the focus is on prioritization of aging

contributions then the evaluations are geared toward the ranking and screening of aging

contributors. Finally, when sensitivity and uncertainty analyses are the principal focus

then variations and distributions in the risk are determined for variations and distributions

in aging behaviors.

The next section identifies the basic questions that need to be answered in setting up an

APSA calculation for any of the above applications. These questions and their answers

provide a framework for carrying out one or more of the above applications. These

questions address the aging data, the test and maintenance models, the PSA information

and the results from the APSA.

58
4.1 Ouestions To Be Addressed in Setting Up an APSA Application

There are four basic questions that need to be answered in setting up an APSA for any

specific evaluation. These questions are:

1. What is the available component aging failure rate data?

2. What is the available test and maintenance information?

3. What is the available type of PSA information?

and

4. What are the aging results of most interest?

The answers to the questions will determine the type of APSA application which can be

best carried out and the type of APSA approach which is most suitable. Figure 6

presents these questions in terms of a decision tree with the possible answers. The

following sections discuss in more detail the alternative answersto each of these

questions and the implications of these answers.

4.2 Impact of Available Component Aging Failure Rate Data

The component aging failure rates which are available can be of three types:

Plant specific aging failure rates,

Generic aging failure rates,

or

Subjective estimates of aging failure rates.

59
FIGURE 6. QUESTIONS TO BE ANSWERED IN SETTING UP AN

APSA EVALUATION

Available aging failure rate data?

I

plant

specific

I I

generic

I

Available test and maintenance information?

subjective data

I 

detailed

information

I I

minimal

information I

Available PSA information?

r ~~~~~~~~~~~~~~~~~~~~~I

event I trees and

fault trees

I

truncated

minimal

I cut sets

Results of most interest?

I

bottom line

numbers

I

pndoitization and sensitivities

60
Plant specific aging failure rates are the most precise data and are based on failure

histories of components at the plant being analyzed. The component failure rate model

(e.g. linear, Weibull, or exponential) can be selected which is most consistent with the

data, and the parameters of the model can be estimated using statistical data analysis

approaches. Plant specific aging failure rates are, however, generally not available, or

are available for only selected components.

Generic aging failure rates are aging failure rates which have been obtained from a

population of plants. The generic aging failure rates represent average aging failure rates

over the components which are combined in the data base. In performing uncertainty

analyses or carrying out sensitivity studies, it is therefore important to include possible

plant specific variations. Generic aging failure rates are potentially obtainable from

existing generic data bases such as the Nuclear Plant Reliability Data System (NPRDS),

if times of failures are recorded. Incomplete records and possible errors in failure

classification in these data bases need to be considered as part of any uncertainty or

sensitivity analyses which are performed.

The last type of data consists of subjective estimates of aging component failure rates.

Because of the lack of plant specific aging data and even generic aging data, subjective

estimates of aging failure rates will often be the data which is most available. An

example of this type of data is the data base which is utilized in NUREG/CR-5510 (7).

Subjective estimates of aging failure rates involve translating engineering information

and experience about a component into an equivalent aging failure rate estimate. If

subjective aging failure rate estimates are used then it is important that sensitivity or

uncertainty analyses be also carried out to evaluate uncertainties and variabilities

associated with the subjective data.

The type of aging data which is principally available is an important factor in

determining the most meaningful focus of application for an APSA. The type of aging

data which is principally available also is an important factor in determining the

meaningful interpretations which should be placed on the results from the APSA. If

plant specific data is principally available then all the different focuses of applications of

an APSA discussed in the previous section are equally meaningful because accurate

aging data relevant to the plant is available. The APSA results furthenore can be

interpreted as being directly applicable to the plant within the associated data

uncertainties. All the different approaches for transforming a PSA to an APSA can be

61
effective with the substitution approach most efficiently providing the bottom line core

damage frequency value and system unavailability values. The risk importance aging

approach is most effective if detailed aging contributors are of prime interest, broken

down into the individual component contributors and the contributions from aging

interactions. Finally, the successive approximation approach can provide quick bounds

or approximations to the aging impacts.

If generic data is principally available then all applications can be carried out but the

results must be interpreted as under the limitation of generic data being used. The most

meaningful applications are those which account for possible plant specific variations by

varying the aging rate data to account for plant specific effects. Results which are not

sensitive to these aging rate variations are the most meaningful. Prioritizations of aging

contributors and sensitivity studies, along with uncertainty analyses, are thus among the

more meaningful applications. With regard to APSA approaches, the successive

stepwise approach is effective for efficiently bounding or approximating the aging

effects. The risk importance aging approach is effective if aging contributor

prioritizations are the focus. The substitution approach is useful if the focus is on final

core damage frequency values. For all these approaches, the effects of plant specific data

variations about the generic data values must again be included.

If subjective aging failure rate estimates are principally available then the aging failure

rate data can have especially large uncertainties. For subjective aging failure data, the

most meaningful applications involve prioritizations of aging contributors and sensitivity

analyses of aging impacts. The meaningful results are those which are account for the

large uncertainties in the subjective aging failure rate data. Extracting meaningful results

thus includes focusing on the order of magnitude of the value and focusing on

relationships between values. The relationships which can be focused on include

relationships between sizes of core damage frequency impacts and sizes of aging rates,

relationships between types of maintenance and resulting aging impacts, and

relationships between types of aging contributors and their aging rates. The risk

importance approach can be useful for identifying these relationships as well as for

prioritizing aging contributors in terms of order of magnitude impacts. The other APSA

approaches can also be useful for these types of results.

62
4.3 Impacts of Available Test and Maintenance Information

There are two levels of test and maintenance information which can be available:

Minimal information, basically providing only the type of activity performed and

its frequency,

or

Detailed historical information providing the times the activity was performed,

the type of activity, degradations monitored and corrected, and pieceparts

replaced.

When minimal information is only available then one basically only knows the type of

activity, i.e. whether a surveillance test, maintenance, or replacement was performed, and

the average frequency of the activity. Preventative maintenances may be differentiated

from corrective maintenances. The frequency of the activity may also only be known

approximately. When only minimal information is available then the basic, good as new

and good as old restoration models described in Chapter 2 are the most meaningful

models which are consistent with the minimal test and maintenance information. These

models are first order models and can be used to obtain a first order evaluation of the

aging impacts.

As described in Chapter 2, the good as new model treats the test or maintenance activity

as basically removing all significant aging effects and restoring the component to as good

as new. The good as old model treats the test or maintenance activity as assuring the

component is operational but as carrying out no major renovations of the component so

as not to affect the age of the component or its failure rate. As was indicated,

surveillance tests which principally check the operational status of the component can be

modeled to be as good as old restoration activities. Maintenances which correct

degradations and repairs can be modeled to be as good as new restoration activities. The

good as old and good as new restoration models require only the frequency of the activity

and hence data requirements are minimal. Sensitivity studies can be carried out by

changing various good as new models to good as old and vice versa. Also, the partial

restoration models previously described in Chapter 2 can be used for sensitivity studies to

study the effects of partial restorations between good as old and good as new.

63
When detailed historical information on tests and maintenances is available then such

information as the time of each test or maintenance, the specific actions that were carried

out, the degradations and component conditions that were observed, and the pieceparts

that were replaced are obtainable. This means that, first of all, information is available to

determine the applicability of the good as old or good as new model for a particular

activity. Information is also available to determine whether preventative maintenances

need to be separated from corrective maintenances as discussed in Chapter 2.

Information may also be available to determine the applicability of the partial restoration

models or piecepart maintenance models described in Chapter 2.

For the more complex test and maintenance models, the parameters of the model can be

determined from the information which is available on the activity. The parameters may

be estimated from engineering information and data analyses. The maintenance data can

be analyzed to not only estimate the parameters, but also to determine the most

applicable model.

When more detailed information is available on the test and maintenance activities, any

of the approaches for transforming a PSA to an APSA can be effective depending upon

the focus of the evaluation. The successive stepwise approach will be useful when only a

bound or first approximation for the resulting core damage frequency is desired. The

substitution approach will be effective when the traditional PSA results are desired but

now with aging effects incorporated. The risk importance approach is most useful for

prioritization and sensitivity studies.

4.4 Impact of PSA Information Which is Available

The type of PSA information which is available affects the completeness and detail to

which aging contributors can be evaluated. The PSA information which is available can

be:

The complete PSA event tree and fault tree models

or can be:

A restricted PSA set of minimal cut sets.

64
For each of these cases, it is assumed that the PSA has been developed to a basic

component level i.e. to an individual valve, pump, and relay level. If the PSA has only

been developed to a grouped component level or to a train level in which individual

components afe not identified then component aging effects cannot be evaluated by

transforming the PSA. For each of the above cases of information, it is also assumed that

the data used for the PSA quantification is also available, which includes the initiating

event frequencies, component failure rate data, the test and maintenance data, and the

human error data.

All the approaches for transforming a PSA to an APSA generally use as basic input the

PSA minimal cut sets which are generated from the event trees and fault trees. In the

first case above, when the complete event tree and fault tree models are available then the

minimal cut sets can potentially be generated to the level needed to include all the aging

component contributors. In particular, the minimal cut sets can be generated to include

all significant aging contributors including minimal cut sets containing multiple aging

contributors.

In the second case, when only a restricted PSA set of minimal cut sets is available then

only those components in the restricted minimal cut sets can be evaluated for their aging

contributions. As was indicated previously, a set of minimal cut sets is usually generated

by the PSA as the contributors which are most important. The set of minimal cut sets is

truncated to contain those minimal cut sets whose probability is above some cutoff value

such as lx108. If this truncated set of minimal cut sets is only available then certain

aging contributions may be neglected, especially multiple aging components in the same

minimal cut set which can significantly increase the cut set probability when aging is

considered.

Consequently, when a restricted set of minimal cut sets is only available then particular

individual component aging contributions and particular multiple component aging

contributions (aging interactions) may be neglected which can change the results. For

any application it is thus important to specifically define the contributions which are

included for the aging evaluations. This applies to the case where any truncated set of

minimal cut sets is used, even when the event trees and fault trees are used to generate an

expanded, but still truncated set of minimal cut sets. The criteria used for selecting the

minimal cut sets and the contributors included and excluded should be carefully

documented.

65
Finally, in addition to the level of PSA information, the scope of contributors included in

the PSA is important since it determines the scope of aging contributors which are

included in the APSA. A standard PSA generally does not consider individual balance of

plant (BOP) contributors, lumping all pertinent contributors into a transient initiating

frequency value. Thus, the effects of aging of BOP contributors cannot be evaluated

using this PSA. PSAs also do not generally include many passive component

contributors such as piping and cables. The PSA should be expanded to include these

other contributors, when impacts from these contributors are desired. In all cases, the

scope of the PSA should be documented.

4.5 Impact of Results Which Are of Most Interest

Finally, for a particular application, there can be specific results which are of most

interest, with other results being of lesser importance. All the APSA approaches can

provide a complete set of risk results. However, as was previously noted, a given

approach is most efficient in providing certain types of results. The successive stepwise

approach is best at providing relatively quick approximations or bounds on the aging

impacts. The substitution approach is best at providing bottom line values for the core

damage frequency and system unavailabilities. The risk importance approach is best at

providing prioritizations of aging contributors and sensitivity results.

As was also previously indicated, the desire for specific results must be tempered with

the availability of aging failure rate data, test and maintenance data, and PSA

information. When minimal data exists then the selected models and the APSA approach

used need to account for the lack of data. Bottom line core damage frequencies and

system unavailabilities can be obtained but uncertainty analyses and sensitivity analyses

need to accompany the results. With little data, the most meaningful results are

sensitivity analyses, prioritizations of aging contributors, and relationships determined

which are not sensitive to specific data values. This applies for any APSA approach

used.

66
5. PRIORITIZATIONS OF AGING CONTRIBUTORS

5.0 Intrduction

This chapter illustrates the applications of an APSA for the objective of prioritizing aging

contributors. The prioritization of the contributions to the core damage frequency from

aging active components will be specifically evaluated. The same methodology could be

applied in prioritizing passive component contributions, provided the PSA contains the

passive components and aging failure rates can be obtained for the passive components.

For the prioritization of active components demonstrated here, a PSA will be used which

has already been developed for a plant. The particular PSA which is used is not of

concern since the focus here is on the basic approaches for using an APSA to prioritize

aging contributors.

For the prioritization of aging contributors, the approach which will be used for

transforming a PSA into an APSA will be the risk importance approach for evaluating

aging effects previously described in Section 3.3. As was described in Section 3.3, the

risk importance approach provides a detailed accounting of the aging contributors

including all the aging interactions. The substitution approach for evaluation aging

effects described in Section 3.2 could also be used, however the prioritization of the

contributors would be in terms of the minimal cut sets instead of the detailed individual

and interaction contributors. The successive stepwise approach could also be used to

produce first approximations of the contributors but again they would be in terms of the

minimal cut sets which contribute to the core damage frequency.

The following sections describe specific steps that need to be carried out in applying an

APSA for prioritization evaluations. Considerations involved in selecting aging failure

rate models and aging failure rate data are described. Selection of test and maintenance

models is also discussed. Finally, organization and grouping of the results for

prioritization applications is discussed. Even though the specific focus is on using the

risk importance approach for prioritizing aging contributors, the considerations apply to

any APSA approach used for prioritizing contributors.

-67
5.1. Application of the Risk Importance Aging Approach

As was discussed in Section 3.3, in the risk importance aging approach, the core damage

frequency increase AC due to aging is expressed as a sum of contribution terms from

successively higher order aging interactions;

AC = AC + AC2 +...+ACn (49)

Where AC1 is the contribution from individual component aging effects, AC2 the

contribution from two component aging interaction effects, etc. The maximum size n of

the interactions is the largest core damage minimal cut sets obtainable from the PSA.

For prioritization applications, we must first decide upon the maximum size of

interactions to consider. Considering all interactions will be exact but can be time

consuming in calculating all the contributions. The higher order interaction terms can

also be repetitive in that the same components will appear in the contributions.

Considering only single component aging effects AC1 will include the dominant

individual components which individually contribute most to the core damage frequency

effects from aging. We shall consider interactions up to second order to include in the

prioritization those additional components which individually may not be important but

which jointly can be important aging contributors. Even though we consider only second

order interactions, the approaches and guidelines we describe are applicable for any size

interactions considered.

When interactions up to second order are considered then Equation (49) for AC

approximates to

AC = AC + AC2 (50)

The first order contribution AC1 is the sum of the individual component aging

contributors;

AC1 = Acj (51)

i

68
where Aci is the core damage frequency contribution from the aging of component i. As

indicated in Section 3.3, Aci can be expressed as a product of the risk importance Si of

the component and the aging effect aging am% on the unavailability of the component,

Aci =Siqi (52)

Similarly, the second order contribution AC2 is the sum of the joint component aging

contributors,

AC2 = yaC1 (53)

j>i

where Acij is the interaction contribution from the simultaneous aging of components i

and j. As was indicated in Section 3.3. the contribution Ic& can be expressed as a

product of the joint risk importance Sij of the component combination and the effect of

simultaneous aging Ach Aqj on the component unavailabilities,

Acij = SijAqiAqj * (54)

All the individual aging contributors and second order contributors are thus identified in

this joint prioritization evaluation. Additional, higher order terms AC3, etc. can be

generated to check whether any new contributors appear.

A personal computer program was constructed to calculate the risk importance

coefficients Si and S4 from the core damage frequency minimal cut sets supplied by the

PSA using the algorithm given in the NUREG/CR-5510(7). All the data in the original

PSA (failure rates, test intervals, initiating event frequencies, etc.) are used to calculate

values for Si and Sij. The aging effects Aq, are calculated with reference to the baseline

values determined in the PSA. The core damage frequency effects AC1 and AC2 are thus

calculated with reference to the baseline core damage frequency in the PSA. To obtain

the total core'damage frequency including aging, one can add the aging contribution AC

to the baseline PSA value. As was indicated in Section 3.3, the advantage of the risk

importance approach is that the original PSA may be used to calculate the risk

importance coefficients, which need to be done only once for as many different aging

analyses that may be carried out which only involve changing Aq4 or Aq%.

69
The core damage frequency increase AC (including AC, and AC2 ) which will be

calculated will be the average increase due to aging between replacements (renewals) of

the component. The average core damage frequency increase is calculated by using the

average unavailability increase Aq between component replacements in Equations (52)

and (54). If the component is not replaced during the plant lifetime then the average

increase over the plant lifetime is used. The average increase applies to any year. The

average increase AC added to the baseline core damage frequency from the PSA will

give the new, average core damage frequency at any year. The appendix gives the time

dependent unavailability formulas which can be averaged to obtain the average Aq.

5.2 Selection of Aging Failure Rate Models and Data

When plant specific failure data is available then the appropriate failure rate aging

models and data would be selected based on this plant data. To determine the aging

models and data for these models, the failure data would need to include at minimum for

each component of interest, the times of failure and times of major overhauls or

replacements. Using statistical approaches, the appropriate failure rate model, e.g.

whether linear, Weibull, or exponential, would be determined by fitting the alternative

models using likelihood or Bayesian approaches.

In lieu of having available plant specific data, generic aging failure rates or subjective

estimates of aging failure rates need to be used. Generic or subjective estimates of aging

failure rates can be useful in providing an initial prioritization of the aging contributors to

help initially focus maintenance activities, monitoring activities, and data collection

activities. When generic or subjective aging failure rates are used then sensitivity studies

or uncertainty analyses can carried to investigate effects of data variations and

uncertainties. he results from the sensitivity or uncertainty analyses can then be

factored into the prioritization conclusions. For the application here, the subjective,

aging failure rate data base in NUREG/CR-5248 (8) is used. This aging failure rate data

base is often called the TIRGALEX data base referencing the committee which had

oversight on the work.

The TIRGALEX aging rate data base assumes a linear aging failure rate model,

70
(55)

where (w) is the age dependent failure rate as a function of the component age w, X. is

the underlying constant failure rate as used in the PSA and a is the component aging rate

(the symbol "a" is used here instead of "t" in chapter 2). For the TIRGALEX data base,

a panel of experts estimated the aging rates a for various classes of components. Though

no systematic illicitation or estimation techniques were used, there was an attempt to be

consistent and to effectively utilize available engineering knowledge.

The TIRGALEX aging rates a are given in Table 8 for the active components in the PSA.

The TIRGALEX aging rates are intended to be subjective, generic aging rates.

NUREG/CR-5248 warns about the uncertainties associated with the values. As a means

of assessing the uncertainties in the TIRGALEX aging rates, NUREG/CR-5510 (7)

compared the TIRGALEX aging rates with aging rates which were obtained from

samples of Licensee Event Report (LER) data, data from the Nuclear Plant Reliability

Data System (NPRDS), and plant specific data. For diesels, pumps, and motor operated

valves, the median aging rate values from the samples of data agreed within

approximately a factor of 10 with the associated TIRGALEX values. For check valves

the TIRGALEX aging rate value was a factor of 10 to 100 lower than specific plant

estimates, principally because of check valve backleakage problems at specific plants.

Thus, the TIRGALEX aging rates generally agreed to within an order of magnitude with

the aging rates estimated from plant data and were biased low when plants had specific

problem components.

The TIRGALEX aging rates were generated in NUREG/CR-5248 for prioritizing

research needs. Thus, the TIRGALEX aging rates are best suited for prioritization

analysis as is carried out here. Because the aging rates are based on subjective judgments

and have large uncertainties, sensitivity analyses are also carried out for the prioritization

applications here. For the sensitivity analyses, two different aging rate data bases are

constructed for the components which were dominant PSA contributors. One sensitivity

aging rate data base represents low aging rates and one represents high aging rates.

Further details of the steps involved in generating the aging rates are provided in

NUREG/CR-5510.

Table 9 gives the low sensitivity aging rates for those components identified as being

dominant contributors in the baseline PSA. The aging rates are low aging rates in that

71
TABLE 8. TIRGALEX AGING RATES USED FOR ACTIVE COMPONENTS

COMPONENT AGING RATE (per hour per year)

Ac Bus 1.OE-09

Air-Operated Valve 4.OE-07

Battery 3.OE-07

Check Valve 4.OE-09

Circuit Breaker 2.OE-08

DC Bus 1.OE-09

Diesel Generator 3.6E-06

Motor-Driven Pump 2.OE-07

Motor-Operated Valve 3.6E-06

Relay 3.OE-07

Safety/Relief Valve 7.OE-07

Transformer 2.OE-09

Turbine Driven Pump 3.OE-06

Solenoid-Operated Valve 6.7E-07

72
the aging rate only doubles the baseline PSA failure rate of the component after 40 years.

All aging rates for other components not shown in the table are kept at their TIRGALEX

values. Table 10 gives the high sensitivity aging rates that are defined for these same

components. All other component aging rates are kept at their TIRGALEX values.

These high sensitivity aging rates are the same as the upper threshold aging rates used in

NUREG/CR-5510 and cause an unavailability of 0.1 after 18 months, which is a

significantly high unavailability and which is characteristic of severe aging.

One final comment should be made regarding the use of the linear failure rate aging

model given by Equation (55). Use of the linear aging model, instead of the Weibull

model or exponential model, ignores nonlinear aging effects exhibited by the

components. The linear aging model can thus be viewed as a first order linear

approximation for the aging behavior of the component. Prioritizations using linear

aging rates can consequently be viewed as first order prioritizations of the risk

importances of component aging effects. Investigations of the impacts of nonlinear

aging effects could then be carried out using appropriate nonlinear models.

5.3 Selection of Test and Models

If test and maintenance effects are to be explicitly incorporated when aging contributors

are prioritized, then appropriate test and maintenance models must be selected. For the

prioritization we shall assume technical specifications are followed at the plant with no

additional scheduled maintenance being carried out. This can be termed the minimal

maintenance situation. The prioritization of contributors which are obtained can then be

used to help focus and structure a risk-based aging maintenance program. Prioritization

of aging contributors under an existing scheduled maintenance program would require

selection of the applicable maintenance models. The prioritization results would then

identify what contributors would need further emphasis and what contributors could be

relaxed in terms of their maintenance activities.

For the prioritization, we thus assume surveillance tests are good as old. That is, if

degradations are detected at a test they are not removed as long as the component is still

functional. We also assume that when a component is found to be functionally failed at a

surveillance test that it is replaced or is repaired so that it is as good as new. This can be

an optimistic assumption if minimal repairs ae only carried out. The assumption

73
TABLE 9. LOW SENSITIVITY AGING RATES USED FOR DOMINANT

CONTRIBUTORS

COMPONENT AGING RATE (per hour per year)

Air-Operated Valve 7.OE-08

Battery 2.OE-08

Check Valve 4.OE-09

Diesel Generator 2.0E-07

Motor-Driven Pump 2.OE-07

Motor-Operated Valve 2.OE-07

Safety/Relief Valve 7.OE-08

Turbine Driven Pump 2.OE-06

TABLE 10. HIGH SENSITIVTY AGING RATES USED FOR DOMINANT

CONTRIBUTORS

COMPONENT AGING RATE (per hour per year)

Air-Operated Valve 1.OE-05

Battery 1.OE-05

Check Valve 1.OE-05

Diesel Generator 1 .OE-05

Motor-Driven Pump 1.OE-05

Motor-Operated Valve 1.OE-05

Safety/Relief Valve 1.OE-5

Turbine Driven Pump 1.OE-05

74
can be chocked by treating repairs to also be good as old.(See the next chapter.) We

assume the same test intervals as used in the basic PSA. We do not assume that testing is

carried out more frequently if aging occurs. The applicable test interval for each

component will be shown in subsequent result printouts. In addition to the surveillance

test interval, we also need to assume efficiencies for the surveillance tests. From Section

2.7 again, the efficiency of a surveillance test is the probability that a given failure is

detected by the test.

Two sets of efficiencies are used for the prioritization evaluations. For one set of

evaluations, the surveillance tests are assumed to have 100% efficiency (efficiency

fraction T = 1). For the second set of evaluations, the surveillance tests are assigned the

efficiencies &r given in Table 2.6 of the TIRGALEX report NUREG/CR-5248. The

efficiencies are reproduced in Table 11. The APSA results from both these efficiency

data sets will be factored into the prioritizations.

5.4 Selection of the Formulas for the Component Aging Impacts

As additional input information required for the prioritization application, we need

formulas for Aq, the aging effect on the component. More specifically, Aq is the increase

in component unavailability over the base PSA value without aging effects;

Aq = q-qO (56)

where q is the component unavailability explicitly including aging and q. is the value

calculated in the base PSA assuming no aging (i.e. assuming a constant component

failure rate).

The formula for Aq, or equivalently for q, for each aging component is required. These

formulas are required, not only for the risk importance approach we are using here, but

also for the substitution approach. For the successive stepwise approach, age-dependent

formulas are not needed, but time steps would need to be selected which apply to all

components and which are used to approximate the time dependent or age dependent

component failure rates for each component

75
TABLE 11. TIRGALEX SURVEILLANCE TEST EFFICIENCIES

COMPONENT TEST EFFICIENCY

Ac Bus 0.45

Air-Operated Valve 0.45

Battery 0.86

Check Valve 0.09

Circuit Breaker 0.45

DC Bus 0.45

Diesel Generator 0.27

Motor-Driven Pump 0.44

Motor-Operated Valve 0.60

Relay 0.18

Safety/Relief Valve 0.82

Transformer 0.62

Turbine Driven Pump 0.44

Solenoid-Operated Valve 0.82

76
If we were also including aging effects on initiating event frequencies (e.g. on the pipe

rupture frequency) then we would also need formulas for the change in initiating event

frequency AX due to aging. However, we will not consider aging effects on initiating

event frequencies since our focus is on prioritizing active safety components. It is useful

to note however that the aging effect AX is simply

=Al o. 0-; (57)

where X is the age dependent failure rate (i.e. initiating event frequency) such as the

Weibull failure rate and A, is the constant value used in the PSA. For the core damage

frequency contributions from aging, AX would then simply replace Aq in Equation (45).

We will prioritize the aging contributors with regard to their average aging effects on the

core damage frequency. The average aging effect for a component is the average

increase Aq due to aging between replacements or renewals of the component.* From

NUREGICR-5510 (7), for a linear aging failure rate, the average unavailability increase

Aq due to aging is

Aq= a(L-T)T aT2 (58) 4 6

where a is the aging rate, L is the replacement interval (or overhaul interval), and T is the

surveillance test interval for the component. The above formula models a surveillance

test as being good as old. The above formula can also be obtained by substituting a

linear aging failure rate into the general formula given in the appendix.

If components are replaced at failure, as we assume, then the replacement interval L for

each component is the mean time to failure for the component plus the time until the

failure is detected. The time until the failure is detected is, on the average, one half the

interval between tests. Since the test interval is generally small compared to the mean

time to failure we shall ignore the additional time until detection.

*If we were to prioritize the contributors for a given time, i.e. at a given plant age, then &q would be the

time dependent unavailability increase. We would need to now the times at which the tests or

maintenances are performed in addition to the intervals.

77
Using the PSA constant failure rate value, the mean time to failure is simply one over the

component failure rate. The value for the mean time to failure for each component is

given as part of the results presented in the subsequent section. Calculation of the mean

time to failure using the PSA failure rate ignores the effects that the additional aging rate

has on the mean time to failure. For the baseline and low sensitivity aging rates, because

the aging rates are relatively small compared to the constant failure rates, these effects

are small, particularly when compared to the uncertainties in the failure rates. For the

high aging rates, neglect of these effects will cause the mean time to failure to be larger

than if these effects were considered. This will add an extra conservatism to these upper

bound evaluations.

Consequenty , we assume

L = (59)

Ao

where 34 is the PSA constant failure rate.

If there are no surveillance tests expected on the component between replacements, then

T is set equal to L in Equation (58) for Aq, as discussed in the appendix. As previously

discussed in Section 2.7, inefficiencies in surveillance tests can be modeled by

interpreting T in Equation (58) to be the effective test interval:

T= Q (60)

ST

where eT is the test efficiency.

Finally, we need to consider the case where the mean time to failure of the component is

larger than the plant lifetime. We will assume an extended plant lifetime of 50 years.

Then from NUREG/CR-5510 or using the formulas in the appendix,

Aq = la[toT+Y3] (61)

78
where to is equal to 50 years. Whether to is set equal to 40, 50, or 60 years should have

little effect on the prioritization results. If there is no surveillance test expected in 50

years then the formula for the unavailability increase with no testing is,

jq I 2 (62)

where again t is 50 years. We thus have all the formulas required for the analysis.

5.5 Detailed Prioritizations of and Component Contributors

Tables 12A and B, 13A and B, and 14A and B present the prioritizations of component

contributors for the three cases which were analyzed, which are termed the base case, the

upper bound sensitivity case, and the lower bound sensitivity case. The base case utilizes

the TIRGALEX aging rates and the TIRGALEX surveillance test efficiencies. The

upper bound case utilizes the high sensitivity aging rates and the TIRGALEX test

efficiencies. The lower bound case utilizes the low sensitivity aging rates and assumes

surveillance test efficiencies of unity.

For each case analyzed, two tables are presented. The first table presents the core

damage frequency increase AC, for individual component aging effects. This gives the

prioritization of individual component aging effects. The second table presents the core

damage frequency increases AC2 for double component aging interactions. This gives

the prioritization of two component aging interactions. For example, Table 12A presents

the ranked individual component contributions for the base case and Table 12B presents

the ranked two component contributions. The total core damage frequency increase from

aging is the sum of the contributions from the two tables. The top 25 contributors are

given in each table, representing approximately 99% of the total contribution to AC1 and

to AC2. The results are straightforwardly obtained using the risk importance approach,

previously described and are organized in a tabular format to explicitly detail information

on the aging contributors.

The first column in a given table is the rank of the contributor according to the impact of

the aging effect on the core damage frequency contribution. The core damage frequency

79
TABLE 12A. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: BASE CASE, SINGLE CONTRIBUTIONS

00

Plant A. Single Cotributions

TRGALEX Aging Raues

TIRGALEX Testing Effciencies

TotalAC: 1.8E-04 /year

Test

Rank Component Name Seasitivity Aging Rate MTBF Aql Inval AC

Coefficient o/yr) (months) (monhs) (/year)

1 LPR-MOV-Fr-1862A 1.5E-04 3.6E-06 167 2.62E01 30 3.9E.05

2 LPR-MOV-FT-1860A 1.5E04 3.6E-06 167 2.6E-01 30 3.9E-05

3 LPR-MOV-Fr-1890A 1AE-04 3.6E-06 167 2.6E01 30 3.5-05

4 HPI-MOV-Fr-1350 6.72.05 3.6E206 167 2.6E-01 30 1.7E-05

S LPR-MOV-Fr-1862B 2.1E-05 3.6E-06 167 2.6E-01 30 5AE.06

6 OEP-DGN-FS-DG01 3.8E-04 3.2-06 72 1AE-02 4 53E-06

7 LPR-MOV-Fr-1860B 2.0E- 3.6E-06 167 2.6E-01 30 5.3E-06

8 0EP-DGN-FR-6HDGI 3.4E-04 3.62-06 72 1AE-02 4 4.82E06

9 OEP-DGN-FS-DG03 2.0E-04 3.6E06 72 1.4E-02 4 2.8E206

10 OEP-DGN-FS-DG02 2.02-04 3.6-06 72 1.4E-02 4 2.8E06

11 0EP-DGN-FR-6HDG3 1.9E-04 3.6E-06 72 AE4-02 4 2.7E06

12 OEP-DGN-FR-6HDG2 1.7E-04 3.6E-06 72 1AE4-02 4 2.5E06

13 PPS-MOV-FT-1535 9.5E-06 3.6E-06 167 2.6E-01 30 2.4E-06

14 HPIJCKV-Fr-CV225 2.1E-03 4.02-9 0 4.8-04 11 1.7E06

15 H-PICKV-Fr-CV25 2.1E-03 4.0-09 0 4.8E-04 11 1.7E.06

16 HPI-CKV-Fr-CV410 2.1E-03 4.0E49 0 4.8E-04 11 1.7E206

17 HPI-MOV-F-1I1SC 5.7E-06 3.6E-06 167 2.6E201 30 1.5E-06

18 HPI-MOV-Fr-1115D 5.7E-06 3.6E2-6 167 2.6E-01 30 1SE-06

19 HpI-MOV-FF-1115B 5.7-06 3.6E-06 167 242.01 30 1.SE-06

20 HPI-MOV-F-1115H 5.7E-06 3.6E-06 167 2.6E-01 30 1.5E06

21 LPR-MOV-FT-1890B 4.5E-06 3.6E206 167 2.6E-01 30 1.2E.06

22 PPS-MOV-FT-1536 3.4E-06 3.62-06 167 2.6E-01 30 8.8E-07

23 HPI-MOV-FT-1867D 2.9E-06 3.6E246 167 2.6E-01 30 7.5E-07

24 OEP-DGN-FR-DG01 5.0E-05 3.6E-06 72 1.E-02 4 7.2E-07

25 SIS-ACI-FA-SISA 1.8E05 3.0E-07 0 1.8E02 6 5.4E-07
TABLE 12B. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: BASE CASE, DOUBLE CONTRIBUTIONS

PlM A: Double Contribution

TIRGAL Aging Rates

iRGALE Testing Efficiencies

Totd,&C 7.6E404 /e

Tast Test

Rank Component Name Sensitivity Aging Rat MP &q1 Inti Componen Name Aging Rate MBF Aq2 Inerval aC _ ____________ Codficent W/yr() (months) (mond) hlyr) (mths) (months) 0fycar) I HPI-MOV-Fr-1115B 19E403 3.606 167 2.6801 30 HPI-MOV-Fr-1115D 3.6-06 167 2.68.01 30 1.38.04

2 HPI-MOV-Fr-1IISC 1-98.03 3.6-06 167 216E;01 30 HPI-MOV-Fr-1115H 3.6E-06 167 2.6E01 30 1.3E04

3 LPR-MOV-Pr-189A 15f03 3.6-06 167 2.68.01 30 LR-MOV-FI-1890B 3.6E06 167 2.6E-01 30 1.0E04

4 LPR-MOV-P1860A 15E-03 3.6E6 167 2.8i01 30 LR-MOV-Ft-1860B 3.66-06 167 2.6E.01 30 1DE004

5 LPR-MOV-FT-1862A 1.5E03 3.6E-06 167 21;E40 30 LPR.MOV-FF.1860B 3.6E06 167 2.6E.01 30 1.0E04

6 LPR-MOV-Fr-1860A 103 3.6E46 167 2A.01 30 LPR-MOV-Fr-1862B 3.6E06 167 2.6E01 30 1.0E04

7 LPR-MOV-Pr-1862A 15803 3.6.06 167 2.6E.01 30 LPR-MOV-PT-1862B 3.6E-06 167 2.6E-01 30 1.0E04

8 SIS-ACr-FA-SISB 6.5E43 3.0E-07 0 1sm2 6 SIS-ACr-PASISA 3.0E47 0 1.8E02 6 5.9E-06

9 RT-ACr-FA4MS 1503 30.07 0 1.8802 6 RMr-ACT-FA-MSB 3.0£-07 0 1.8E02 6 1AE.06

10 OEPON-Ft-6HD03 5S.03 3.806 72 IAE-02 4 OEP-WN-FR G1 3.6E06 72 IAE02 4 .IE06

11 OEP-DGN-FS-DOOl 4.9E45 3.6E-06 72 IAE-02 4 OEP-DGN-FS-D02 3.6E06 72 IAE02 4 9.9E07

12 OEP-DWN-FS-DGO1 4.9E-03 3.6E46 72 IA.E02 4 OEP-DON-FS-D03 3.6806 72 IAE-02 4 9.9E-07

13 OEP-DWN-P-D01 4.0E03 3.6E-06 72 1AE42 4 OEP-DGN-RD02 3.6E-06 72 IAE02 4 8.1E-07

14 OEP-DINFS-DWOI 4.0E-03 3.68E06 72 IA 2 4 OEP-DGN-FR-6HDO3 3.6-06 72 IAE02 4 8.1E07

15 O£P-DON-FS-DGO2 408.03 36E.06 72 1A.E02 4 0P-DGN-FR-MHDOI 3.6E-06 72 1AE-02 4 8.1E07

16 OEP-DGN-FR-6HDO1 4.0E-03 3..06 72 IAE402 4 0EP-DN-FR-6HDG2 3.6E06 72 IAE42 4 8.1E07

17 OEP WN-PS-W03 3.9E43 3.6806 72 IAE02 4 OEP-DGN-FR6HDGI 3.rz.06 72 1.4E02 4 7.8E-07

18 OEP-DOWN-FS-DG01 5.E-03 3.6E06 72 1.4E02 4 MSS-SRV-00-SOSRV 7.0-07 22 3AE03 22 2AE-07

19 U.l-MDP-FS-SllB 1--03 2.0E07 86 5.98.04 2 IBMMOV-1862A 3.6-06 167 2.6E01 30 2.3E-07

20 LPI-MDP-FS-SllA 1E03 2.OE-07 86 5.8804 2 -MOV-Fr-1on 3.68.06 167 2.6801 30 23E07

21 LPI-MDP-FS-SllB 1.5E.03 2.0E-07 86 5.M804 2 LR-MOV--1860A 3.6E06 167 2.6E.01 30 2.3E.07

22 LPI-MDP-FS-SIIA 1.5E03 2.0E07 86 5.8844 2 LPR-MOV-PT-1862B 3.6E-06 167 2.6E01 30 23E07

23 OEP-DGN-FR-6HDGI 4.6803 3.6E06 72 IAE02 4 MSS-SRV-O SSRV 7.0E-07 22 3.4E03 22 2.2E07

24 PPS-MOV-FC-1536 2.9E-06 3.6E-06 167 2681 30 PPS.MOVC-1535 3.6E-06 167 2.6E.01 30 .9E07

25 OEP-DGN-PS-DW03 9.1E04 3.6E.06 72 1AE02 4 OEP-DGN-FR-DG01 3.68.06 72 1AE42 4 1.8E-07

00P"a
TABLE 13A. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: UPPER BOUND CASE, SINGLE CONTRIBUTIONS

Pat A: Sing Contlbutions

High Aging Razcs

TIROALEX Tesdg Eficici es

Total AC_ .OE-02 /year

Test

Rank Component Namo Smwsiivity Aging Rate MIBF ql Interval AC

Coefficiet A/yr) (months) (months) /yer)

1 MPI-cKV-Fr.CV225 2.IE-03 lOE-05 0 7.OE-01 11 2.SE03

2 HPI-CKV-Fr-CV410 2.1E-03 1.OE-05 0 7.E-1 11 2.4E-03

3 HPI-CKV-FI-CV25 2.1E-03 1.E05 0 7.OE-01 11 2.4E-03

4 AOC-CKV-FI-CV145 5.OE-04 1.OE-5 0 7.0E41 11 5.8E-4

5 ACCCCV-FT-CV147 5.OE-04 .OE-05 0 7.OE-41 11 5.8E-04

6 ACC-CKV-FT-CV130 S.OE-04 1.OE-05 0 7.OE41 11 5.8E-04

7 ACC-CKV-FT-CV128 S.OE-04 1.OE05 0 7.OE01 11 5.8E-04

8 LPR-MOV-FT-1862A 1.5E-04 1.OE-5 167 5.lE401 30 7.8E-05

9 LPR-MOV-Fr-1860A 15E-04 1.OE05 167 S.lE41 30 7.8E45

10 LPR-MOV-FT-1890A 1.4E-04 1.OE45 167 5.lE-01 30 7.OE-05

11 HPI-MOV-Fr-1350 6.7E05 1.OE05 .167 S.1E01 30 3.4E-05

12 OEP-DGN-FS-DG01 3.8E-04 1.OE-05 72 3.9E02 4 1.5E-05

13 OEP-DGN-FR-6HDG1 3.4E-04 1.OE05 72 3.9E02 4 1.3E05

14 LPR-MOV-F-1862B 2.1E-5 1.OE-05 167 5.1E01 30 .1E-05

15 LPR-MOV-FT-1860B 2.OE-05 1.OE45 167 5.IE-41 30 1.OE-05

16 OEP-DGN-FS-DGO02 2.OE04 .OE-05 72 3.9E02 4 7.9E-06

17 OEP-DGN-FS-DG03 2.OE04 O-05 72 3.9E 02 4 7.9E.06

18 OEP-DGN-FR-6HDG3 1.9E04 1.E-05 72 3.9E-02 4 7.6E-06

19 OEP-DGN-FR-6HD02 1.7E-04 1.0E05 72 3.9E02 4 6.8E 06

20 PPS-MOV-FT-1535 9.5E06 LOE.05 167 .IE-01 30 4.8E-06

21 MSS-CKV-FT-SGDHR 4.1E06 1.OE-0S 0 7.OE-01 11 4.7E-06

22 HPI-MOV-F-ll15C 5.7E-06 1.OE-5 167 5.1E41 30 2.9E-06

23 HPI-MOV-Fr-Il 15D 5.7E-06 1.OE05 167 5.lE01 30 2.9E-06

24 HPI-MOV-F-1SE 5.7E06 .OE-05 167 5.lE01 30 2.9E-06

25 HPI-MOV-Fr-1115B 5.7E06 1.OE-05 167 5.1E-41 30 2.9E-06

00
TABLE 13B. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: UPPER BOUND CASE, DOUBLE CONTRIBUTIONS

Plan A: Double Contributions

High Aging Rats

TIRGALEX Testing Effiiencies

-__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Total AC: 4.5E 03 1year

Test Test Rank Component Name Sensitivity Aging Rate MlMF AqI Intetvl CompoentName Aging Rate MF Aq2 Interval AC ______ Coefiet ~hrlyr) (months) (monds) _ _ (I r) (months) (months) year) I HP -MOV-F-1115B ISE03 1.02-05 167 5.12.01 30 HPI-MOV-Frl.lSD 1.04-05 167 S.1E01 30 4.9E.04 2 -MOV-F-1115C .9E-03 1i02.5 167 5.E-01 30 HP-MOV-FT-I1IS1 1.0E-05 167 5.IE-01 30 4.9E04 3 HPK-CKV-0CV28 1.3-02 1.0E45 0 7.0E01 11 HPI-MDP-FR-1A24H 1.0EM 86 2.9E'02 2 4.4E04 4 LPR-MOV-FT-1860A 1.53 1.-05 167 5.1301 30 LPR-MOV-F-1862B 1.01105 167 5.IE-01 30 3.91.04 S LPf-MOV.PT-1890A E 4-03 1OiS 167 5.12-O1 30 -MOV-F-18B 10.0E5 167 5.1E-01 30 3.9E.04 6 LPR-MOV.IT-1860A 1.E-03 1.0E'0S 167 5.11.01 30 LPR-MOV-FT-1860B 1.0E5 167 .1E-01 30 3.91.04 7 LP-MOV-FT-1862A 15E-03 1.o0s 167 .M2-01 30 UR-MOV-Pr-1862B 1.05 167 5.1E-01 30 3.9E04 8 LPR-MOV-FT-1862A 1SE03 1MME40 167 S.1E-01 30 LPR-MOV-F-1860B 1M 167 5.IE01 30 3.9E.04 9 AFW.TDP-FS-FW2 5AE-03 1.0E.05 72 2A0 2 4 142 1i0205 0 7.0E01 11 1.54-0 10 HPi-CKV4O-CV258 4.0fi03 1.0E05 0 7.0fi41 It HnP-MDP-FR-IA6HR OE4S 86 2.92.02 2 1A.4 11 AFW-MDP-FS-W3A 3.-03 1.0E-05 86 29E02 2 AFW.CKV-OO-CV157 1025 0 7.0E-01 11 1.2E-04 12 AFW {X4-O.CV172 3.6-03 1.0.45 0 7M01 11 AFW-MDP-FS-FW3B 1.0E-0S 86 2.9E02 2 1.2E-04 13 PPS-MOV-FT-1535 1.1E04 1S.05 167 5.1"1 30 AFW.CV-C142 1.2-05 0 7.04-01 11 6.7E05 14 AFW-CKV-00.CV142 .lE204 1.005 0 7.021 11 PPS.MOV-FT-1536 1.05 167 5.1fi01 30 6.7E05 15 LPI-MDP-FS-S[IA 1.503 1.005 86 2.9E4-2 2 IPIKV4O-CVS8 1.0E5 0 7.0E01 11 5.1E05 16 LPI-MDP-FS-SIB 1-03 1.0E45 86 2.913-2 2 LPI-CV0-CVSO 1.02-05 0 7.0E-01 11 5.IE-05 17 MSS-SRVOSGSRV 7.92.04 10-M 22 4.91-02 22 AFW..CVOO6CV172 1.0E.5 0 7.0-01 11 4.52.05 18 AFW-CKV.00.CV157 6.4E05 1.04-05 0 7.0E41 4 11 PPS-MOV-PT-1536 1.0£M 167 5.1E01 30 3.84-05 19 AFW-CKV-00-CV172 6.4ES 1I05 0 7.02-01 11 P1S-MOV-1536 102M 167 5.1E-01 30 3.8E-05 20 PI-MOV-PT-1535 6.4E45 1.0E45 167 S.1E-01 30 AFW-CKV4XO-CVS7 1.0-O0 0 7.0E-01 11 3.8M05 21 PPS-MOV-PT-1535 6AE-05 1.02.05 167 5.1E01 30 AFWCIV-OO.CV172 1.02-0S 0 7.04-01 11 3.820 22 OEP-DGN-FS-D0I 6.-04 1.0-05 72 3.9E2 4 AFW.CKV4XO-CV172 1.02-05 0 7.0E-01 11 3.04-05 23 LPI-MDP-FS-SIIB 1.5-03 1.0£-05 86 2.92 2 LPR-MOV-FI-1860A 1.0M.5 167 5.1-01 30 2.2110 24 LPI.MDP-FS-SIIA 1.5503 1.04-05 86 2.913-02 2 j-MOV-FT-1862B 1.0S05 167 5.1-01 30 222.05 25 LPI.MDP-FS-SIIA 15203 1.0E-05 86 2.9E-02 2 LPR-MOVFr-1860B 1.0E5 167 5.1-01 30 2.2205
TABLE 14A. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: LOWER BOUND CASE, SINGLE CONTRIBUTIONS

Plant A. Single Conuibutons

Low Aging Ratcs

Efficiency = 1

Total AC: 6AE-06 /year

Test

Rank Component Name Sensitivity Aging Rate MTBF hql Ineval AC

Coefficient (hr/yr) (months) (monahs) (/year)

i LPR-MOV-FT-1862A 1.5E04 2.OE-07 167 8.8E-03 18 13E-06

2 LPR-MOV-Fr-1860A 1.5E-04 2.0E-07 167 8.8E 03 18 1.3E-06

3 LPR-MOV-FI-1890A 1.4E-04 2.OE-07 167 8.8E-03 18 1.2E-06

4 HPI-MOV-Fr-1350 6.7E-05 2.OE-07 167 8.8E-03 18 5.9E-07

S HPI-CKV-Fr-CV225 2.1E-03 5.0E-09 0 5.SE-05 1 1.9E-07

6 HPI-CKV-Fr-CV410 2.1E-03 5.OE-09 0 5.5E-05 1 1.9E-07

7 HPI-CKV-FI-CV2S 2.1E-03 5.0E09 0 5.5E-05 1 1.9E-07

8 LPR-MOV-FT-1862B 2.1E-0S 2.0E-07 167 8.8E-03 18 1.8E-07

9 LPR-MOV-FI-1860B 2.0E-05 2.0E-07 167 8.8E-03 18 1.8E-07

10 AFW-TDP-FS-FW2 6.8E-05 2.0E-06 72 2.2E-03 1 1.5E-07

11 SIS-ACT-FA-SISA 1.8E-05 3.OE-07 0 3.3E-03 1 9.8E-08

12 SIS-ACr-FA-SISB 1.8E-05 3.0E-07 0 3.3E-03 I 9.8E-08

13 PPS-MOV-FT-1535 9.5E-06 2.0E-07 167 8.8E-03 18 8.4E-08

14 OEP-DN-FS-DG01 3.8E-04 2.0E-07 72 2E2-04 1 8.2E-08

15 OEP-DGN-FR-6HDGI 3.4E-04 2.0E-07 72 2.2E-04 1 7.4E-08

16 AFW-TDP-FR-2P6HR 2.6E-05 2.0E-06 72 2.2F-03 I 5.6E08

17 HPI-MOV-F-lllSB 5.7-06 2.0E-07 167 8.8E-03 18 SbE-08

18 HPI-MOV-FT-111SD 5.7E-06 2.0E-07 167 8.8E-03 18 S.OE-08

19 HPI-MOV-Fr-ll15C 5.7E-06 2.0E-07 167 8.8E-03 18 S.OE-08

20 HPI-MOV-FI-111SE 5.7E-06 2.0E-07 167 8.8E-03 18 5.0E-08

21 ACC-CKV-F-CV130 5.0E-04 5.OE-09 0 5.5E-05 1 4.6E-08

22 ACC-CKV-FF-CV145 5.0E-04 S.0E-09 0 5.5E-05 1 4.6E-08

23 ACC4CV-FT-CV128 5.0E-04 5.0E-09 0 5.5E-05 1 4.6E-08

24 ACC-CV-Fr-CV147 5.0E-04 5.0E-09 0 5.5E-0S I 4.6E-08

25 OEP-DGN-FS-DG02 2.0E04 2.OE-07 72 2.2E-04 1 4.3E-08
TABLE 14B. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: LOWER BOUND CASE, DOUBLE CONTRIBUTIONS

Plant A, Double Contributions

Low Aging Rates

Efrciency mI

Test Test

Rank Component Nane Sensitivity Aging Rat MIBP Aql Interal Component Name Aging Rate M F Aq2 InterMal C

coefdent Llr) (months) (monts) _ _ /yr) (monts) (monf) year) SISB 6.5-03 3.0F507 0 3.3E.03 I SIS-ACr-PA-SISA 3.OE.07 0 33E3 1 1.9E507

2 HPI-MOV-F-1115C 19E03 2Afi07 167 8-03 18 HP-MOV-Fr-1115B 2.OE-07 167 81.03 18 1.S-07

3 HPI-MOV-FT-I 15B ISE-03 2.0547 167 88i503 18 HPI-MOV-FT-1115D 2.05-07 167 8.8E 03 18 15.07

4 LPR-MOV-Fr-1862A 1.5E03 2.E407 167 880 18 -MOV-PT-186OB 2.05-07 167 8.8E03 18 1.2507

S LPR-MOV-Fr-1862A 1.503 2.OE-07 167 8.8503 18 LPR-MOV-PT18B 2.OE07 167 88M03 18 1.7

6 LPR-MOV-Fr-1860A 1.5E-03 2.0E-07 167 8. 3 18 LPR-MOV-FT-186 2.OE407 167 8.8-03 18 125.07

7 LPR-MOV-FT-1860A 1SE53 2.0-07 167 8.8-03 18 LPR-MOV-PT-1860B 2.OE07 167 8.8E-03 18 1.2E.07

8 LPR-MOV-Fr.180A 1S0 2.05.07 167 8.503 i8 LP1-MOV -1890B 2.07 167 8.8E.03 18 12E07

9 RMT-ACT-AARM5 1.5E03 3.05-07 0 335.03 1 RMT-ACr-PAMS 3.0E-07 0 33E03 1 4.508

10 Lt-MDP-FS-SIlB 15E03 2.05.07 86 2.6E-0 I EPR-MOV-PT-180A 2.05.07 167 8.8503 18 3.4E09

11 Ul-MDP-FS-SIIA 1543 2507 86 2.65304 I LPlMOV-FT-1860B 2.0E-07 167 8.8E.03 18 3AE-09

12 ln-MDP-F5-SIIB 1E-03 2.0E07 86 2.E04 1 LPR-MOV-F-1862A 2.0E07 167 8.8E03 18 3.4E09

13 l-MDP-FS-SIIA 1.5E03 2.OE407 86 2.544 1 LR-MOV-F-18m 2.0E07 167 8E03 18 3.4E509

14 LPR-MOV.FT-162A 1.0E-03 2.0.7 167 8.M-03 18 LPIDP-FR-B21HR 2.007 86 2.6E04 1 2.3E9 15 LPR-MOV-F-1862B 1.0E03 2.OE.07 167 88.03 18 LPl-MDP-VR-A2IHR 2.0E07 86 2.6E-04 1 235.09 16 LPR-MOV-F1-1860B 1.0E03 2.05.07 167 8M-03 18 I-MDP.FR-A2IHR 2.007 86 2.6E.04 1 2.3E

17 LPR-MOV-FT1860A tLOE03 2.507 167 8M03.4 18 LPI-MDP-FR-B2IHR 2.5-07 86 2.6E-04 1 2.3E509 18 AFW-TDP-FR-2P6RR I.E04 2.0E06 72 225.03 1 A A-PA-M3B 3.047 0 335E03 1 2.1E-09

19 APW-TDP-FR-2P6HR 1.8E04 2.056 72 22 3 1 AW-ACr-PA-P3A 3.5-07 0 33-03 1 2.IE09

20 LPI-MDP-FS-SIIA 15.03 2507 86 265-4 1 SS-ACT-FA-SISB 3.0E07 0 33E-03 1 2.15E09

21 LPI-MDP-PS-SIIB 1503 2.0E07 86 2.04 1 SIS-ACrT-A-SISA 3.0E-07 0 33E03 1 2.1E09

22 UR-MOV-F1862B 5.0E-04 2.OE-07 167 88M3 18 2.0547 MMP-R- 86 2.6E-04 1 l.E-09 23 LPR-MOV-FT-1862A 5.0E04 2.0E-07 167 8.8E-03 18 -P-R-B 4 2.0547 86 2.6544 1 1.1E49 24 AFW-TDP-FS-FW2 SAE03 2.OE06 72 2-03 I AFW-CKV-00.CV142 5.0E-09 0 5.55.05 I l.E-09 25 AFW-TDP-FS-FW2 135i03 2.0E-06 72 22E03 1 MSS-SRv.MSGSRV 7.0EM 22 3.1E04 18 9.0E-10
contribution from every aging component and every combination of aging components in

the PSA is determined allowing the contributions to be ranked in detail. The second

column in the table is the name of the component as defined in the PSA. The component

name identifies the system, component type, failure mode, and specific component

identifier. The codes for the identifiers used in the PSA are given in Table 15.

The third column in a given table is the risk sensitivity coefficient, or risk importance

coefficient, Si or Sij for the contributor. The coefficient gives the core damage frequency

importance of the contributor as determined by the original PSA. Basically, Si or Sij is

the change in core damage frequency per unit change in the unavailability of the

contributor. The value of the risk sensitivity coefficient, or risk importance coefficient,

is determined by the basic design and operational procedures of the plant.

The next three columns give the component aging rate, component replacement interval,

and component test interval which determine the component unavailability increase Aq

caused by aging. The aging effect Aq is determined using the equations previously

given. Because we are assuming the component is replaced at failure, the replacement

time is the mean time to failure (denoted as MTBF in the tables)*. Where there is no

MTBF given, the mean time to failure is larger than 50 years and the formula for a

nonreplaceable component (Equation (61) or (62)) is used. The test interval given is the

effective test interval for the base case and upper bound case. For the lower bound case,

test efficiencies of 1 were assumed as was indicated.

It is useful to print out the aging rate, replacement interval, and test interval as shown to

identify the factors which determine the aging effect Aq. The core damage frequency

increase AC due to aging is the aging effect on the contributor multiplied by the risk

importance of the contributor. For the single component contributor, the aging effect is

simply Aq1 and AC is the product of the sensitivity coefficient Si and Aqc. For the double

component contributors, the aging effect is Aqi Aqj and AC is the product of the

sensitivity coefficient Sij and Aqi Aq.

The tables thus provide all the ranked contributors to the core damage frequency increase

AC due to aging. The risk importance factor (sensitivity coefficient) and the aging effect

factor which combine to give AC are explicitly given and the aging rate, replacement

* The mean time between failure (MBF) includes the component repair time, which is assumed to be

small compared to the mean time to failure (MlF. Hence MTFB-2 MITP.

86
TABLE 15. COMPONENT IDENTIFIERS

SYSTEM CODE

ACC - Accumulators

AFW - Auxliary Feedwater

HPI - High Pressure Injection

LPI - Low Pressure Injection

SIS - Safety Injection System

LPR - Low Pressure Recirculation

PPS - Primary Pressure Relief

OEP - Onsite Emergency Power

MSS - Main Steam System

COMPONENT CODE

ACT- Actuator

CKV - Check Valve

DGN - Diesel Generator

MDP - Motor Driven Pump

MOV - Motor Operated Valve

SRV - Safety Relief Valve

TDP - Turbine Driven Pump

FAILURE MODE CDE

FA - Fail to Actuate

FR - Fail to Run

FS - Fail to Start

FT - Fail to Transfer

00 - Fail to Open

87
interval, and test interval which determine the aging effect Aq are explicitly identified.

The tables can now be used to help focus aging control and aging management activities.

5.6 Groud Comnent Prioitizations

The detailed prioritizations in Tables 12, 13, and 14 can also be used to obtain grouped

prioritizations of the component contributors in which the components are grouped

according to various criteria. We will demonstrate the grouping approach by grouping

contributors which have the same order of magnitude contribution. Tables 16, 17 and 18

provide the grouped prioritizations of the contributors by order of magnitude of their

core damage frequency (AC) contribution. Te groupings of the contributors in the

tables thus focus on the general sizes of core damage frequency contributions. The

groupings also serve to account for uncertainties in the calculated contributions.

Table 16 groups the component contributors in Tables 12A and 12B for the base case by

order of magnitude contribution. Each component in a double contributor set in Table

12B is assigned to a group in Table 16 based on the size of the double component

contribution AC. Thus, the grouping combines the single and double contributors into

one overall prioritization. Tables 17 and 18 provide similar grouped prioritizations for

the upper bound case and lower bound case, respectively. From Tables 16, 17, and 18 it

is observed that the same contributors often appear even when different aging rate data

are used, although in some cases new contributors appear.

Table 19 combines Tables 16, 17, and 18 and gives the top order of magnitude

contributors from each of the three tables, then the second highest order of magnitude

contributors etc. Table 19 is thus a relative way of incorporating sensitivity results into

one prioritization. Table 20 is another way of combining the sensitivity study results into

one grouped prioritization by identifying all contributors above a given value of AC.

Table 20 is thus a threshold approach for combining the results from the sensitivity

studies. Other groupings of the contributors can also be carried out depending on the

specific objectives of the analysis.

88
TABLE 16. COMPONENTS PRIORITIZED BY ORDER OF

MAGNITUDE CONTRIBUTION: BASE CASE

Contributor Range of AC

1E-5 to 1E4

HPI-MOV-FT- 0 15B

HPI-MOV-FT-1 1 15C

HPI-MOV-FT-l1l SD

HPI-MOV-FT-1 115E

LPR-MOV-FT-1860A

LPR-MOV-FT-1860B

LPR-MOV-FT-1862A

LPR-MOV-FT-1862B

LPR-MOV-FT-1890A

LPR-MOV-FT-1890B

HPI-MOV-FT-1350

0

0

1E-6 to 1E-5 0

1E-7 to E-6

SIS-ACT-FA-SISA

SIS-ACT-FA-SISB

OEP-DGN-FS-DG0

OEP-DGN-FR-6HDGl

OEP-DGN-FS-DG02

OEP-DGN-FS-DG03

OEP-DGN-FR-6HDG3

OEP-DGN-FR-6HDG2

PPS-MOV-FT-1535

HPI-CKV-FT-CV225

HPI-CK V-FT-CV25

HPI-CKV-FT-CV410

RMT-ACT-FA-RMTSA

RMT-ACT-FA-RMTSB

0

0

a

0

.

0

0

89
TABLE 17. COMPONENTS PRIORITIZED BY ORDER OF MAGNITUDIE

CONTRIBUTION: UPPER BOUND CASE

- - - - - - Contributor

HPI-CKV-Fr-CV225

HPI-CKV-FT-CV410

HPI-CKV-FT-CV25

ACC-CKV-F-CV147

ACC-CKV-FT-CV145

ACC-CKV-FT-CV130

ACC-CKV-FT-CV128

HPI-MOV-FT-I 1 SE

HPI-MV-FT- 11 5D

HPI-MOV-FT-l 1 15C

HPI-MOV-FT-1115B

HPI-MDP-FR-1A24H

HPI-CKV-OO-CV258

LPR-MOV-FT-1890B

LPR-MOV-FT-1890A

LPR-MOV-FT-1862B

LPR-MOV-FT-1862A

LPR-MOV-FT-1860B

LPR-MOV-FT-1860A

AFW-TDP-FS-FW2

AFW-CKV-OO-CV142

HPI-MDP-FR-1A6HR

AFW-MDP-FS-FW3B

AFW-MDP-FS-FW3A

AFW-CKV-O-CV172

AFW-CKV-OO-CV157

Range of AC

IE-3 to 1E-2

0

IE-4 to 1E-3

0

0

0

Contributor

LPR-MOV-FT-1862A

PPS-MOV-FT-1536

PPS-MOV-FT-1535

LPI-MDP-FS-SI1B

LPI-MDP-FS-SI1A

LPI-CKV-OO-CV58

LPI-CKV-OO-CV50

MSS-SRV-OO-SGSRV

HPI-MOV-FT-1350

OEP-DGN-FS-DG01

CPC-MDP-FR-SWA24

CPC-CKV-OO-CV113

LPI-MDP-FR-B21HR

LPI-MDP-FR-A21HR

OEP-DGN-FR-6HDG1

OEP-DGN-FS-D03

OEP-DGN-FS-DG02

OEP-DGN-FR-6HDG2

PPS-MOV-FC- 1536

PPS-MOV-FC-1535

OEP-DGN-FR-6HDG3

LPI-MDP-FR-B24HR

LPI-MDP-FR-A24HR

SIS-ACT-FA-SISB

SIS-ACT-FA-SISA

MSS-CKV-F1-SGDHR

OEP-DGN-FR-DG01

CVC-MDP-FR-2A1HR

HPI-MOV-FT-1867D

RMT-ACT-FA-RMTSB

RMT-ACT-FA-RMTSA

OEP-DGN-FR-DG03

OEP-DGN-FR-D&02

AFW-MDP-FS

Range of AC

IE-5 to IE-4

0

0

0

0

0E6to1-

0

0

0

0

90
TABLE 18. COMPONENTS PRIORITIZED BY ORDER OF

MAGNITUDE CONTRIBUTION: LOWER BOUND CASE

Contributor Range of AC

Contributor Range of AC

1E-7 to 1E-6

LPR-MOV-FT-1862A

LPR-MOV-FT-1860A

LPR-MOV-FT-1890A IE8to10

0

HPI-MOV-FT-1350 iE8toISIS-ACT-FA-SISA

SIS-ACT-FA-SISB

HPI-CKV-FT-CV225

HPI-CKV-FT-CV25

IHPI-CKV-FT-CV410

LPR-MOV-FT-1862B

LPR-MOV-FT-1860B

AFW-TDP-FS-FW2

HPI-MOV-FT-1 1 15B

HPI-MOV-FT- 1 15C

HPI-MOV-FT-1115D

HPI-MOV-FT-i l 1SE

LPR-MOV-FT-1890B

0

0

0

S

0

1E-8 to 1E-9

PPS-MOV-FT-1535 0

OEP-DGN-FS-DG01

OEP-DGN-FR-6HDG1

AFW-TDP-FR-2P6HR

ACC-CKV-FT-CV128

ACC-CKV-FT-CV130

ACC-CKV-FT-CV145

ACC-CKV-FT-CV147

RMT-ACT-FA-RMTSA

RMT-ACT-FA-RMTSB

OEP-DGN-FS-DG02

OEP-DGN-FS-D03

OEP-DGN-FR-6HDG3

OEP-DGN-FR-6HDG2

PPS-MOV-FT-1536

AFW-ACT-FA-PMP3A

AFW-ACT-FA-PMP3B

HPI-MOV-FT-1867D

0

4

la

0

a

91
TABLE 19. RELATIVE ORDERING OF THE COMPONENT

CONTRIBUTORS: COMBINATIONS OF THE THREE CASES

Contributor

HPI-CKV-FT-CV225

HPI-CKV-FT-CV25

HPI-CKV-FT-CV410

HPI-MOV-FT-I 15B

HPI-MOV-FT-11 15C

HPI-MOV-FT-Il 15D

HPI-MOV-FT-1115E

LPR-MOV-FT- 1860A

LPR-MOV-FT-1860B

LPR-MOV-Fr-1862A

LPR-MOV-FT-1862B

LPR-MOV-FT-1890B

LPR-MOV-FT-1890A

ACC-CKV-FT-CV128

ACC-CKV-FT-CV130

ACC-CKV-FT-CV145

ACC-CKV-FT-CV147

HPl-MOV-FT-l 115B

HPI-MOV-FT-1 l 15C

HI-MOV-FT-ll15D

HPI-MOV-FT-l lSE

HPI-CKV-OO-CV258

HPI-MDP-FR-1A24H

LPR-MOV-FT-1860A

LPR-MOV-FT-1860B

LPR-MOV-FT-1862A

LPR-MOV-FT-1862B

LPR-MOV-FT-1890A

LPR-MOV-FT-i890B

AFW-CKV-O00CV142

AFW-TDP-FS-FW2

HPI-MDP-FR-1A6HR

AFW-CKV-OO-CV157

AFW-CKV-OO-CV172

AFW-MDP-FS-FW3A

AFW-MDP-FS-FW3B

HPI-MOV-FT-1350

SIS-ACT-FA-SISA

Relative

Contribution

1st order of

magnitude

0

.

0

0

0

2nd order of

magnitude

0

0

*:

.

.

.

0

Contributor

LPR-MOV-FT-1862A

PPS-MOV-FT-1536

PPS-MOV-FT-1535

LPI-MDP-FS-SIlB

LPI-MDP-FS-SIlA

LPI-CKV-OO-CV58

LPI-CKV-OO-CV50

MSS-SRV-OO-SGSRV

HPI-MOV-FT-1350

OEP-DGN-FS-DG01

CPC-MDP-FR-SWA24

CPC-CKV-OO-CV113

LPI-MDP-FR-B21HR

LPI-MDP-FR-A21HR

OEP-DGN-FR-6HDG1

Relative

Contribution

3rd order of

magnitude

.

OEP-DN-FS-DG03

OEP-DGN-FS-DG02

OEP-DGN-FR-6HDG2

SIS-ACT-FA-SISB

SIS-ACT-FA-SISA

OEP-DGN-FR-6HD3

HPI-CKV-FT-CV225

HPI-CKV-FT-CV410

HPI-CKV-FT-CV25

RMT-ACT-FA-RMTSB

RMT-ACT-FA-RMTSA

AFW-TDP-FR-2P6HR

ACC-CKV-FT-CV147

ACC-CKV-FT-CV145

ACC-CKV-FT-CV130

ACC-CKV-FT-CV128

AFW-ACT-FA-PMP3B

AFW-ACT-FA-PMP3A

HPI-MOV-FT-1867D

0

0

0

0

S

0

a

0

S

0

S

0

0

._ ..

92
TABLE 20. ABSOLUTE ORDERING OF THE COMPONENT

CONTRIBUTORS: COMBINATION OF THE CASES

Contributor Above IE-3

HPI-CKV-FT-CV225

HPI-CKV-FT-CV410

HPI-CKV-FT-CV25

Contributor Above 1E4

ACC-CKV-FT-CV147

ACC-CKV-FT-CV145

ACC-CKV-FT-CV130

ACC-CKV-FT-CV128

HPI-MOV-FT-1115E

HPI-MOV-FT- 115D

HPI-MOV-FT-1115C

HPI-MOV-FT-1 1 15B

HPI-MDP-FR-1A24H

HPI-CKV-O-CV258

LPR-MOV-FT-1890B

LPR-MOV-FT-1890A

LPR-MOV-FT-1862B

LPR-MOV-FT-1862A

LPR-MOV-FT-1860B

LPR-MOV-FT-1860A

AFW-TDP-FS-FW2

AFW-CKV-OO-CV142

HPI-MDP-FR-1A6HR

AFW-MDP-FS-FW3B

AFW-MDP-FS-FW3A

AFW-CKV-OO-CV172

AFW-CKV-OO-CV157

Contributor Above 1E-5

LPR-MOV-FT-1862A

PPS-MOV-FT-1536

PPS-MOV-FT-1535

HPI-MOV-FT-1115B

HPI-MOV-FT- 11 15C

HPI-MOV-FT-1115D

HPI-MOV-FT-1115E

LPR-MOV-FT-1860A

LPR-MOV-FT-1860B

LPR-MOV-FT-1862A

LPR-MOV-FT- 1862B

LPR-MOV-FT-1890A

LPR-MOV-FT-1890B

LPI-MDP-FS-SIIB

LPI-MDP-FS-SI1A

LPI-CKV-00-CV58

LPI-CKV-OO-CV5O

MSS-SRV-OO-SGSRV

HPI-MOV-FT-1350

OEP-DGN-FS-DG01

CPC-MDP-FR-SWA24

CPC-CKV-OO-CV113

LPI-MDP-FR-B21HR

LPI-MDP-FR-A21HR

OEP-DGN-FR-6HDG1

OEP-DGN-FS-DG03

OEP-DGN-FS-DG02

OEP-DGN-FR-6HDG2

93
6. IDENTIFICATION OF RISK-DIRECTED AGING MANAGEMENT

STRATEGIES

6.0 Innyduction

Once the aging contributors are prioritized with regards to their risk contributions, then

aging management strategies can be focused on those contributors which are assessed to

be relatively high. This chapter illustrates how such risk-directed aging management

strategies can be identified and can be evaluated. The prioritized aging contributors

obtained in the previous chapter will be used as a demonstration. In many cases, the riskdirected aging strategies need not necessarily involve large resources since the aging

controls can be pinpointed on the relatively few, top ranked contributors to the core

damage frequency increase caused by aging. The risk-directed aging management

strategies which are investigated involve scheduled replacement of the high aging

contributors and implementation of more frequent or more effective surveillance tests on

these high contributors. Since there are relatively few high contributors which have been

identified, the additional resources involved would not necessarily be large.

Furthermore, the additional resources required could be trade-off against less frequent

testing on the risk-unimportant components. The last section of the chapter further

investigates the impacts of replacing operational tests with condition-monitoring tests.

6.1 Risk-Directed Aging Management Strategies

We shall consider the base case prioritization results obtained in the previous chapter.

The same approaches would be used for the other results obtained using the different data

bases. In the previous chapter, Tables 12A and 12B give the dominant aging contributors

which are obtained for the base case. These tables are reproduced as Tables 21A and

21B on the following two pages. These contributors constitute approximately 99% of the

increase in core damage frequency due to aging.

From Tables 21A and 21B, the top contributors consists of the motor operated valves

(MOVs) in the Emergency Core Cooling System (HPWR). There are 14 motor

operated valves involved. The base case testing program involved testing the valves

every 18 months and replacing the valves at failure. The first risk-directed aging

management strategy investigated involves replacing the valves every 5 years

94
TABLE 21A. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: BASE CASE, SINGLE CONTRIBUTIONS

Plant A.- Single Contributions

TIRGALEX Aging Rates

TIRGALEX Testing Efficiencies

Total AC: I .8E04 year

Test

Rank Component Name Sensitivity Aging Rate M1hF Interval Aql AC

Coefficient (fr/yr) (months) (months) (/ye=)

LPR-MOV-FT-1862A 1.5E-04 3.6E-06 167 30 2.6E-01 3.9E-05

2 LPR-MOV-FT-1860A 1.5E-04 3.6E.06 167 30 2.6E-01 3.9E-05

3 LPR-MOV-FT-189OA 1AE-04 3.6E-06 167 30 2.6E-01 3.5E-05

4 HPI-MOV-Fr-1350 6.7E-05 3.6E06 167 30 2.6E-01 1.7E-OS

5 LPR-MOV-FT-1862B 2.1E-05 3.6E-06 167 30 2.6E-01 S.4E-06

6 OEP-DGN-FS-DG01 3.8E-04 3.6E-06 72 4 1AE-02 53E-06

7 LPR-MOV-FT-1860B 2.OE-05 3.6E-06 167 30 2.6E-01 5.3E-06

8 OEP-DGN-FR-6HDG1 3AE-04 3.6E-06 72 4 1.E-02 4.8E-06

9 OEP-DGN-FS-DG03 2.OE44 3.6E-06 72 4 1.4E-02 2.8E-06

10 OEP-DGN-FS-DG02 2.OE-04 3.6E-06 72 4 1.4E-02 2.8E-06

11 OEP-DGN-FR-6HD03 1.9E-04 3.6E-06 72 4 1AE-02 2.7E-06

12 OEP-DGN-FR-6HDG2 1.7E-04 3.6E-06 72 4 1.4E-02 2.5E-06

13 PPS-MOV-FT-1535 9.5E-06 3.6E-06 167 30 2.6E01 2.4E-06

14 HPI-CKV-Fr-CV225 2.1E-03 4.0E-9 720 11 4.8E44 1.7E46

15 HPI-CKV-FT-CV25 2.1E-03 4.OE-09 720 11 4.8E-04 1.7E06

16 HPI-CKV-FT-CV410 2.1E-03 4.OE-09 720 11 4.8E-04 1.7E-06

17 HPI-MOV-FT-1115C 5.7E-06 3.6E-06 167 30 2.6E-01 1.5E06

18 HPI-MOV-FT-1115D 5.7E-06 3.6E06 167 30 2.6E01 1.5E06

19 HPI-MOV-FT-1115B 5.7E 06 3.6E-06 167 30 2.6EO1 1.5E06

20 HPI-MOV-Fr-1115E 5.7E-06 3.6E-06 167 30 2.6E-01 1.5E-06

21 LPR-MOV-FT-1890B 4.5E06 3.6E06 167 30 2.6E41 1.2E06

22 PPS-MOV-FT-1536 3.4E-06 3.6E-06 167 30 2.6E-01 8.8E-07

23 HPI-MOV-FT-1867D 2.9E06 3.6E06 167 30 2.6E-01 7.5E07

24 OEP-DGN-FR-DG01 5.0E-05 3.6E-46 72 4 1AE-02 7.2E-07

25 SIS-ACT-FA-SISA 1.8E05 3.0E-07 720 6 1.8E-02 5AE47

'C

(I,
TABLE 21B. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: BASE CASE, DOUBLE CONTRIBUTIONS

Plant A. Double Coiuibuious

llRGALEX Aging Raw

TIRGALEX Testing Effcicws

Total AC: 7.6E-04 ycu

Tcst _Te

Rnk Component Nam Sensitivity Aging Raw Wv F Interval hql COMP0etNma Aging Raw P Ierval Aq2 AC

Coefficient (ib/yr) (1len1is) (mos) _l/yr) (months) (1mnu) (lyea)

HPI-MOV-FT-111SB 1.E-03 361-06 167 30 2.01 HP-MOV-Fr-I11SD 3.6E06 167 30 2.6E-01 1.3E-04

2 HKI-MOV-Fr-1I1C L9E43 3606 167 30 21-01 HPI-MOV-F-1115E 3.6E-06 167 30 2A-01 1.3E04

3 LPR-MOV-FT-1890A 1.5E-03 36E-06 167 30 2601 LPR-MOV-Fr-18908 36E-06 167 30 2.6E-01 1.0E-04

4 LPR-MOV-F-186OA 1SE-03 3.606 167 30 2.6E-01 LPR-MOV-F-1860B 3.6E-06 167 30 2.6E-01 1.004

5 LPR-MOV-Fr-1862A 15E-03 3.6E-06 167 30 2.6E1 LPR-MOV-F-1860B 3.6E-06 167 30 2.6E-01 1.004

6 LPR-MOV-FT-l86A 1.5E-03 3.6E-06 167 30 26101 LPR-MOV-FT-1862B 3.6E-06 167 30 2.6E-01 1.E-04

7 LPR-MOV-Fr-1862A 1.5E-03 3.6E-06 167 30 2.1-01 LPR-MV-Fr-186 3.6E06 167 30 2.6E-01 1.01-04

8 SIS-ACT-FA-SISB 6.5E-03 3.0E-07 720 6 1.8E-02 SIS-ACT-FA-SISA 3.0E-07 720 6 1.8E-02 5.9E-06

9 RMT-ACr-FA-RTSA 1.5E3 30E-07 720 6 1.8E-02 RMF-AC-FA-RMSB 3.OE-07 720 6 1E-02 1.4E-06

10 OEP-DGN-FR-6HDG3 5.6E-03 3.1-06 72 4 1.4E-02 0EP-DGN-FR-6HDG1 3.6E-06 72 4 14-02 I.IE-06

11 OEP-DGN-FS-DG01 49E-03 3.6E-06 72 4 1.4E-02 OEP-DGN-FS-DG02 3.6E-06 72 4 1AE-02 9.9E-07

12 OEP-DGN-FS-DG01 4.9E-03 36E-06 72 4 1.4E.02 OEP-DGN-FS-D03 36E-06 72 4 1AE4-02 9.9E-07

13 OEP-DGN-FS-DG01 4.0E03 3E6-06 72 4 IAE-02 OEP-DGN-FR-6HDG2 31-06 72 4 14-02 8.1E07

14 OEP-DGN-FS-DG01 4.0Ei43 3.6E-06 72 4 1AE-02 OEP-DGN-FR-6HDG3 3.1-06 72 4 1.E02 8.1E-07

15 OEP-DGN-FS-DG02 4.0F1-03 3.6E-06 72 4 1.4E402 0EP-DGN-FR-6HDCI 3.6E-06 72 4 IAE-02 8.1E-07

16 0EP-DN-FR-6HDGI 41-03 36E-06 72 4 1.4E-02 OEP-N-R 2 3.6E-06 72 4 1AE4-02 8.1E-07

17 OE.P-DGN-FS-DG 3 3.9E-03 3.6E-06 72 4 1.4E02 OEP-DGN-FR-6HDG1 3.6E-06 72 4 AE-02 7.8E-07

18 OEP-DN-FS-DG0 SE-03 3.6E-06 72 4 IAE4-02 MSS-SRV-00-SGSRV 7.01-07 22 22 3.41-03 2AE4-07

19 LPI-MDP-FS-SIlB 1.5E-03 2E-07 6 2 5.83-04 LPR.MOV-FT-1862A 3.63-06 167 30 2.6E-01 233E-07

20 LPl-MDP-FS-SllA 15E-03 2.01-07 86 2 51-04 LPR-MOV-F-1860B 3.6E-06 167 30 2.63-01 233E-07

21 LPI-MDP-FS-SllB 1.5E-03 20-07 86 2 5.8-04 LPR-MV-FF-1&0A 3.6E-06 167 30 2.6E-01 23E-07

22 LPI-MDP-FS-SllA I.5E43 2.0E-07 86 2 58-04 LPR-MOV-FI-1862B 3.6E-06 167 30 2.6E-01 23E-07

23 0P-DN-FR-6HDGI 4.6E-03 3.6E-06 72 4 1.4E-02 MSS-SRV-00-SOSRV 7E-07 22 22 3.4E-03 2.2E-07

24 PPS-MOV-FC.1536 2.9E-06 3.-06 167 30 2.63-01 PPS-MOV.FC-1535 3.6E06 167 30 2.6E-01 1.9E-07

25 OEP-DGN-FS-DG03 9.1E-04 31E-06 72 4 1.4E-02 0EP-DGN-FR-DG01 3.6E-06 72 4 IAE-02 1.8E07
(60 months) and improving the test and increasing the test frequency so that the effective

test interval is 6 months.

Tables 22A and 22B give the new results for this first risk-directed aging management

strategy. This enhanced aging management strategy results in an average core damage

frequency increase due to aging of 3.8 x 10-5 + 1.9 x 10- = 5.7 x 10-5 per year. This

compares to the base case core damage frequency increase of 1.8 x 10-4 + 7.6 x 104 =

9.4 x 10 4 per year. The risk-directed aging management strategy thus results in a factor

of 16 reduction in the core damage frequency increase due to aging. A significant

reduction in risk effects due to aging is thus achieved by focusing on the 14 riskimportant motor operated valves.

In addition to the motor operated valves, the prioritized aging contributors for the base

case in Tables 21A and 21B also identify as important risk contributors the diesel

generators (DGN), the three check valves (CKV) in the High Pressure Injection (HPI)

System, and the four Actuation Trains (ACr). Thus, a second risk-directed aging

management strategy is identified which involves carrying out the MOV tests and

replacements in the first strategy plus improving the test efficiency on the three diesels so

that the effective test interval is 1 month, replacing the three check valves every 20 years

(240 months) and replacing the four actuation trains every 20 years. (The necessary

requirements to improve the diesel test efficiency was assessed by personnel

knowledgeable of the test.)

Tables 23A and 23B give the new values for the aging contributors corresponding to the

second risk-directed aging management strategy. This second enhanced aging

management strategy results in an average core damage frequency increase from aging of

1.8 x 10-5 + 5.1 x 106 = 2.3 x 10-5 per year, which represents a factor of 41 reduction as

compared to the base case. Thus, by focusing on relatively few additional, risk important

aging contributors the core damage frequency increase due to aging is further

significantly reduced.

As a summary of strategies evaluated, Figure 7 illustrates the core damage frequency

increase due to aging for the base case, the first risk-directed aging management strategy,

and the second risk-directed aging management strategy. Instead of the absolute

increases, the relative core damage frequency increases due to aging may be of more

interest where the relative increase is the absolute increase divided by the original core

97
TABLE 22A. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: FIRST RISK-DIRECTED STRATEGY, SINGLE CONTRIBUTIONS

Plant A. Single Contributions

First Aging Control Strategy

TIRGALEX Aging Rates

TIRGALEX Testing Efficiencies Total AC: 3.8E-05 /year

Test

Ra& Component Name Sensitivity Aging Rate MTBF interval Aql AC

Coefficient ([ulyr) (months) (mont) (/Yea)

1OEP-DGN-FS-DG01 3.E-04 3.6E-06 72 4 1.4E-02 5.3E-06

2 OEP-DGN-FR-6HDG1 3.4E04 3.6E-06 72 4 1.4E-02 4.8E-06

3 LPR-MOV-Fr-1862A 1.5E04 3.6E-06 60 * 6 1 I.9E-02 2.9E-06

4 LPR-MOV-Fr-1860A 1.SE-04 3.6E-06 60 * 6 1 l.9E-02 2.9E-06

5 OEP-DGN-FS-DG02 2.OE-04 3.6E-06 72 4 1.4E-02 2.8E-06

6 OEP-DGN-FS-DG03 2.OE-04 3.6E-06 72 4 1.4E-02 2.8E-06

7 OEP-DGN-FR-6HDG3 1.9E404 3.6E-06 72 4 1.4E42 2.7E06

8 LPR-MOV-FT-1890A IAE-04 3.6E-06 60 * 6 I.9E-02 1 2.6E-06

9 OEP-DGN-FR-6HDG2 1.7E-04 3.6E-06 72 4 1.4E-02 2.5E-06

10 HPI-CKV-FT-CV225 2.1E-03 4.OE-09 720 11 4.8E-04 1.7E-06

11 HPI-CKV-Fr-CV25 2.1E03 4.OE-09 720 11 4.8E-04 1.7E-06

12 HPI-CKV-Fr-CV410 2.1E-03 4.OE-09 720 11 4.8E-04 1.7E-06

13 HPI-MOV-FT-1350 6.7E-05 3.6E06 60 * 6 * 1.9E-02 1.3E-06

14 OEP-DGN-FR-DG01 5.0E05 3.6E-06 72 4 1.4E-02 7.2E-07

15 SIS-ACT-FA-SISA 1.8E-5 3.OE-07 720 6 1.8E-02 5.4E-07

16 LPR-MOV-Fr-1862B 2.1E-05 3.6E06 60 * 6 1 l.9E-02 4.OE-07

17 LPR-MOV-Fr-1860B 2.OE-05 3.6E-06 60 * 6 * 1.9E-02 3.9E-07

18 PPS-MOV-FT-1535 9.5E-06 3.6E-06 60 * 6 * 1.9E-02 1.8E-07

19 HPI-MOV-FT-11158 5.7E-06 3.6E-06 60 * 6 * l.9E.02 I.IE-07

20 HPI-MOV-FT-ll15D 5.7E06 3.6E-06 60 ' 6 * 1.9E-02 l.E-07

21 HPI-MOV-Fr-1115C 5.7E-06 3.6E-06 60 * 6 * 1.9E-02 IE-07

22 HPI-MOV-Fr-1115E 5.7E-06 3.6E-06 60 * 6 1.9E-02 .1E-07

23 LPR-MOV-FT-1890B 4.5E-06 3.6E-06 60 * 6 * 1.9E-02 8.5E-08

24 PPS-MOV-FT-1536 3.4E-06 3.6E06 60 * 6 * 1.9E-02 6.5E-08

25 HPI-MOV-FI-1867D 2.9E06 3.6E-06 60 6 * 1.9E-02 5.6E-08

ao

* - Control Value
TABLE 22B. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: FIRST RISK-DIRECTED STRATEGY: DOUBLE CONTRIBUTIONS

Plant A: Double Contributions

Second Aging Control Stategy

TIRGALEX Aging Rates

TIRGALEX Testing Efficiencies Total AC: 5.1E06 year

Test Test

Rank Component Nae Sensitivity Aging Rate MTBP Interval &qi Component Name Aging Rate MTDP Interval Aq2 Ac

Coefficient (/hrlyr) (mnths) (mot) (or/yf) (months) (months) Vyeff)

I HPI-MOV-FT-111SC 1.9E603 3.E.06 60 6 1.9-2 HPI-MOV-FT-1115 3.6E-06 60 6 1.902 6.8E-07

2 H1P-MOV-FI-11SB 1.98E03 3A-06 60 6 1.9E-02 HPI-MOV-Fr-1115D 3.6-06 60 6 1.9E.02 6.SE-07

3 LPR-MOV-FT-1862A 103 3.66h06 60 6 1.9f.02 LPR-MOV-Fr-1862B 3.6E-06 60 6 I.9E02 S.4E.07

4 UR-MOV-FT-186OA I.5-03 3.6E-06 60 6 19E-02 LPR-MOV-FT-1860B 3.6E06 60 6 I.9E-02 S.4E47

S LPR-MOV-FT-1860A 156-03 3.6E606 60 6 I.9E-02 LFR-MOV-Fr-1862B 3.6E06 60 6 1.9E02 5.4E-07

6 UR-MOV-FT-1890A 1S03 3.6E-06 60 6 I.9E-02 UR-MOV-FT-1890B 3.6E-06 60 6 19E-02 5AE-07

7 LPR-MOV-FT-1862A 15E-03 3.6E06 60 6 I.9E-02 LPR-MOV-Fr-18608 3.6E-06 60 6 I.9E-02 5.4E.07

8 SIS-ACr-FA-SISB 6.5E-03 3.0E-07 240 6 6.0E-03 SIS-ACT-FA-SISA 3.0E-07 240 * 6 6.OE-03 2.3E-07

9 0EP-DGN-FR-6HDG3 S.6E-03 3.6E-06 72 1* 3.9E-03 OEP-DN-FR-a I 3.6E-06 72 1 3.9E-03 8.6E0

10 OEP-DN-FSDGO01 4.96-03 3.-06 72 1 3.9E-03 OEP-DGN-FS-DG03 3.6E-06 72 1 * 3.9E-03 75E-08

11 OEP-DN-FS-WD01 4.9-03 3.6E-06 72 1 3.9E03 0EP-DN-FS-DO2 3.6E4-6 72 1 * 3.9E-03 7.5E-08

12 0EP-DGN-FS-DG01 5.6-03 3.6E-06 72 1 * 3.9E-03 MSS-SRV-OSGSRV 7.0E-07 22 22 3AE-03 6.7Ea

13 OEP-DGN-FS-DG01 4.0643 3.6E-06 72 * 3.9E-03 OEP-DGN-FR-6HD02 3.6E606 72 1a 3.9E03 62E08

14 0EP-DN-FS-DW01 4.0E-03 3.6E-06 72 1 * 39E-03 0EP-DGN-FR-6HDG3 3.6E-06 72 1 * 3.9E-03 6.2E08

15 0EP-DN-FS-DO2 4.04-03 3.6E-06 72 1a 39E43 0EP-DN-FR-DGI 3.6E06 72 1* 3.9E03 6.2E08

16 OEP-DGN-FR-6HDG1 4.6E-03 3.6E06 72 1 * 39E03 MSS-SRV-00-SGSRV 7.0E-07 22 22 3AE-03 6.1E-08

17 OEP-DGN-FR-6HDG1 4.0E-03 3.6E-06 72 1 O.3.9E-03 OEP-DGN-FR6HDG2 3.6E-06 72 1 3.9E-03 6.1E08

18 OEP-DGN-FS-DG03 39E-03 3.6E-06 72 1 39E-03 0P-DGN-FR-6HDGI 3.6E-06 72 1 a 3.9E-03 6.OE-08

19 RMT-ACr-FA-RMTSA 15-03 3.0607 240 a 6 6.0E03 RMTACr-PA-RMSB 3.0-07 240 a 6 6.0E-03 SAE08

20 LPI-MDP-FS-SIIA IS6-03 2.0-07 86 2 5.86-04 LPR-MOV-Fr.1862B 3.6E-06 60 6 196-02 1.7E08

21 LPI-MDP-PS-SIIB 1.5E-03 2.0E07 86 2 5.8E.04 LPR-MOV-Fr-1860A 3.6E-06 60 6 I.9E-02 1.7E-08

22 LPI-MDP-FS-SIIB 15E.03 2.067 86 2 5.8-04 LPR-MOV-F-1862A 3.6E-06 60 6 19E-02 1.7E48

23 LPI-MDP-FS-SIIA 15-03 2.0E-07 86 2 5.804 LR-MOV-Fr-l86R 3.6E-06 60 6 19E-02 1.7E.08

24 OEP-DGN-FS-DG03 9.1-04 3.6E-06 72 1 3.9E-03 0EP-DON-FR-DGO01 3.6E-06 72 1 * 39E-03 1AE-08

25 PPS-MOV-FC-1536 2.9E-6 3.6E-06 60 6 I.9E-02 PPS-MOV-FC-1535 3.6£-06 60 6 1.9E-02 .IE-09

* - CotlAtO VAIe
TABLE 23A. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: SECOND RISK-DIRECTED STRATEGY, SINGLE CONTRIBUTIONS

Plant A. Single Contributions

Second Aging Control Strategy

TIRGALEX Aging Rates

nRG AEXTesting Efficiencies Total AC; .8E-05 /year

Test

Rank Component Name Sensitivity Aging Rate MTF Interval Aq1 AC

Coefficient (/hr/yr) (months) (months) (/year)

1 LPR-MOV-FT-1862A 1.5E-04 3.6E-06 60 6 I.9E.02 2.9E-06

2 LPR-MOV-FT-1860A 1.5E-04 3.6E 06 60 6 1.9E-02 2.9E.06

3 LPR-MOV-Fr-1890A IAE-04 3.6E-06 60 6 1.9E-02 2.6E-06

4 OEP-DGN-FS-DG01 3.8E-04 3.6E-06 72 1 * 3.9E-03 1.5E-06

5 OEP-DGN-FR-6HDGl 3AE-04 3.6E-06 72 1 * 3.9E-03 13E-06

6 HPI-MOV-FT-1350 6.7E.05 3.6E 06 60 6 1.9E-02 13E-06

7 OEP-DGN-FS-DG02 2.OE04 3.6E-06 72 1 * 3.9E-03 7.8E07

8 OEP-DGN-FS-DG03 2.OE-04 3.6E-06 72 1 3.9E03 7.8E-07

9 OEP-DGN-FR-6HDG3 1.9E-04 3.6E-06 72 1 * 3.9E03 7.5E-07

10 OEP-DGN-FR-6HDG2 1.7E-04 3.6E.06 72 1 * 3.9E03 6.8E-07

11 LPR-MOV-F1-1862B 2.1E-45 3.6E-06 60 6 1.9E.02 4.OE-07

12 LPR-MOV-Fr-1860B 2.OE-05 3.6E-06 60 6 1.9E-02 3.9E-07

13 HPi-CKV-Fr-CV225 2.1E-03 4.OE-09 240 * 11 1.6E.04 3.4E-07

14 RPI-CKV-Fr-CV4l0 2.1E-03 4.OE-09 240 * 11 1.6E-04 3.3E-07

15 HPI-CKV-FT-CV25 2.IE-03 4.0E-09 240" 11 1.6E-04 33E-07

16 OEP-DGN-ER-DG01 5.OE-05 3.6E-06 72 1 * 3.9E-03 2.OE47

17 PPS-MOV-FT.1535 9.5E-06 3.6E 06 60 6 1.9E-02 1.8E-07

18 HPI-MOV-FT-1115B 5.7E-06 3.6E-06 60 6 1.9E 02 l.lE-07

19 HPI-MOV-FT-II1SE 5.7E-06 3.6E-06 60 6 I.9E02 I.IE-07

20 HPI-MOV-Fr-1115D 5.7E.06 3.6E-06 60 6 1.9E02 l.E07

21 HPI-MOV-Fr-1115C 5.7E-46 3.6E-06 60 6 1.9E-02 1.1E-07

22 SIS-ACT-FA-SISA 1.8E-05 3.0E-07 240 6 6.OE.03 L.IE-07

23 LPR-MOV-Fr-1890B 4.5E-06 3.6E-06 60 6 1.9E02 8.5E.08

24 PPS-MOV-FT-1536 3.4E-06 3.6E-06 60 6 1.9E02 6.5E-08

25 HPI-MOV-Fr-1867D 2.9E06 3.6E-06 60 6 I.9E.02 5.6E48

* - Control Value
TABLE 23B. CORE DAMAGE FREQUENCY INCREASE FROM AGING ACTIVE COMPONENTS

PLANT A: SECOND RISK-DIRECTED STRATEGY, DOUBLE CONTRIBUTIONS

Plant A: Double Contribution

Fust Aging Control Strategy

TRGALEX Aging Rates

TIRGALEX Testing Efficiencies Total, C: 1.9E-05 yet

Test Test

Rank ComponentNane Senitiviy Aging Rate MTBP Inteval Aqi Component Name Aging Rate WMFB Interval Aq2 AC

Coefficient _h/'yr) (monds) (months) (flh/yr) (months) (months) Qbw)

I SIS-ACT-FA-SISB 6.5E403 3.0E7 720 6 1.8H-02 SIS-ACr-FA-SISA 3.0=-07 720 6 l.86.02 5.96.06

2 RMT-ACT-FA-RMTSA 1.5E-03 3.4-07 720 6 1.8E02 RMI-ACr-FARMTSB 3.OE07 720 6 1.8E-02 1AE-06

3 OEP-DGN-FR-6D03 5.6E03 3.6-06 72 4 IAE4Q OEP-DGN-FR-6HDGI 3.6E06 72 4 I4E-02 I.IE-06

4 0EP-DGN-FS-D01 4.03 3.6E-06 72 4 1.4E02 OEP-DGN-FS-D02 3.6E-06 72 4 1AE-02 9.9E-07

S OEP-D0N-FS-DG01 4.9E43 3.6E06 72 4 1.4E-02 OEP-DGN-FS-DG03 3.6E06 72 4 1AE402 9.9E07

6 0EP-DGN-FS-DG01 4.0E-03 36E-06 72 4 IAE-02 OEP-DGN-FR-6HDG2 3.6E06 72 4 1.4E-02 8.1E-07

7 OEP-DGN-FS-D01 4.0E03 3.6E-06 72 4 IAE-02 OEP-DGN-FR-6G3 3.6E06 72 4 1AE02 8.1E07

8 OEP-DGN-FS-D002 4.0E03 3.6E06 72 4 1.4E-02 OEP-DGN-FR-6HDGI 3.6E-06 72 4 14E02 8.1E07

9 OEP-DGN-FR-6HDG1 4.0E-03 3.6E06 72 4 1.E02 OEP-DGN-FR-6HDG2 3.6E-06 72 4 1.4E-02 8.1E07

10 OEP-N-FS-DG03 3.9E03 3.6E-06 72 4 E4-02 OEP-DGN-FR-6HDGI 3.6E-06 72 4 1.4E-02 7.8-07

11 HPl-MOV-FT-1115B .9E43 3.6E-06 60 * 6 .9E-02 HPI-MOV-Fr-1115D 3.6E-06 60 * 6 * I9E02 6.8E-07

12 HPI-MOV-FT-111SC I.9E-03 3.6E-06 60 * 6 I9E-02 HPI-MOV-Fr-1115E 3.6E.06 60 * 6 * .9E-02 6.8-07

13 LPR-MOV-Fr-1862A I SE-03 3.6E-06 60 * 6 * 19E.02 LPR-MOV-FF-1860B 3.6E06 60 * 6 * I9E-02 5.4E-07

14 LPR-MOV-FT-1862A IE-03 3.6E-06 60 * 6 1.9E02 LPR-MOV-FT-1862B 3.6E06 60 * 6 * I.9E02 5.46.07

15 LPR-MOV-FT-1860A 1.5E03 3.6E06 60 * 6 1 9E02 LPR-MOV-Fr-1862B 3.6E06 60 * 6 0 I.9E-02 5.4E.07

16 LPR-MOV-Ft-1860A 1.5E-03 3.6E-06 60 * 6 * .9E-02 LPR-MOV-FT-1860B 3.6E-06 60 0 6 * 19E-02 5.4.07

17 LPR-MOV-F-1890A 1.5-03 3.6E-C6 60 * 6 19E02 LPR-MOV.FT-18M0B 3.6E-06 60 ^ 6 0 1.9E-02 S.4E-07

18 OEP-DGN-FS-DG01 S.OE-03 3.6E-06 72 4 1.4E-02 MSS-SRV-SGSRV 7.06-07 22 22 3AE03 2.4E-07

19 OEP-WN-FR.G1 4.6E-03 3.6E-06 72 4 1.4642 MSS-SRV-00-SGSRV 7.0E-07 22 22 3.4E-03 2.2E-07

20 OEP-DGN-FS-D03 9.1E44 3.6E-06 72 4 1A4-02 OEP-DGN-FR-DG01 3.6E-06 72 4 IAE-02 1.8E-07

21 LPI-MDP-FS.SIIA 1.5E-03 2.0647 86 2 5.8E-04 LPR-MOV-FT-1862B 3.6E-06 60 * 6 * 1SE-02 1.7E-08

22 LPl-MDP-FS-S1B ISE-03 2.0E07 86 2 5.8E-04 LPR-MOV-FT.1862A 3.6E-06 60 * 6 * I9E-02 1.7E8

23 LPI-MDP-FS-SlB 1.6-03 2.OE-07 86 2 5.8E44 LPR-MOV-Fr-1860A 3.6E-06 60 * 6 l.9E-02 1.7E-08

24 LPI-MDP-FS-SlA 1.5E-3 2.0E-07 86 2 5.8-04 LPR-MOV-FT-1860B 3.6E-06 60 * 6 * 1.9E02 1.7E-8

25 PPS-MOV-FC-1536 2.9E06 3.6E06 60 * 6 19E-02 PPS-MOV-FC-1535 3.6E-06 60 * 6 * 19E-02 .IE-09

C0

- conuol Value
FIGURE 7. CORE DAMAGE FREQUENCY INCREASE DUE TO AGING:

MINIMAL MAINTENANCE VERSUS RISK-DIRECTED CONTROL

1 .OE-03:

AC

per year

1.OE-04.

............................... ......................................................

......................................................................... ..................

.............................................................. ............................

..............................................................................

:::::::::::::::::::::::::::':::::::::::::::::::::::::::::::::::::::::::.:::::::::::.............::

.. . . . .. .. .. .. . . . . . . .. . . . .. . . .. .. . . .. 0... ... . . .. . . ................ .. . . . . . . . .. . . . .. . . . .. .. . . . . . .. . .. .. .. . . . . .

ow ow oow oow oow M1lm ................... ~l l ll l T11 ............................. 11

,tXX,/X - /,zZ, 111 m I...........m.........1...... 111.....

1.OE-05 

PWR

_ MINIMAL MAINTENANCE

EE RISK-DIRECTED STRATEGY 2

M RISK-DIRECTED STRATEGY I

FIGURE 8. RELATIVE CORE DAMAGE FREQUENCY INCREASE DUE TO

AGING: MINIMAL MAINTENANCE VERSUS RISK-DIRECTED CONTROL

1.OE+02

AC

per year

1.OE+01

1.OE+OO:

: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ............... ..... =:.:=................................. .................................................. :............................................................................................

........................ ........................ .. ...... .. ..... .. ........................... .......................... ................. ............... ......................................

..... ..................................................... ......................................................... ............ ........... ................. ................. ................................ ..

......... ..... .m !...... ...................................................................................................

................... .... |||S................................................................................. ...............

::.::: . . . .. . .. . . .. . :: -:-:: . :::.::; ;;...... ;..;;. . . .. . . . . . . .. .. . . . . . . . .. . ... .. ..... ............. ............ .. .. .... ........................................... ..............................

..................... .................. ............................. ............................ ..

, .......................... ..... .................. ......................................... .......... . ...

........................ ..................... ................................................................

................................................................................ ............................................................

1 .OE-01 - :,nr. .

PWR

_ MINIMAL MAINTENANCE

M RISK-DIRECTED STRATEGY 2

M RISK-DIRECTED STRATEGY 1

102
damage frequency increase in the standard PSA. Figure 8 illustrates the relative core

damage frequency increase due to aging for the base case and the risk-directed aging

management strategies. ( The tables of aging contributions can be simply changed to

relative contributions by dividing by the original PSA core damage frequency). Figures

7 and 8 again illustrate the significant control of aging effects which can be achieved by

focusing on the risk important aging contributors.

Other alternative aging management strategies directed toward the risk important

contributors could be evaluated by using the appropriate test and maintenance models to

calculate the aging effects Aq and the subsequent core damage frequency impact AC.

The core damage importances Si, Sij would remain the same and would not need to be

recalculated. The formulas and approaches which have been presented allow these

alternative evaluations to be straightfowardly carried out.

103
7. TIME DEPENDENT AGING EVALUATIONS

7.0 Intducion

In evaluating the risk effects of aging, either the average effects of aging or the time

dependent effects of aging can be calculated. The previous two chapters focused on

evaluations of the average risk effects of aging. Determining the average effects of aging

involves averaging the time dependent component unavailabilities over the period

between replacements of the component or over given time periods (such as the plant

lifetime). The average component unavailabilities or unavailability increases are then

used in the PSA model to determine the average increase in core damage frequency and

other average risk effects. These average aging contributions are straightforward to

calculate and generally have reduced uncertainties due to the time averaging effect.

When time dependent aging effects are determined then time dependent component

unavailabilities (or unreliabilities) are utilized. The time dependent component

unavailabilities are input to the PSA to obtain the time dependent core damage frequency

with aging or the time dependent increase in core damage frequency due to aging. The

average aging contribution can also be obtained by time averaging the results over

appropriate periods of time. The time dependent aging results provide more detailed

information, however they involve more detailed calculations and have larger

uncertainties due to the additional details.

This chapter demonstrates how time dependent aging results can be obtained using the

models and approaches given in the previous chapters. Basically, to obtain time

dependent aging results, the aging contributions at a given time are used in the formulas,

e.g. Equation (45), instead of the average aging contributions. The calculations are

repeated at different time points with the appropriate time dependent component

unavailabilities used at each time point. The core damage frequency which is obtained at

each time point then provides a time track of the effects of aging which can be used for

monitoring and predicting aging effects. However, more accurate component aging

failure rates are required for these time dependent evaluations.

104
7.1 Basic Time Dependent Eauations

We shall again consider the risk importance approach for the APSA approach, however

the general time dependent models we present apply to any APSA approach used. For

the risk importance approach, the increase in core damage frequency AC due to aging is

again from Equation (45) of Section 3.3

ac = Si~li + Sij.. qihqj+.--+YSI2-nAql-.. qn (63)

j>i

Si, Sij, etc. are again the core damage frequency importances determined from the

standard PSA. The increases in component unavailability Ach due to aging are now the

time dependent unavailability increases. Now, from standard reliability theory, and as.

also given in the appendix, the time dependent unavailability q(t) at given time t is

generally

q(t) = 1-exp(- JA(w)dw) 4)

(tT-tR)

where

X(w) the age dependent component failure rate at age w (65)

tR = the time of the last replacement or renewal of the component (66)

and

tT - the time of the last operational surveillance test (good as old (67)

test) of the component

the symbol.(tT - tR)+ denotes the maximum of zero and (tT - tR), i.e.

(tT-tR) =tT-tR; tT>tR (68)

105
=0 ;tTStR (69)

Thus, in Equation (64) if the last renewal is before the last test (tT>tR), the age of the

component at the start of the test is tT - tR. If the renewal occurs after the test (tTtR)

then the age starts again at zero.

The time dependent increase in component unavailability Aq due to aging is the

difference between the time dependent component unavailability with aging q(t) and the

time dependent unavailability without aging q,(t)

Aq= q(t)-qO(t) (70)

where

qO(t) = l-ex(-A(t-tT)) (71)

and where X is the constant component failure rate. Note that the last time of renewal tR

does not enter q,(t) since aging and hence renewal is not considered. The average value

of %(t) over a test interval is the average component unavailability used in a standard

PSA. The average value of Aq(t) over a renewal interval is the average increase in

component unavailability due to aging which was utilized in the applications discussed in

the previous two chapters along with the assumption of a linear aging failure rate.

7.2 Time Dependent Equations for a Linear Aging Failure Rate

We will consider the linear aging failure rate with no threshold and will describe how the

threshold age can be later incorporated into the results. The linear aging failure rate with

no threshold is again

A(w)=A+aw (72)

where X is the constant failure rate, a is the aging rate and w is the age of the component.

Substituting the linear aging failure rate into the general formula for q(t), Equation (64),

gives

106
t-tft 1 (73)

q(t)=1-exp - J(A +aw)dw

(tT-tR) .

We shall consider the case when tR<tT and hence (tT - tR)+ = tT - tR. When tR2tT then

the results which are obtained will apply by assuming tT=tR since the time of last renewal

also then serves as a the time of the last equivalent surveillance test. For tR<tT

t-tR 

q(t)= 1-exp - |(A+aw)dw (74)

tT-tR 

or

q(t) = 1-exp{-4(t- tT) a((t - tR)2 -(tT -tR)2)] (75)

The difference in availability Aq(t) is then

Aq(t) = 1-exp[)A(t-tT)-2a((t-tR) -(tT - tR) )]-[1-ekp(-A(t-tT))] (76)

Expanding the exponential to first order gives the simple result

Aq(t)= 1 a((t-t)2-(tT-tR))

2

This first order equation gives accurate results to at least two significant figures when

Aq(t) < 0.1 otherwise, the exact equation, Equation (76), can be used. A threshold age

can be incorporated into Equation (76) or (77) by subtracting the threshold age from t;

the squared terms in the Equations(76) and (77) will then only be nonzero if they are

larger then the threshold age.

If the component is tested at intervals of T and is replaced or renewed at intervals of L

then

107
tT = []T (78)

and

n tR -(79)

ILI

where "[x]" denotes the greatest integer function, e.g. [9.34] = 9. For periodic testing

and renewal, Equations (78) and (79) can then be substituted into Equations (76) or (77)

for Aq(t).

7.3 Applications of the Time Dependent. Linear Aging Failure Rate Equations

For a given application, Aq(t) can be determined at a given time point for each aging

component using Equation (76) or (77). The Aq(t) for each aging component can then be

substituted into Equation (63) for the time dependent core damage frequency due to

aging AC = AC(t). These calculations are then repeated for the time points of interest.

Note that the core damage frequency Si, Sij ,etc. are not dependent on time and need to

be computed only once from the standard PSA.

Figure 9 shows the time dependent core damage frequency increase AC(t) due to aging

that is calculated for the basic case evaluation carried but in Chapter 5. The same base

case data is used as in Chapter 5, except that time dependent aging effects are calculated

instead of time-averaged aging effects. As in Chapter 5, the renewal interval for each

component is assumed to be the components mean time to failure. In Figure 9, the time

points are selected to correspond to the test times for each component. The components

with the same test interval are assumed to be tested at the same time, sequentially so as

not to violate technical specifications.

A more general evaluation of Aq(t) can be obtained by using the equations in Appendix

which can account for nonlinear aging effects and for the randomness of failure times

when components are only replaced at failure. Figure 9 is useful for showing the time

tracking information which is obtained from time dependent evaluations. The total core

damage frequency at any given plant age is then AC(t) plus the baseline value in the

108
FIGURE 9. TIME DEPENDENT CORE DAMAGE FREQUENCY INCREASE AC

DUE TO AGING

3.5E-03

Actives

(per year)

2.5E-03 . -- .. . . .

2.OE-03 . .. . .. /

OI .5E-03

5.OE-04 /t; /f~~~~~~~~~~~~~~- atses

5 .O E E 4 . ..... .......................... ... ... I.... ......................

O.OE+00

0 100 200 300 400 500

Plant Age (Months)
PSA. The sudden drops in the core damage frequency increase AC(t) in Figure 9 occur

when the motor operated valves in the Emergency Core Cooling System are replaced at

failure. The high peaks in AC indicate that replacement only at failure for these critical

components is not adequate, and more frequent replacement or overhaul of the dominant

failure contributors is needed. This is a similar result as found in Chapter 5 where

average aging effects were utilized. Calculations of the time dependent aging effects.

provides useful information on the growth of the aging effects, indicating the times at

which the aging effects become significant

110
8. SENSITIVITY AND UNCERTAINTY EVALUATIONS

8.0 Intmduction

One of the most useful applications of an APSA is for sensitivity and uncertainty studies.

Both sensitivity studies and uncertainty analyses involve systematically changing

variables in the APSA and then determining the core damage frequency changes. An

uncertainty analysis differs from a sensitivity study in that probability distributions are

also assigned to the variables which represent the probabilities for the different values

which a variable may assume. Using uncertainty propagation techniques, a probability

distribution is then determined for the core damage frequency, which gives the

probabilities for the different core damage frequency values. A sensitivity study does not

utilize probability distributions but simply changes the input values and determines the

resulting change in the core damage frequency.

The variables which are changed in a sensitivity study or uncertainty study can not only

be data values, but can also be models and assumptions. In an APSA, sensitivity or

uncertainty studies can be performed for different possible aging behaviors for the

components, for alternative maintenance effects, alternative test effects, or alternative

repair effects. By designing appropriate sensitivity or uncertainty studies, the capability

of a given test and maintenance program to control aging risk effects over a range of

plausible alternatives can be systematically evaluated. These evaluations can help guide

and focus aging management activities.

This chapter illustrates uncertainty and sensitivity analyses which can be carried out

using an APSA. The following section first shows an application of uncertainty analysis

by assigning uncertainty distributions to the data used in an APSA. The subsequent

sections illustrate sensitivity analyses which can be carried out to evaluate the risk

sensitivities to aging and to maintenance strategies.

8.1 Uncertainty Analysis of Data Used in an APSA

The uncertainty analysis which is described is also described in NUREG-1362 (9).

Further information is provided here on the basic principles and applications of such an

analysis. An uncertainty analysis is carried out in an APSA to assess the uncertainties

one has in the aging results and to identify the dominant contributors to the uncertainty.

111
A data uncertainty analysis involves assigning error ranges to the data used in an APSA.

The error range assigned to a data input represents the different possible values the data

input may have because of uncertainties associated with collecting and estimating the

data. The probability distribution associated with the error range gives the probability

that the data will have any of the specific values in the range.

In a standard PSA, the input data which are assigned associated uncertainties include the

initiating event frequencies, component failure rates, test and maintenance intervals and

downtimes, and human error rates. For an APSA, the additional input data which have

uncertainties include the component aging failure rates, and test and maintenance data

describing the aging control effects of the test or maintenance. The component aging

failure rates will generally have the largest uncertainties.

To illustrate a data uncertainty analysis performed for an APSA, uncertainties are

determined for the aging impacts calculated in Chapter 5 which utilized the risk

importance approach and the linear aging failure rate model. Error ranges are assigned to

the data used for the base case evaluation. Error ranges are specifically assigned to the

component aging rates which are used, to the component mean times to failure (MTBF)

which are used as the component replacement times, and to the TIRGALEX testing

efficiencies which are used. Error ranges are also assigned to the risk importance

coefficients Si, Sij coming from the PSA.

An error ranges is generally defined in a PSA by assigning an error factor to a midpoint

data value. The upper value of the error range is defined as the data value times the error

factor and the lower value is the data value divided by the error factor. The data value is

thus the midpoint value of the range. This error range is generally defined to be a 90%

error range with the upper value being a 95% value and the lower value being a 5%

value. There is thus a 90% probability that the data value will lie in the defined range.

The error factors assigned to each piece of data for the APSA uncertainty analyses are

given below:

Data Type Error Factor

Component aging rate 10

Surveillance test efficiency 2

Component MTBF 2

Risk importance coefficient 5

112
The assignment of the above error factors is described in NUREG-1362 (9) and also in

NUREG/CR-5510 (7). Basically, the error factor of 10 on each component aging rate

covers uncertainties and plant specific variations that were observed by comparing the

TIRGALEX aging rate values with values estimated using plant failure data for selected

components. The error factor of 2 for each test efficiency basically gives test efficiency

values from 0 to 1 (the efficiencies are truncated at 1). The error factors for each

component MTBF and each risk importance coefficient (Si and Sjj) are assigned based on

PSA uncertainties.

The probability distribution assumed for each error range is a log uniform distribution

with the given upper and lower values. The log uniform distribution is a flat distribution

on a log scale. The log uniform is used in PSA uncertainty analyses when any factor

increase in the data value or any factor decrease in the value, within the range of possible

values, is equally likely. The log uniform distribution is thus a nonpreferential

distribution.

Before using the error ranges and probability distributions, one must decide whether

different data values are independent or are correlated with one another. Recent PSAs

assume data for a similar components to be totally correlated. (See for example

Reference (1).) For example, failure rates for all motor operated valves are assumed to be

totally correlated. When data are totally correlated then the data follow the same

probability distribution and are not independent with separate, similar distributions. To

be consistent with PSA approaches, all aging rates, MTBFs, and testing efficiencies for a

given type of component (eg. motor operated valves) are assumed to be totally

correlated. Further details are given in NUREG/CR-55 10.

The error ranges and probability distributions for the data are then propagated through

the APSA calculations to obtain the error ranges and probability distributions on the

APSA results. Standard Monte Carlo simulation approaches are used in the PSA for this

propagation and these same approaches can be applied to the APSA. References (1)

through (3), as well as NUREG/Cr-5510 (7), describe the simulation approaches and

computer codes which are available to automatically carry out the calculations once the

data error ranges and probability distributions are assigned.

Figure 10 shows the output of the uncertainty analyses in terms of the probability

distribution obtained for the core damage frequency (CDF) increase due to aging.

113
FIGURE 10. UNCERTAINTY ANALYSIS OF AGING EFFECTS: PLANT A

CCDF

100%

80%

60%

p"

40%

20%

0%

-6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1

Log (Increase in Core Damage Frequency)
The y-axis of the figure is the probability that the CDF increase exceeds a given value on,

the x-axis. The x-axis is the log to the base 10 of the CDF increase; the x-axis is thus the

exponent of 10 of the CDF increase. The curve of the probability distribution on these

axes is termed a complementary cumulative distribution function, or ccdf, in standard

PSA terminology.

In the figure, ccdf curves are given for the single component contribution to the CDF

increase, for the double component interaction contribution, and for the total CDF

increase due to aging. The ccdf curves can be used to obtain error ranges for the output

results. For example, a 90% error range for the total CDF increase has a lower value of

approximately lx1O35 = 3x104 per year (corresponding to a y-value of 95%) and an

upper value of approximately lxlIO-- 5 = 3x10-2 per year (corresponding to a y-value of

5%). More accurate values can be obtained from the associated tables which are

produced as part of the uncertainty analysis. Error ranges for the single and double

contributions can be obtained in a similar manner.

Uncertainty ccdfs and associated error ranges can be obtained for every aging

contributor, in addition to the sum totals for the singles and doubles shown in Figure 10.

These ccdfs and error ranges can be used to describe the uncertainties and confidences

which are associated with quantifying the CDF effects of aging. The lower end point of

an error range (eg. the lower bound) can be used to define the minimal aging effect and

the upper end point (the upper bound) can be used to define the maximum aging effect

which account for data uncertainties. The ccdf curves themselves can also be used in

more formal decision approaches for cost-benefit and optimization studies.

8.2 Sensitivity Studies of the Effects of Different Aging Rates

Sensitivity studies differ from uncertainty analyses in that no probability distribution is

assigned to the input variables which are changed. Only input values are changed. By

appropriately designing a sensitivity study and by systematically varying selected

variables, significant amount of information can be obtained on the sensitivities of risks

to aging effects and to test and maintenance practices.

To investigate the sensitivity of the core damage frequency effects to aging, a very

useful and straightforward sensitivity study to carry out is to vary component aging

failure rates over a plausible range and then determine the resulting core damage

115
frequency effects under given maintenance practices. To aid in the interpretation of the

results, the component aging failure rates can be expressed in a relative form which

indicates the relative size of the aging occurring. For the linear aging failure rate model,

the component aging rate is thus expressed as a relative percentage increase per year in

the baseline component failure rate.

If a is the component linear aging failure rate, then expressing a as a relative fraction of

the constant, baseline component failure rate Xb, we have

a rAO (80)

or

r= a (81)

10

In percentage (%) terms

r(in %) = a x 100 (82)

Ao

If the aging rate a has units of the failure rate change per year as in Table 8 in Chapter 5

then r has the units of per year. Thus, r gives the percentage increase in the component

failure rate per year due to aging. Note, that r can be larger than 100% per year.

Expressing the aging rate of the component as a relative percentage increase per year has

several advantages for aging sensitivity studies. The aging rate of a component can be

systematically varied by varying r from 0% through 100%. Higher values of r can also

be used. The aging rates of a group of components can also be simultaneously varied by

varying the one parameter r. For example, assigning r = 10% to all the motor operated

valves in the Emergency Core Cooling System describes the situation where all the

valves are aging with a relative increase in their failure rates of 10% per year.

116
Another important advantage in focusing on the relative aging behavior is that

component aging can then be classified into different engineering categories which

represent different degrees of aging, such as a small degree of aging, a moderate degree

of aging, or a severe degree of aging. The risk impact, eg. CDF increase, which results

from different degrees of aging can then be evaluated for given test and maintenance

practices to assess the adequacy of the practices in controlling aging effects. Table 24

gives one categorization of different degrees of aging along with the corresponding

percentage increase in the failure rate. Also given is the associated time period in which

the baseline failure rate doubles due to the aging. These values are consistent with aging

that has been observed in samples of data that have been evaluated (see for example

NUREG/CR-5510 (7)), with the significant aging corresponding to harsh environment

effects such as due to unpurified water environments or high temperatures. These

relative values appear to be applicable for a range of absolute aging rates and baseline

failure rates.

As a demonstration aging sensitivity studies, Figure 1I shows the core damage frequency

increase for a plausible range of aging behaviors up to significant aging. he plant

analyzed is the same one as analyzed in Chapter 5 for the prioritization analyses. For the

present sensitivity study, mQnthly testing (good as old testing) of all active components is

assumed. Failed components are assumed to be replaced with new components. No

burn-in problems are assumed (ie. the replaced components are good as new).

Figure 11 shows the average core damage frequency increase (per year) between

replacements versus annual percentage increase in component failure rate due to aging of

all active components. All the active components are assumed to be aging with the same

relative percentage increase in their failure rate (The baseline failure rate for each

component is that defined in the baseline PSA.). Aging of passive components and

structures is not considered in this particular sensitivity study.

The baseline core damage frequency for the plant is approximately 3x10 5 per year from

the standard PSA. This sensitivity study thus shows that aging effects are controlled over

a range of plausible aging for the given plant under the policy of monthly testing and

replacement at failure with new components. Even with a relative aging of 100%, where

all component failure rates are doubled each year, the core damage frequency increase

due to aging is still held to approximately 3xlO-5 per year which is still comparable to the

baseline core damage frequency of 3x10-5 per year. For moderate to minor aging, the

117
TABLE 24. RELATIVE AGING FAILURE RATE CATEGORIES

Category Relative Failure Rate Failure Rate Doubling

Increase (per year) Period (yrs)

Minor aging 10% 10 yrs

Moderate aging 30% 3 yrs

Significant aging 100% 1 yr

118
aging effects on the core damage frequency are controlled to be significantly less than the

baseline core damage frequency.

The aging control which is exhibited in Figure 11 is due to monthly testing with replacement at

failure. Failed components are not down for significant times until detected by a monthly test,

and failed components are replaced with new components, removing all previous aging effects.

Other policies which involve less frequent testing or which do not replace all failed components,

but only the most important contributors, could also achieve effective aging control.

Prioritization of the dominant contributors similar to that performed in Chapter 5 would identify

the components which are most important to test and replace to control aging impacts. The

dominant contributors would now need to be obtained for the range of aging rates that are

defined to be plausible.

8.3 Sensitivity Studies of the Effects of Different Test and Replacement/fRepair Policies

Sensitivity studies can also be usefully carried out to evaluate different aging management

policies for their control of aging effects on risk. Figure 12 shows the average core damage

frequency increase per year due to aging under two different surveillance test intervals. The

PSA is again the same as that used in the previous sections. Replacement at failure is again

assumed and only active component aging is considered. All active components again are

assumed to be aging with the same relative aging rate.

The monthly testing line (T = 1 month) is the same result as given in the previous section in

Figure 11. The semi-annual testing line (T = 6 months) corresponds to semi-annual testing of all

active components. With semi-annual testing the core damage frequency increase due to aging

is considerably higher and becomes larger than the baseline core damage frequency with

moderate aging (20% - 30%). Thus, monthly testing of the key contributors is important if no

additional scheduled maintenance is performed. The prioritization of contributors as done in

Chapter 5 would show those components for which it is important to control the test interval to

be 1 month.

Finally, as a sensitivity study Figure 13 shows the impact of a policy of replacement of failed

components versus a policy of repair of failed components. The replacement curve is the same

as in Figure 11 (but on a log scale). For a replacement policy again, failed components are

119
FIGURE 11. CORE DAMAGE FREQUENCY INCREASE FOR A PLAUSIBLE RANGE OF AGING

REPLACEMENT AT FAILURE: MONTHLY TESTING

AC

Co

3.5E-05

3.OE-05

2.5E-05

2.OE-05

1 .5E-05

1.OE-05

5.OE-06

O.OE+OO

. . . . . . ............................................. ....... . . . . . . . . . . . . . . . . . . . ... . . . . .. . . . . .. . . . .

<...................... ........... I...................................... ........... ............... ..... .... .............

{ ~ ~~ ~~~ I I 

0% 25% 50% 75% 100%

Relative Aging Rate (% Increase in Failure Rate Per Year)
FIGURE 12. CORE DAMAGE FREQUENCY INCREASE FOR A PLAUSIBLE RANGE OF AGING:

REPLACEMENT AT FAILURE: TWO DIFFERENT TEST INTERVALS

3.OE-04

T=1 Mo. +FT=6Mo.

AC 2.5E-04 . ..

2.OE-04 _ ... ,7

A, 1~~~~~.O E -0 4 . .... . . . . . . . . . . . . . . . . . ............... . .... . . . . .. . . . . . .. . . . . .. . . . . . ... .... . . . . . . . . . . .

w~~~~ .5E1 .O E - 0 4 ... . . . . . . . ..

5 .O E -0 5 ... .... . .. . .. ........ ... ... .... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

O.OE+OO

0% 25% 50% 75% 100%

Relative Aging Rate (% Increase in Failure Rate Per Year)
FIGURE 13. CORE DAMAGE FREQUENCY INCREASE FOR A PLAUSIBLE RANGE OF AGING:

REPLACEMENT AT FAILURE VERSUS REPAIR AT FAILURE: MONTHLY TESTING

1.OE-02 _.................................................................................................................. .............................

AC

1 .OE-03 . ...... 0 .. ...... ..... . . . . .. . . . . . ........ ............ .. ... ........ . .... . .. .. .. .................. .. .. .. . . . . I ... . . . . . . _ .......... ....................................................................................................................................

.... I..... ................... .......................................................................................................

1.OE-04 .............. 1.OE-N~~. _........... ...................................................................................

_ . .. . . . .. . . . . . . . . . . . . . . . . . . . . .......................... .................. . . . . . . . . . . . . . . . .

1.OE-05 ............ ~~~~.... ............. ......... ............ ~~~~~~~~~~~~~~~.................. I .................

1.QE-06 -/............._ ..................................... i.-::.. .: -................ Replacem ent - R e pr ....................... .... .....

_....... .................................................................................. ..................................................................

1.0E-07 I I I

0% 25% 50% 75% 100%

Relative Aging Rate (% Increase in Failure Rate Per Year)
replaced with new components. For the repair policy, it is assumed that failed

components are restored to an operational status but are not replaced with new

components. Aging effects are thus not significantly removed. The repair is thus treated

to be as good as old. The repair curve is very much higher than the replacement curve,

showing significant core damage frequency effects from aging even at minor component

aging (5% - 10%). It is thus extremely important to replace or overhaul the dominant

components instead of repairing them to control aging impacts on the core damage

frequency. Prioritization of the components would again identify those components

which need to be focused on for aging management.

123
9. CONSIDERATIONS IN USING A PSA TO EVALUATE THE RISK

EFFECTS FROM AGING OF PASSIVE COMPONENTS.

9.0 introducin

To use the PSA for evaluation of risk effects from aging of passive components, it is first

of all important that a plant specific PSA be constructed to evaluate and quantify the core

damage frequency associated with the plant's design and procedures. For the most

comprehensive PSA, all major passive components should be incorporated, otherwise it

will not be possible to explicitly evaluate the risk effects from aging of these passive

components. In this final chapter, important concepts and considerations are discussed

involving the reliability modeling of passive components and their aging effects. As part

of the risk evaluation of aging work, a separate report is planned which will discuss the

special points involved in modeling passive component aging in greater detail.

9.1 The Role and Use of PSA to Evaluate the Reliability of Passive Components and

Their Risk Impacts

PSAs have not generally included the detailed risk contributions.from passive

components and structures (e.g. pipes, vessels, containments). The passive contributions

which can be analyzed in greater detail include:

(a) Initiating events

- Primary circuit failures

- Pressure shell failures

- Steam generator tube ruptures

(b) System related contributions

- control rod failures

- pipe breaks

- vessel failures

- missile generation and impact

- pipe whip phenomena

124
(c) Containment contributions

- steel shell

- closures

Most of these contributions are presently incorporated into a PSA in only a general way

using failure rates based on generic information or expert judgement.

In particular cases there have been more formal analyses to derive a failure probability

for specific components. When more formal analyses are carried out then a probabilistic

fracture mechanics (PFM) model is often used to model the probability distributions of

various parameters including:

* flaw size and location

* failure to detect particular flaw sizes

* material property variations

* changes of material properties through life

These probability distributions are then combined to evaluate, for example, the

probability of the vessel exceeding its design criteria. The analyses are used to

determine, among other things,

* the probabilities of failure of the passive components

* the important inspection activities which have an impact on the failure

probabilities

In principle, detailed models could be developed for all major passive components and

associated failure probabilities derived.

For systems analyses performed in PSAs, as was observed from the previous

demonstrations, typically the active components (e.g., pumps, valves) are only

considered in detail. The reason is that relatively small failure rates are used for the

passive components. Also, expert judgement tends to limit the importance of passive

component contributions. As a consequence, interactions between active and passive

components (e.g., different loads as a consequence of various failure modes) are

generally incorporated in only a limited way. Aging can cause these contributions to be

more important.

125
One example of an interaction between active and passive components is the safety issue

related to pressurized thermal shock. In this event scenario, the thermal loads (stresses)

at the primary piping and reactor pressure vessel (RPV) are strongly dependent on the

function and/or malfunction of the active components in the emergency core cooling

system (ECCS) and other systems. Conversely, the failure modes of the passive

components influence the failures of the actives in this scenario. This interacting process

can be modeled in an age dependent PSA.

A PSA can thus represent a framework and an analysis tool to integrate the behavior of

active and passive components, prioritizing the importance (contribution) of each

involved component to the overall risk. The traditional deterministic safety analysis

process generates limited insights regarding the risk importances of passive components

and structures. The PSA (or PRA) can show the risk importance of different assumptions

(e.g., break location or parameters, e.g., load cycles, critical stress intensity factor) used

in these safety analyses. By incorporating probabilistic models of passive component

failures into a PSA, one can then generate answers as to not only where breaks are most

likely, but where they most effect the core damage frequency or risk. This stochastic

modeling - PSA integration combines design, manufacturing and~operating aspects and

allows a risk prioritization of the contributors and associated parameters.

9.2 Aging Component Reliability Models Required for PSA Aging Evaluations.

In aging evaluations of a plant, one is confronted with four basic phenomena causing

time dependent changes in material behavior of passive components:

- Fatigue

- Embrittlement

- Crack Growth

- Surface degradation (friction, erosion, corrosion)

Passive component modeling for PSA applications need therefore to focus on these basic

phenomena.

A passive component reliability analysis can be demonstrated where a loading stress

interacts with strength. Consider a state function S of the form,

126
- I . S = strength - stress (83)

If both the stress and the strength are random variables with defined probability

distributions, S will also be a random variable with a defined probability distribution.

When SO, the passive component is said to be in the safe state. Failure occurs when

SO (when loading and therefore stress is larger than strength). If S is normally

distributed, then the ratio of S-E(S), where E(S) is the expected value, and e(S) where

e(S) is the standard deviation is a standard normal random variable.

More generally, the probability can be computed that the structure will fail i.e., that S<O.

The state function can furthermore be extended to multiple controlling variables, with

different distributions,

S = S (X1, x 2, * * Xn) (84)

These types of models need to be utilized when evaluating passive component failure

probabilities (unrellabilities) to insert into the equation for the core damage frequency

increase, such as Equation (45).

9.3 The Crack Growth Phenomenon.

A probabilistic fracture mechanics crack growth analysis can be expressed in terms of a

multi-variate state function, ie. Equation (84). The result from a crack growth analysis

can be the probability versus time that the crack will propagate and cause component

failure, i.e., S-O. To carry out the reliability analysis, an initial crack size distribution

and a probability distribution for detecting a given crack size by non destructive

inspection (NDI) can be used. The effect of NDI can be explicitly incorporated using

Bayesian updating,

P(F 1) P(F)P(I/F) (85) P(I)

where P(F/I) is the updated structural failure probability given that an inspection has

been carried out. P(F) is the structural failure probability before the inspection, P(U) is

the NDI reliability, and P(IF) is the probability of detection given the failure.

127
Instead of calculating failure probabilities, an alternative procedure is to update the crack

size only. NDI can be considered as providing new information on current crack sizes,

and can be used to constrain the updating to specific crack sizes. Bayesian approaches

can again be used to obtain associated probabilities.

9.4 The Corrosion Phenomenon

The deterioration process due to corrosion generally affects the reliability of passive

components. The corrosive effects depend on the loading process and on the

environmental conditions in the systems to which the component is exposed. Due to the

uncertainties inherent in the loading process, as well as in the manufacturing and

operating process, a variety of variables need to be considered as being random. Because

of the non-normal properties of these variables and the non-linear characteristics of the

state function, general simulation methods need to be used to estimate the failure

probability of the passive components due to corrosion effects. Normally the

deterioration process of fatigue is analyzed utilizing models that describe the crack

growth rate per load cycle.

To explicitly consider the deterioration process of corrosion, a corrosion factor C. is

often introduced. This factor depends on the loading process and the environmental

conditions to which the passive component is exposed. Based on data, the corrosion

factor C, can be approximated by a function of the stress intensity factor, the frequency

of loads and the stress ratio, and the applied loading process. Corrosion can significantly

decrease the structural reliability of passive components versus time and therefore it can

be important to consider such effects in an age dependent PSA.

9.5 Stochastic Analysis as a Complement to Deterministic Crack Growth Analysis

In the design process, and the safety assessment of operating strategies of passive

components, typically a deterministic crack growth approach (DCGA) is often used. The

DCGA provides a single value prediction for crack size at a given service time for a

single structural detail, but it does not quantity structural reliability and the importance of

different contributors. Over the past years reliable passive reactor components have been

obtained based on DCGA, good design/analysis methods and practices, quality

manufacturing, and effective inspection and quality control. However, in view of the

benefits of using a PSA, and the special issues associated with aging, a PSA approach

128
can be applied to complement existing deterministic practice (e.g. DCGA) to estimate the

failure probabilities of passive components and the importances of different passive

components as risk contributors. Passive components and interactions between passive

components and active components can then be prioritized in the same detail as active

components can. With appropriate probabilistic failure models which can include those

aging failure rate models in Chapter 2 and by expanding the PSA to include passive

component contributors, the risk effects of aging from passive components can thus be

analyzed and be prioritized in the same manner as active components are.

129
10. SUMMARY AND CONCLUSIONS

An age-dependent PSA, or an APSA, is different from a standard PSA in that an APSA

explicitly evaluates the risk effects of aging. Age dependent component failure rates are

utilized, and test and maintenance activities are explicitly analyzed for their control of

aging effects. Specific models have been presented for different aging failure rate

behaviors and for different effects of tests and maintenances in controlling aging. These

models can be incorporated into a PSA to explicitly evaluate aging effects.

Different approaches can actually be used to incorporate the aging models and to

transform a PSA to an APSA. Three basic approaches were described in detail along

with their specific features. These descriptions and the detailed models presented allow

any PSA to be transformed to an APSA.

Different applications of an APSA were described which include bottom-line

evaluations, evaluations of maintenance effectiveness, prioritization analyses, and

sensitivity and uncertainty analyses. These different applications were reviewed in light

of aging failure data which is available, test and maintenance data which is available,

PSA information which is available, and meaningful results which can be obtained.

Specific applications were then demonstrated involving prioritizations of aging

contributors, identification of risk-directed aging management strategies, evaluation of

time dependent aging effects, data uncertainty analyses, sensitivity analyses of the risk

impacts of aging, and sensitivity analyses of the effectiveness of different test and

maintenance practices in controlling the risk impacts from aging. These studies illustrate

the significant amount of useful information which is obtainable from an APSA even if

accurate aging failure rate data is not available. Finally, specific considerations were

discussed in determining the time dependent and age dependent failure probabilities for

passive components which can then be utilized in the general formulas for the aging

impacts on risk.

130
REFERENCES

1. NUREG/CR-4550, "Analysis of Core Damage Frequency from Internal Events",

Volume 1, September 1987.

2. NUREG/CR-4350, "Probabilistic Risk Assessment Course Documentation",

Volumes, 1-7, August 1985.

3. NUREG/CR-2300, "PRA Procedures Guide", Volume 1, January 1983.

4. H. Ascher and H. Feingold, Repirable Systems Reliability, Marcel Dekker, New

York, 1984.

5. MS. Abdel-Hammeed, E. Cinlar, and J. Quinn, eds, Reliability They and

Models, Academic Press, New York, 1984.

6. B.V. Gnedenko, Mathematical Methods of Reliability Theory, Academic Press,

New York, 1969.

7. NUREG/CR-55 10, "Evaluations of Core Melt Frequency Effects Due to

Component Aging and Maintenance", June 1990.

8. NUREG/CR-5248, "Prioritization of TIRGALEX-Recommended Components

for Further Aging Research", October 1988.

9. NUREG-1362, "Regulatory Analysis for Proposed Rule on Nuclear Power Plant

License Renewal", July 1990.

131
APPENDIX: GENERAL FORMULAS FOR AGING COMPONENT

UNRELIABILiTIES AND UNAVAILABILrTIES

132
APPENDIX: GENERAL FORMULAS FOR AGING COMPONENT

UNRELIABILrTIES AND UNAVAILABILITIES

Let X(w) be the age dependent component failure rate, where X(w) can be any form and

can include a threshold age. The component can be either an active component or

passive component. The component unreliability is the probability that the component

fails to operate successively for a given interval. The component unreliability can be

calculated from the following formulas depending upon the initial conditions:

1-exp -A(w')dw')

= the probability of failure before age w

given the component was known to be

last up at age zero:

(1)

= the probability of failure before age w

given the component was known to be

(2)

' w' last up at age wa .

When the component was last checked will depend upon the testing schedule. The above

formulas can be transformed to time dependent formulas by using the age of the

component at the given time w = w(t) .

The component unavailability is the probability that the component is down and is unable

to function. The component unavailability can be calculated from the following formulas

depending upon the initial conditions:

I-exp-JA(w'

x

w . 1-exp- f)(w

A = the probability that the component is

dwJ ) down at age w given that the

component was last known to be up at

age zero:

(3)

(4)

r')dw'

= the probability that the component is

down at age w given the component

was last known to be up at age w. .

133
Note that formulas (3) and (4) are similar in form to formulas (1) and (2). The difference

is that operating failure rates are generally used in formulas (1) and (2) while standby

failure rates are used in formulas (3) and (4).

When a maintenance or restoration is performed on the component then formulas (3) and

(4) still apply with the component age measured from the last maintenance or restoration

on the component. For a restoration where the age is reset to zero then formulas (3) and

(4) apply with the age w being the age since the last restoration. For a maintenance

involving a partial restoration which resets the component age to a value w, then

formulas (3) and (4) apply with the age w being the age of the component since the last

partial restoration where the age begins at wl.

Associated time dependent formulas for the unavailability can be obtained by using the

ages that correspond to given imes. For example, if the component was renewed at to

with no subsequent checking or maintenance then the unavailability q(t) at time t is

q(t) = 1- exP( 1 L(w')dw)

where the component age at time t is t-tD.

If the component was last known to be up at time % i.e. last tested at ta , then the

component unavailability q(t) is

1 t-to (6)

q(t)=I-e xp- fA(w')dw'

ta-to( 

where t3 - o is the age wa at the last test or check. Similar transformations can be used

for the component unreliabilities in Equations (1) and (2).

Finally, for average component unavailabilities the above age dependent or time

dependent component unavailabilities are averaged over given time intervals. Averages

over intervals between tests give the average unavailability between tests and averages

134
over intervals between replacements give te average unavailability between

replacements. Differences from the baseline PSA unavailabilities give the increases in

unavailability (or unreliability) due to aging, either for time dependent or for averaged

results.

135
NRC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

(2-89) EAuunWd byNRC. Add Vol.Sp., Re.

NRCM 1102, and Addendum Numbers If any.

3201,3202 BIBLIOGRAPHIC DATA SHEET

(See isttons on the reverse) NUREG/CR-5587

2. TITLE AND SUBTITLE SAIC-92/1137

Approaches for Age-Dependent Probabilistic Safety

Assessments with Emphasis on Prioritization and . DATE REPORT PUBLISHED

Sensitivity Studies MONt1

August 1992

4. FIN OR GRANT NUMBER

L1072

5. AUTHOR(S) 6. TYPE OF REPORT

Technical

7. PERIOD COVERED f(ic/lswve Dites)

W.E. Vesely

S. PERFORMING ORGANIZATION - NAME AND ADDRESS If NRC. provide Division, Office or Reon, US Nuckar RegulatorY miion anmili Art; If contractor provide um e nd meiliv addss.)

Science Applications International Corporation

655 Metro Place South, Suite 745

Dublin, OH 43017

9. SPONSORING ORGANIZATION -NAME AND ADDRESS f NRC, type 'Sane as aove" If contracto, provke NRC Divion, Offkc or Region, U.S Nucear Reulatory Commission,

anedfilng addreVsJ

Division of Engineering

Office of Nuclear Regualtory Research

U.S. Nuclear Regulatory Comission

Washington, DC 20555

10. SUPPLEMENTARY NOTES

11. ABSTRACT 2W wory or a

Approaches are described for incorporating component aging reliability models into

a probabilistic safety assessment (PSA), or probabilistic risk assessment (PRA), of

a nuclear power plant. These approaches and procedures are described from a

technical standpoint and are not to be interpreted as having any regulatory

implications. Component aging failure rate models and test and maintenance aging

control models are presented for utilization. Different approaches for carrying

out the aging evaluations are given. Demonstrations are given involving prioritizing

aging contributors, evaluating maintenance effectiveness, carrying out time dependent

evaluations, and carrying out uncertainty and sensitivity analyses of aging effects.

12. KEY WORDS/DESCRIPTORS (ist words or phrset h will asit weaheinocaetherort.) 13. AVAILABILITY STATEMENT

Probabilistic Safety Assessment Unlimited

Probabilistic Risk Assessment 14. SECURITY CLASSIFICATION

Aging Evaluations (This Pe)

Component Reliability Mbdels Unclassified

This Report)

Unclassified

15. NUMBER OF PAGES

1 .PRICE

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