Industry Performance of 

Relief Valves at

U.S. Commercial Nuclear

Power Plants through 2007 

Office of Nuclear Regulatory Research

NUREG/CR-7037

INL/EXT-10-17932
NOTICE

This information was prepared as an account of work sponsored by an agency of the U.S. 

Government. Neither the U.S. Government nor any agency thereof, nor any of their 

employees, makes any warranty, express or implied, or assumes any legal liability or 

responsibility for any third party‘s use, or the results of such use, of any information, apparatus, 

product, or process disclosed herein, or represents that its use by such third party would not 

infringe privately owned rights. The views expressed herein are not necessarily those of the 

U.S. Nuclear Regulatory Commission.
Industry Performance of

Relief Valves at

U.S. Commercial Nuclear

Power Plants through 2007 

Manuscript Completed: December 2010 

Date Published: March 2011 

Prepared by

T.E. Wierman, C.D. Gentillon, INL

B.M. Brady, NRC 

Idaho National Laboratory

Idaho Falls, ID 83415

J. Lane, NRC Project Manager

NRC Job Code Numbers Y6546 and N6890 

Office of Nuclear Regulatory Research

NUREG/CR-7037

INL/EXT-10-17932
iii

ABSTRACT 

This report characterizes current industry average performance for relief 

valves at U.S. commercial nuclear power plants using data through 2007. It uses 

data obtained from the Institute for Nuclear Power Operation‘s Equipment 

Performance and Information Exchange (EPIX) database and Licensee Event 

Reports (LERs). It describes the parameter estimation process used to derive the 

failure probabilities on demand (using beta distributions), failure rates (using 

gamma distributions), maintenance unavailabilities, and initiating event 

frequencies for use in Level 1 Standardized Plant Analysis Risk (SPAR) models 

of U.S. commercial nuclear power plants. The methods employed in this report 

are conventional estimation methods as documented in NUREG/CR-6823, 

―Handbook for Parameter Estimation for Probabilistic Risk Assessment.‖

The characterization of current industry average performance is an important 

step in maintaining up-to-date risk models. Studies have indicated that industry 

performance of most components has improved since the 1980s and early 1990s. 

For most relief valve component performance estimates, data for 1997–2007 are 

used to characterize current industry average performance. However, data from 

1987 to 2007 are used to characterize relief valve response to unplanned 

shutdown events. 
iv
v

CONTENTS 

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

ACKNOWLEDGMENTS ........................................................................................................................... xi

ACRONYMS ............................................................................................................................................. xiii

1. INTRODUCTION .................................................................................................................................... 1

2. RELIEF VALVE DESCRIPTIONS ......................................................................................................... 3

2.1 High-Capacity Relief Valves .......................................................................................................... 3

2.1.1 Power-Operated Relief Valves................................................................................................ 4

2.1.2 Pressurizer Safety Valves ....................................................................................................... 6

2.1.3 Relief Valve Interlocks and Cold Overpressure Protection .................................................... 6

2.1.4 Atmospheric Dump Valves ..................................................................................................... 7

2.1.5 Main Steam Code Safety Valves ............................................................................................ 7

2.1.6 BWR Code Safety Valves ..................................................................................................... 10

2.1.7 BWR Safety Relief Valves ................................................................................................... 10

2.2 Low-Capacity Relief Valves ......................................................................................................... 15

3. OPERATION DATA ACQUISITION ................................................................................................... 17

3.1 Acquiring Operational Data .......................................................................................................... 17

3.1.1 EPIX Data ............................................................................................................................. 17

3.1.2 LER Data .............................................................................................................................. 19

4. OPERATIONAL DATA CHARACTERIZATION ............................................................................... 21

4.1 Determining Standby Time for Rates............................................................................................ 21

4.2 Encoding Demand Information ..................................................................................................... 21

4.3 Encoding Failure Information ....................................................................................................... 22

4.4 Estimating Test Demands ............................................................................................................. 24

4.4.1 EPIX Data ............................................................................................................................. 24

4.4.2 Five-Year Test Data .............................................................................................................. 25

4.4.3 Overall Test Demand Data .................................................................................................... 26

5. CALCULATION METHODS ................................................................................................................ 27

5.1 Parameter Distributions ................................................................................................................. 27

6. RISK-BASED ANALYSIS OF THE EXPERIENCE ............................................................................ 31

6.1 High-Capacity Relief Valves ........................................................................................................ 31
vi

6.1.1 High-Capacity Demands ....................................................................................................... 31

6.1.2 High-Capacity Failure Probabilities...................................................................................... 38

6.1.3 High Capacity Failure Rates ................................................................................................. 44

6.2 Low Capacity Relief Valves ......................................................................................................... 44

6.3 Uncertainty Distributions .............................................................................................................. 48

6.4 Uncertainty Results ....................................................................................................................... 49

7. ENGINEERING ANALYSIS OF THE EXPERIENCE ......................................................................... 63

7.1 Industry Trends ............................................................................................................................. 63

7.2 Factors Affecting Relief Valve Reliability .................................................................................... 84

7.2.1 Method of Detection ............................................................................................................. 84

7.2.2 Relief Valve Failure Causes .................................................................................................. 87

7.2.3 Relief Valve Type ................................................................................................................. 90

8. COMPARISON OF CURRENT RESULTS WITH HISTORICAL ESTIMATES ............................... 91

9. SUMMARY ............................................................................................................................................ 95

10. REFERENCES ..................................................................................................................................... 97

Appendix A—Relief Valve Coding Guidance .......................................................................................... A-1 

Appendix B—Distributions for Relief Valve Estimates ........................................................................... B-1 

Appendix C—Relief Valve Response Modeling ...................................................................................... C-1 

FIGURES 

Figure 1. Pressurizer relief valve configuration. .......................................................................................... 5

Figure 2. Main steam ADV air actuation. .................................................................................................... 6

Figure 3. Main steam safety configuration. ................................................................................................. 8

Figure 4. PWR main steam code safety valve.............................................................................................. 9

Figure 5. Direct acting SRV. ...................................................................................................................... 11

Figure 6. Pilot actuated SRV, actuation function dependent on the pilot. ................................................. 12

Figure 7. Pilot actuated SRV, actuation function not dependent on the pilot. ........................................... 13

Figure 8. Three stage pilot operated SRV, actuation function not dependent on the first stage pilot. ....... 14

Figure 9. Direct acting pressure relief valve diagram. ............................................................................... 15
vii

Figure 10. Probability of MSS PORV demand given PWR scram. ........................................................... 68

Figure 11. Probability of RCS PORV demand given PWR scram. ........................................................... 68

Figure 12. Probability MSS PORV demand is automatic. ......................................................................... 69

Figure 13. Probability RCS PORV demand is automatic. ......................................................................... 69

Figure 14. MSS PORV fail to open (event). .............................................................................................. 70

Figure 15. MSS PORV fail to open automatic (scrams). ........................................................................... 70

Figure 16. MSS PORV fail to open (scrams). ............................................................................................ 71

Figure 17. MSS PORV fail to open (testing). ............................................................................................ 71

Figure 18. MSS PORV fail to close/reseat (event). ................................................................................... 72

Figure 19. MSS PORV fail to close (scrams). ........................................................................................... 72

Figure 20. MSS PORV fail to close (testing). ............................................................................................ 73

Figure 21. MSS PORV spurious operation. ............................................................................................... 73

Figure 22. RCS PORV spurious operation. ............................................................................................... 74

Figure 23. MSS PORV setpoint out of specification. ................................................................................ 74

Figure 24. Probability of MSS SVV demand given PWR scram............................................................... 75

Figure 25. Probability of RCS SVV demand given PWR scram. .............................................................. 75

Figure 26. MSS SVV fail to close/reseat (per event). ................................................................................ 76

Figure 27. MSS SVV fail to close/reseat (per valve demanded in a scram). ............................................. 76

Figure 28. MSS SVV setpoint out of specification. ................................................................................... 77

Figure 29. Probability of SRV demand given BWR scram. ...................................................................... 77

Figure 30. Probability SRV demand is automatic. ..................................................................................... 78

Figure 31. Probability SRV demand from direct pressure. ........................................................................ 78

Figure 32. Probability SRV failure to open given one or more demands in a BWR scram (per event). ... 79

Figure 33. Probability of SRV failure to open, per demand (data from BWR scrams). ............................ 79

Figure 34. SRV fail to open (data from testing). ....................................................................................... 80

Figure 35. SRV spurious operation. ........................................................................................................... 80
viii

Figure 36. SRV setpoint out of specification. ............................................................................................ 81

Figure 37. RVLC fail to open. ................................................................................................................... 81

Figure 38. RVLC fail to close/reseat. ........................................................................................................ 82

Figure 39. RVLC spurious operation. ........................................................................................................ 82

Figure 40. RVLC setpoint out of specification. ......................................................................................... 83

Figure 41. RVLC leakage. ......................................................................................................................... 83

Figure 42. PWR MSS relief valve failure detection methods. ................................................................... 84

Figure 43. PWR RCS relief valve detection methods. ............................................................................... 85

Figure 44. BWR SRV failure detection methods. ...................................................................................... 86

Figure 45. RVLC detection methods. ........................................................................................................ 86

Figure 46. PWR MSS relief valve failure causes distribution. .................................................................. 88

Figure 47. PWR RCS relief valve failure causes distribution. ................................................................... 88

Figure 48. BWR SRV failure causes distribution. ..................................................................................... 89

Figure 49. RVLC failure causes distribution. ............................................................................................ 89

Figure 50. Failure comparison of SRV sub-types. ..................................................................................... 90

Figure 51. Comparison of historical relief valve reliability estimates. ...................................................... 92

TABLES 

Table 1. Types of relief valves. .................................................................................................................... 1

Table 2. Numbers of low-capacity relief valves at various sizes. .............................................................. 16

Table 3. Listing of relief valve device counts in EPIX. .............................................................................. 17

Table 4. Relief valve EPIX component population distributions per plant. .............................................. 18

Table 5. Safety, safety relief, and power operated relief valve manufacturers (from EPIX). .................... 19

Table 6. Number of unplanned demands (different component/RVsys are counted separately). .............. 22

Table 7. Failure modes (functions) that might occur on unplanned and test demands for relief valves. ... 23

Table 8. Use of failure detection methods in computing relief valve estimates. ....................................... 24

Table 9. EPIX relief valve test demand estimate hierarchy. ...................................................................... 25
ix

Table 10. EPIX relief valve overview of the results of the test demand calculations. ............................... 26

Table 11. Relief valve demands on initiating events grouped by functional impact, 1988-2007. .............. 33

Table 12. Minimum, nominal, and maximum numbers of pulses per scram for various initiating events 

grouped by functional impact. .......................................................................................................... 34

Table 13. Relief valve demands on scrams, with scram classification based on the initial plant fault. ..... 35

Table 14. Listing of data element extensions. ............................................................................................ 35

Table 15. Demand profile details for PWR power-operated relief valves. ................................................ 37

Table 16. Demand profile details for PWR code safety valves. ................................................................ 38

Table 17. Demand profile details for BWR (main steam system) safety relief valves. ............................. 38

Table 18. Failure probabilities for PWR power-operated relief valves (behavior after scrams). .............. 40

Table 19. Additional failure probabilities for PWR power-operated relief valves (behavior after scrams).41

Table 20. Failure probabilities for PWR code safety valves (behavior after scrams). ............................... 42

Table 21. Failure probabilities for BWR (main steam system) safety relief valves. ................................. 43

Table 22. Failure probabilities based on testing (EPIX). ........................................................................... 43

Table 23. Failure rates, per valve per reactor critical year. ........................................................................ 45

Table 24. RVLC failure probabilities (5-year testing) for both PWRs and BWRs. ................................... 46

Table 25. RVLC failure rates, per valve per calendar year for both PWRs and BWRs. ........................... 47

Table 26. Relief valve demands on scrams, 1988-2007. ............................................................................ 50

Table 27. Demand profile details from scram data for PWR power-operated relief valves. ..................... 51

Table 28. Demand profile details from scram data for PWR code safety valves. ..................................... 52

Table 29. Demand profile details from scram data for BWR (main steam system) safety relief valves. .. 53

Table 30. Failure probabilities for PWR power-operated relief valves. .................................................... 54

Table 31. Failure probabilities for PWR code safety valves. ..................................................................... 56

Table 32. Failure probabilities for BWR safety relief valves. ................................................................... 57

Table 33. Failure rates, per valve per reactor critical year. ........................................................................ 59

Table 34. RVLC failure probabilities (5-year testing) (both plant types). ................................................. 60

Table 35. RVLC failure rates, per valve per calendar year. ....................................................................... 61
x

Table 36. Overview of statistically significant RV trend findings. ............................................................ 63

Table 37. Overview summary of RV trend analyses. ................................................................................ 65

Table 38. Failure cause code descriptions. ................................................................................................ 87

Table 39. Comparison of historical estimates with this report. .................................................................. 93
xi

ACKNOWLEDGMENTS 

The authors would like to acknowledge the valuable comments and direction 

provided by Don Marksberry, NRC/RES, Rudy Bernhard, NRC/Region II, and 

John Lane, NRC/RES. 
xii
xiii

ACRONYMS 

ADV atmospheric dump valve 

AFW auxiliary feedwater system 

ASME American Society of Mechanical Engineers 

ASP accident sequence precursor 

BRIIE Baseline Risk Index of Initiating Events 

BWR boiling water reactor 

CNID constrained noninformative distribution 

EB empirical Bayes 

EPIX Equipment Performance and Information Exchange 

FY fiscal year 

ID identification 

INPO Institute of Nuclear Power Operations 

JNID Jeffreys noninformative prior distribution 

LER licensee event report 

MPT minimum pressurization temperature 

MSIV main steam isolation valve 

MSPI Mitigating Systems Performance Index 

MSS main steam system 

NI non-informative 

NRC Nuclear Regulatory Commission 

PORV power-operated relief valve 

PRA probabilistic risk assessment 

PWR pressurized water reactor 

RCS reactor coolant system 

RHR residual heat removal 

RVLC low-capacity relief valve 

SDP Significance Determination Process 

SORV stuck open relief valve 

SPAR standardized plant analysis risk 

SRV safety relief valve 

SVV code safety valve 

WAT water system 

WATD dirty water system 
xiv
1

Industry Performance of Relief Valves at

U.S. Commercial Nuclear Power Plants 

through 2007

1. INTRODUCTION 

The U.S. Nuclear Regulatory Commission (NRC) maintains a set of risk models, called standardized 

plant analysis risk (SPAR) models, for the operating U.S. commercial nuclear power plants. Currently, 

there are 104 commercial nuclear plants that generate electricity in the U.S. The collective group of 

plants is termed the ―industry‖ in this report (O‘Reilly et al., 2005). SPAR models are used by the NRC 

on a day-to-day basis to support risk-informed decision-making activities such as the accident sequence 

precursor (ASP) and significance determination process (SDP) programs. The primary objective of the 

ASP Program is to identify, document, and rank operating events most likely to lead to inadequate core 

cooling and core damage. The main purpose of the SDP is to determine the safety significance of 

inspection findings. 

In addition to supporting the ASP and SDP analyses, SPAR models confirm licensee risk analyses 

submitted in support of license amendment requests. In risk assessments, relief valves are important 

because energy must be removed in the decay heat removal function (which protects the reactor core) and 

pressure must be released in the overpressure function (which protects piping and components). 

Therefore, it is important that the SPAR models reflect current plant performance. This report documents 

the work performed to generate SPAR model inputs that represent current industry relief valve 

performance. 

Four types of relief valves are considered in this report: safety relief valves (SRVs), power-operated 

relief valves (PORVs), American Society of Mechanical Engineers (ASME) code safety valves (SVVs), 

and low-capacity relief valves (RVLCs). Table 1 briefly describes these valves. The valves and their use 

in nuclear power plants are described in more detail in Section 2. 

Table 1. Types of relief valves. 

Description Use in Pressurized Water Reactors Use in Boiling Water Reactors

Power-operated 

relief valve

Primary method for reactor coolant system 

and main steam system decay heat removal 

and pressure relief. The main steam system 

PORV are also called atmospheric dump 

valves.

Minor use in main steam system for decay 

heat removal and pressure relief at six plants.

Code safety valve Direct-acting (actuated only by pressure) 

valves that provide overpressure design 

protection and backup decay heat removal 

capability for the reactor coolant system and 

main steam system.

Minor use for main steam system

overpressure design protection and backup 

decay heat removal capability at 14 plants.

Safety relief valve Not used. Main steam system decay heat removal and 

pressure relief.

Low-capacity relief 

valve

In many systems these valves provide 

overpressure design protection. Direct 

acting.

In many systems these valves provide 

overpressure design protection. Direct 

acting.

The data sources for this study were the Equipment Performance and Information Exchange (EPIX) 

and licensee event reports (LERs). Data from the Institute of Nuclear Power Operations (INPO) EPIX 

data were reviewed to characterize the relief valve component performance. The EPIX operational data 

describe relief valve performance (full fiscal years) between October 1, 1997, and September 30, 2007. 
2

Although the EPIX database started on January 1, 1997, fiscal year (FY) 1998 is the first full fiscal year 

for which data are available. 

LER data were limited to two databases from updated risk studies: initiating events and shutdown 

initiating events (NRC, 2010a). There are 3,024 LERs in the initiating event database from calendar year 

1987 to 2007 and 14 records in the shutdown initiating event database from 1991 to 2007. Each initiating 

event LER was reviewed to determine whether SRVs, PORVs, or SVVs were actuated and/or demanded 

(observed lift) and whether they failed. Each shutdown initiating event LER was reviewed for (a) failures 

of the minimum pressurization temperature (MPT) function (the MPT function is a lowered setpoint used 

while shutdown to protect the RCS from overpressure at low temperatures) of the PORVs and (b) events 

caused by spurious operation of decay heat removal system RVLCs leading to loss of coolant. 
3

2. RELIEF VALVE DESCRIPTIONS 

The four types of relief valves considered in this report can be broken into two groups: high-capacity 

relief valves (PORVs, SVVs, SRVs) and low-capacity relief valves. The valves are used differently in the 

two types of nuclear plants. Pressurized water reactors (PWRs) use PORVs and SVVs in primary 

systems installed in piping coming from the steam space of the pressurizer (see Figure 1). Each PWR 

main steam line contains atmospheric dump valves (ADVs collected under the PORV component) and/or 

SVVs upstream of the main steam isolation valve (MSIV) (see Figure 2). PORVS and SVVs are used in 

only a few boiling water reactor (BWR) plants. BWR PORVs, SVVs, or SRVs are mounted on a 

horizontal portion of the main steam lines inside the drywell. These valves provide overpressure 

protection for the reactor vessel and associated piping systems. In addition, selected SRVs are used by 

the automatic depressurizing system, one of the emergency core cooling systems. To provide adequate 

protection, typically eleven safety relief valves are used. Some of the older BWRs have a small number 

of safety valves in addition to the SRVs. PWR plants do not use SRVs. RVLCs are used in both plant 

types. 

2.1 High-Capacity Relief Valves 

At U.S. nuclear power plants, the relief of overpressure conditions and removal of decay heat in the 

main steam and PWR primary coolant systems are accomplished though the use of PORVs, SVVs 

(―safeties‖), and SRVs. PORVs are primary system devices; atmospheric dump valves are poweroperated valves in the secondary system—both are denoted as PORVs in this report. Likewise, PWR 

pressurizer safety valves and code safety valves are both denoted as SVVs in this report. The turbine 

bypass valves are not included in this study, although they are used for heat rejection and depressurization 

purposes when the condenser is available. 

The SPAR model requirements for data on these devices are 

1. The probability of relief valves and safety valves lifting given specific transients. 

The SPAR models include events to account for the probability of a relief valve demand given an 

initiating event. These conditional probability events currently only apply to the relief from the 

primary system (reactor coolant system [RCS] in PWRs and main steam system [MSS] in 

BWRs). This data collection and analysis has been designed to provide more current and more 

specific conditional probabilities of various relief valves opening during specific transients 

(including the PWR MSS relief valves). 

2. The probability of the relief valves and safety valves failing to reseat after opening. 

The SPAR models include basic events that model the failure of relief valves to reseat. In 

addition, the medium passing through the relief valve is also modeled so that there are separate 

events for failure to reseat for steam and liquid. The reseat is successful if the normal reseat 

pressure occurs and the relief valve reseats. There is also interest in whether the relief valve, 

having failed to reseat as expected, eventually reseats at a lower pressure, which is generally a 

recovery action. 

3. Given multiple relief valve and safety valve cycles, is the relief valve more or less likely to 

reseat? 

The multiple opening of relief valves is not currently modeled in SPAR. However, the ASP 

analyses have tried to analyze the probability of relief valve failure, given multiple openings for 

some recent events. Currently, each lift is treated as an independent chance for the relief valve to 

fail. This relief valve study gathered information about multiple openings to provide a basis for 

calculating failure probabilities after multiple demands in a single initiating event. 
4

4. The probability of relief valves and safety valves failing to lift. 

The SPAR models include the requirement for relief and safety valves to lift and relieve pressure 

in the anticipated transient without scram (ATWS) event tree. The failure to open is important in 

the ATWS sequence in that the pressure boundary is assumed to rupture on relief valve failure, 

which leads directly to core damage. 

5. Spurious operation of relief valves and safety valves. 

The SPAR models do not generally model the spurious operation of relief valves (other than as an 

initiating event). The spurious operation includes early lifting and spurious actuation of control 

circuitry. 

The following bullets describe some of the other data collection criteria: 

 For the dual-action SRVs, the failures are described for direct pressure, automatic, and manual modes 

of operation separately. 

 For the PORV and SRV automatic actuation, the sensors and coincidence circuitry are included 

within the relief valve boundary. Only full failures of the sensor/activation circuitry are included in a 

failure event (i.e., one redundant pressure sensor failing that does not, by itself, preclude automatic 

operation of the relief valve assuming all other sub-components function). Manual and automatic 

actuations are identified. In addition, the mode of failure (whether the automatic function was the 

only function affected or whether both the manual and automatic functions were affected) is 

identified. 

 Many of the EPIX failure records are for setpoint drift or out-of-specification lift or reseat pressures. 

Testing data is only identified as a failure ≥ ±10% around setpoint. Above the ±10% criteria is failure 

to open; below the ±10% criteria the failure mode is spurious operation. Late opening may preclude 

the injection of auxiliary feedwater (AFW), high-pressure injection, high-pressure coolant injection, 

etc., which is related to the setpoint failure mode. 

 When the plant has gone solid or almost solid, the chance of multiple (chattering) lifts of PORVs is 

higher because the pressure is relieved and built back up more quickly than when the plant has a 

sufficient steam blanket. The data collection specifies the relief medium (steam, mixture (2-phase), 

or liquid) to capture failures under different conditions. 

 Whether the relief valve failure is recovered or recoverable is recorded for all failures. Recovery is 

considered to be an action taken by the operator within a short period of time that performs the 

intended operation. Maintenance activities, however expeditious, are not considered a recovery. 

2.1.1 Power-Operated Relief Valves 

In a PWR the pressurizer is normally equipped with one or two PORVs, which limit pressure in the 

reactor coolant system to below the actuation of the high-pressure reactor trip. The operation of the 

PORVs also limits the operation of the fixed high-pressure SVVs. The PORVs are air- or motor-operated 

and can be opened or closed automatically or by remote manual control. The air-operated PORVs have a 

backup air supply system to maintain the PORVs operable for 10 minutes following a loss of instrument 

air. Remotely operated block valves are provided to isolate the PORVs if excessive leakage occurs. The 

PORVs are designed to limit the pressure in the pressurizer to a value below the high-pressure reactor trip 

setpoint for design transients up to and including a 50% step load decrease with full steam dump 

actuation. The PORVs, with additional actuation logic, are also used to mitigate potential RCS cold 

overpressurization transients during cold shutdown conditions. 

The failure of the pressurizer PORVs are present in several accident sequences that lead to core 

damage. There are two general failure modes for the relief valves. First, the failure of the PORVs to shut 

when required leads to the need for recirculation cooling of the reactor, and the subsequent failure of the 

recirculation mode of the emergency core cooling system results in core damage. The second failure is 
5

the failure to open when required for the purpose of initiating feed and bleed cooling for the reactor. This 

failure of heat removal results in core damage. Probable causes of a loss of the PORVs are 

1. Failure of the PORVs to open on demand 

2. Failure of the block valve to shut to isolate a stuck open relief valve 

3. Failure of the power supply to the PORVs. 

Studies on importance measures have shown that the PORVs are not a major contributor to risk 

achievement or risk reduction (NRC, 1990). 

Figure 1. Pressurizer relief valve configuration. 
6

Figure 2. Main steam ADV air actuation. 

2.1.2 Pressurizer Safety Valves 

The pressurizer SVVs are totally enclosed pop-open-type valves (similar to the main steam SVV 

discussed in Section 2.1.5). The valves are spring-loaded, self-actuating, and have backpressure 

compensation designed to prevent the reactor coolant system pressure from exceeding the design pressure 

by more than 10%. This meets the requirements of the ASME Boiler and Pressure Code, Section III. The 

set pressure of the safety valves is approximately 2485 psig. 

A water seal is maintained below each SVV seat to minimize leakage. The nominal 6-in. pipes 

connecting the pressurizer nozzles to their respective SVVs are shaped in the form of a loop seal. 

Condensate, as a result of normal heat losses to ambient, accumulates in the loop and floods the valve 

seat. This water seal prevents steam and hydrogen gas from passing by the safety valve seats. If the 

pressure inside the pressurizer exceeds the setpoint of the SVVs, they will lift and the water from the loop 

seal will discharge during the accumulation period. 

Because of the high pipe and pipe support loads caused by these ―water slugs,‖ catch pots were 

designed and placed immediately downstream of the relief and safety valves. A total of four of these slug 

diversion devices are installed (one for each of the SVVs and one for the PORV combined discharge). 

The slug diversion devices are located at the change in pipe direction so that the water slugs flow into the 

devices and are trapped. These devices are totally passive and ensure that the piping system is not 

subjected to stresses or loads beyond allowable code. A temperature indicator in the safety valve 

discharge manifold alerts the operator to the passage of steam caused by leakage or valves lifting. 

Acoustic monitors are also provided for each valve to provide a positive indication of leakage or SVV 

operation. 

2.1.3 Relief Valve Interlocks and Cold Overpressure Protection 

The PORVs attached to the pressurizer are provided with an interlock to prevent an inadvertent 

operation of these valves if pressurizer pressure is less than a nominal 2335 psig. This interlock prevents 
7

the failure of either a single pressure transmitter or the failure of the master pressure controller from 

inadvertently opening a PORV. 

Accidentally opening a PORV is in effect a small-break loss-of-coolant accident out of the top of the 

pressurizer, which causes a depressurization of the reactor coolant system. An interlock is built into the 

system via a second bistable, which is actuated from a separate independent pressure transmitter. The 

second bistable‘s setpoint is established at 2335 psig. Using this configuration, it takes two channels, 

sensing a pressure equal to or greater than 2335 psig, in conjunction with the valve operating switch in the 

AUTO position to open a PORV. 

The standardized technical specifications require that the low-temperature overpressure protection 

system (consisting of either two PORVs or an RCS vent) be operable whenever the RCS cold leg 

temperature is less than a predetermined value. The normal position of the low temperature overpressure 

protection switch (one per PORV) is the block position. When the pressure, as indicated by the wide 

range of pressure detectors, is < 375 psig, the operator is directed by the plant‘s operating procedures to 

place these switches in the unblocked position. This action arms the overpressure protection circuitry and 

all that is needed for actuation of the PORVs is for pressure in the reactor coolant system to increase to a 

value greater than the cold overpressure bistable setpoint. The control room operator can override the 

automatic signals and manually open or close either PORV. Manual control is independent of the 

pressurizer safety injection block interlock and the cold overpressure protection system because the 

manual open signal provides a direct input to the ―or‖ logic used to actuate the PORV. 

2.1.4 Atmospheric Dump Valves 

The atmospheric dump valve (ADV) (called a PORV in the coding database) in each PWR steam line 

is a 6-in. air- or motor-operated, spring-opposed globe valve capable of relieving approximately 10% of 

the rated steam flow at no-load pressure from each steam generator (2.5% of the total steam system flow). 

The ADVs are mounted outside containment on the main steam support structure and upstream of the 

MSIVs. Each ADV has a nominal setpoint, which is approximately half the difference between the noload steam generator pressure and the lowest set pressure of the safety valves. The ADVs thus lift to 

relieve an overpressure condition before the safety valves do. In addition to providing overpressure 

protection for the steam generators and the Seismic Category I portion of the main steam system, the 

ADVs provide a means of removing heat from the reactor coolant system. If the main condenser is 

unavailable or the steam dumps (to the main condenser) are inoperable, the ADVs are automatically or 

manually controlled (or are operated in a pressure control mode that can be set to control the cooldown 

rate) from the control room to relieve steam to the atmosphere and thereby cool down the plant. The 

ADVs thus allow the removal of decay heat (the steam generators would be fed by the AFW system to 

provide the secondary inventory for heat removal). The ADVs can also be operated from the remote 

shutdown station. 

Figure 2 illustrates the development of an air signal to open an ADV. The ADV fails shut on a loss of 

instrument air or electrical signal. Figure 2 also shows the backup nitrogen control system for the ADVs. 

A worst-case fire is projected to disable both the electrical signals and the pneumatic supplies to the 

ADVs; the nitrogen control system allows ADV operation under such conditions. To operate an ADV 

with the backup system, the plant‘s nitrogen system is un-isolated and a three-way ball valve is 

repositioned to admit nitrogen to the ADV actuator (the ball valve is normally positioned to admit 

instrument air to the ADV actuator). The nitrogen regulator is then adjusted to obtain the desired opening 

signal. 

2.1.5 Main Steam Code Safety Valves 

Each main steam line has several spring-loaded steam generator SVVs (see Figure 3 and Figure 4). 

The safety valves provide overpressure protection for the steam generators and the main steam piping. 

The valves have staggered set pressures to provide an increased relieving capacity with an increasing 
8

overpressure. The set pressures for the five valves are a nominal 1170, 1200, 1210, 1220, and 1230 psig; 

the highest setpoint is less than 110% of the steam generator design pressure in accordance with the 

ASME Boiler and Pressure Vessel Code. In addition to providing overpressure protection, the safety 

valves remove plant decay heat when the steam dumps and secondary ADVs are unavailable. 

The SVVs relieve to the atmosphere via opposing discharge ports. They are located on the main 

steam support structure outside containment. The exhaust stacks for the safety valves and the ADVs 

extend above the turbine building roof. 

Each main steam line contains steam flow transmitters, steam pressure transmitters, a radiation 

monitor upstream of the MSIV, and a second radiation monitor downstream of the MSIV. These 

instruments provide inputs for plant control and protection as well as indication and alarms (see Figure 2). 

Of the four pressure transmitters on each steam line, one supplies an input for actuation of that line‘s 

ADV. The other three provide inputs to the feedwater control system and to the reactor protection 

system. The three protection-grade channels provide inputs to the protection logic for (1) the high steam 

line differential pressure engineered safety features actuation and (2) the high steam flow engineered 

safety features actuation and steam line isolation. Two of the protection-grade channels provide density 

compensation for separate steam flow channels. Four of the plant‘s 12 protection-grade steam line 

pressure channels provide inputs to the AFW pump speed controllers. All of the pressure transmitters are 

located outside containment and upstream of the MSIVs. 

Figure 3. Main steam safety configuration. 
9

Figure 4. PWR main steam code safety valve. 
10

2.1.6 BWR Code Safety Valves 

The BWR SVVs are spring loaded, direct acting valves, lifting when steam pressure reaches or 

exceeds the spring tension. They discharge directly to the drywell atmosphere. Lift pressure for these 

valves is about 1250 psig. The BWR safety valves are similar to the PWR MSS SVVs (see Figure 4).

2.1.7 BWR Safety Relief Valves 

The SRVs are dual-acting valves: they may be actuated directly by steam pressure (pressure mode); 

or remotely by manual operation of a switch, actuated by a pressure switch, or as part of the automatic 

depressurization system (actuation mode). All SRV discharges are piped directly to the suppression pool. 

These SRVs can be grouped into two distinct sub-types of dual-acting valves. 

1. Direct acting. The direct-acting SRVs (Figure 5) use an attached actuator to overcome the 

spring tension in the main part of the SRV to open the valve without the assist of system 

pressure in actuation mode. Direct-acting SRVs function much the same as the code safety 

relief valves in the pressure mode. 

2. Pilot actuated. The pilot-actuated SRVs use a pilot assembly to either open a second stage 

disk or directly cause the main valve disk to move. The pilot-actuated SRVs can be further 

broken down into types: 1) those that need the pilot to actuate in order to operate in the 

actuation and pressure modes (Figure 6), 2) those that do not require the pilot for the 

actuation mode (Figure 7), and 3) three-stage SRVs (Figure 8). In all three types, the pilot 

assembly is always used in the pressure mode. 

a. In the pressure mode, the SRVs are actuated via a pilot-sensing port that senses main 

steam line pressure and applies it to the volume inside the bellows. When the 

pressure inside the bellows overcomes the pilot pre-load and setpoint adjustment 

spring pressure, the pilot valve‘s disc will open, putting main steam line pressure on 

top of the second stage piston, opening the second stage disc, and relieving pressure 

off the top of the main valve piston. Main steam line pressure on the bottom of the 

main valve piston opens the main valve disc and pressure is relieved to the 

suppression pool. 

b. In the actuation mode of operation, air pressure is applied to the air actuator by 

energizing the solenoid-operated valve. For the Type 1 valves above, the air operator 

directly operates the pilot piston. For the Type 2 valves above, the air operator 

directly opens the second stage disc by mechanically depressing the second stage 

piston. For three-stage SRVs, a second pilot valve is actuated that is independent of 

the primary pilot valve. The main valve will then open as described above, 

regardless of system pressure. The solenoid-operated valve may be energized by a 

remote manual switch (in the control room) or by the automatic depressurization 

system logic. All SRVs may be operated by the remote switch; generally only six are 

used for automatic depressurization system operation. 
11

Figure 5. Direct acting SRV. 
12

Figure 6. Pilot actuated SRV, actuation function dependent on the pilot. 
13

Figure 7. Pilot actuated SRV, actuation function not dependent on the pilot. 
14

Figure 8. Three stage pilot operated SRV, actuation function not dependent on the first stage pilot.
15 

2.2 Low-Capacity Relief Valves 

Smaller relief valves are often used in isolated parts of systems where (a) a check valve or directional 

control valve prevents pressure from being relieved through the main system relief valve or (b) where 

pressures must be relieved at a set-point lower than that provided by the main system relief. These small 

relief valves are also used to relieve pressures caused by thermal expansion of the fluids. These relief 

valves are typically simple spring-operated relief valves. The valves are in most systems with various 

fluid mediums: water, air, gas, hydraulic fluid, etc. 

Figure 9 shows a typical direct-acting relief valve. System pressure simply acts under the valve disk 

at the inlet to the valve. When the system pressure exceeds the force exerted by the valve spring, the 

valve disk lifts off its seat, allowing some of the system fluid to escape through the valve outlet until the 

system pressure is reduced to just below the relief setpoint of the valve. All direct-acting relief valves 

have an adjustment for increasing or decreasing the set relief pressure. Some direct-acting relief valves 

are equipped with an adjusting screw; the screw is usually covered with a cap, which must be removed 

before an adjustment can be made. Some type of locking device, such as a lock nut, is usually provided 

to prevent the adjustment from changing through vibration. Other types of direct-acting relief valves are 

equipped with a hand wheel for making adjustments to the valve. Either the adjusting screw or the hand 

wheel is turned clockwise to increase the pressure at which the valve will open. In addition, most relief 

valves have an operating lever or some other type of device to allow manual cycling or gagging the valve 

open for certain tasks. 

The RVLCs are primarily important in SPAR low power shutdown models when they fail to reseat or 

spuriously open. The models are used for SDP and ASP evaluations. 

Figure 9. Direct acting pressure relief valve diagram. 
16 

Relief valve reliability is a critical element for shutdown risk evaluations of sequences that result in 

loss of inventory from a stuck open relief valve and for pressurized thermal shock sequences that result 

from the relief valve‘s failure to open and potentially reclose. Recently, an SDP analysis was performed 

in which the values for residual heat removal (RHR) relief valve reliability were assumed to be the same 

as for PORV reliability. This report provides estimates that can be used in probabilistic risk assessment 

(PRA) applications for these types of valves. 

Table 2 shows the breakdown of the low-capacity relief valves by size and system type. The largest 

population is the 1/2 to 2-inch size. The next largest population is the unknown valve size category. 

EPIX does not require detailed information for all of the devices. 

Table 2. Numbers of low-capacity relief valves at various sizes. 

Nominal Inlet Size

(in.)

System

Total Gas RHR Steam Water

Under 1/2 109 4 105

1/2 to 1.99 6578 37 627 139 5775

2 to 3.99 824 20 131 25 648

4 to 11.99 306 2 71 17 216

12 to 19.99 94 81 13

20 to 39.99 57 53 4

40 to 60 1 1

Over 60 15 15

Unknown 2495 222 33 262 1978

Total 10479 281 862 581 8755

The RVLC devices were screened to include only those in the listed system types. The excluded 

RVLCs included those installed in fuel oil, hydraulic oil, offgas, and hydrogen systems. 
17 

3. OPERATION DATA ACQUISITION 

This section describes the process taken to acquire data and process the data to the point where 

statistical and engineering analyses could be performed. The statistical analyses are described in 

Section 5 and Section 6.3. Engineering analysis is shown in Section 7. 

3.1 Acquiring Operational Data 

Two data sources were used for this study: EPIX (1997 to 2007) and LERs (1987 to 2007). The 

EPIX time period was chosen because that was the total of the EPIX database. The LER period was 

chosen to be longer than the EPIX time period to avail the analysis of the longest possible time period, 

which enhances the estimation of rare events. Collection and interpretation of relief valve data involved a 

three-step process: identification of candidate data records in LERs and EPIX, creation of the schema for 

the data collection, and analyst data coding and review. 

3.1.1 EPIX Data 

Over one million devices, each with a unique device identification (ID), are described in EPIX. 

Among these devices, nearly 13,000 were flagged as being relief valves applicable to this study. The 

study is restricted to the 104 currently-operating nuclear power plants. Table 3 summarizes the counts of 

relief valve types identified in the EPIX device table. 

Table 3. Listing of relief valve device counts in EPIX. 

System SRV PORV SVV RVLC

PWR MSS — 278 1176 339

PWR RCS — 129 190 86

BWR MSS 419 — 62 229

Other — — — 9670

Total 419 407 1368 10323

A physical component in the EPIX database can be described by a set of device IDs (for example, a 

valve, valve body, and corresponding valve operator are considered to be separate devices). The valve 

device is the whole valve (body and operator) and is known as a ―key‖ device. The EPIX reliability data 

provide information about operational and testing and/or total demands for particular device IDs 

corresponding to the physical, or key, components. The reliability data are attached to exactly one device 

ID, the key device ID, for a particular physical component. For the purposes of this study, only the key

device IDs were flagged for data collection and analysis. 

EPIX failure data are also attached to the device IDs. Each time a failure record referred to a device 

ID identified as a relief valve key component, that failure record was reviewed for applicability to this 

study and the data were collected and coded. 

To ensure completeness in the relief valve component list, the data were compared between plant 

units for each component type and system. As shown in Table 4, the component counts are fairly 

consistent across plants and systems for the SRVs, PORVs, and SVVs. However, there is much variation 

between plants in the identified number of RVLCs for each system. For example, BWR main steam 

RVLCs vary from 1 at one plant to 44 at another. This variation, present in EPIX, could cause data from 

plants with many components to dominate certain industry averages. It is beyond the scope of the current 

study to investigate this effect. Table 5 shows the relief valve counts by manufacturer as listed in EPIX. 
18 

Table 4. Relief valve EPIX component population distributions per plant. 

PWRs BWRs

Comp System

Component Count per Unit with 

the Component

Comp System

Component Count per Unit 

with the Component

Low Median Mean High Low Median Mean High

PORV MSS 0 4 4.5 13 SRV MSS 4 11 11.7 20

RCS 0 2 2.1 3

SVV MSS 8 18 17 26 SVV MSS 1 2.5 4.6 9

RCS 2 3 2.8 4

RVLC AFW 1 2 2.6 6 RVLC CCW 1 7 10.2 39

CCW 4 19 23.7 95 CDS 1 3 5.7 33

CDS 1 7.5 8.6 37 CHW 10 10.5 10.5 11

CFC 5 5 14. 32 CIS 1 2 8.3 87

CHW 1 5 9.1 31 CRD 1 3 3.9 15

CIS 1 2 12.3 120 CTS 2 5.5 5.5 9

CSR 1 2 3.2 12 EPS 1 16 18.9 64

CTS 1 3 3.7 7 ESW 2 6 7.9 33

CVC 1 9 9.3 22 FHS 3 3 3.0 3

CWS 1 1 1 1 FWS 1 4 9.8 26

EPS 1 18 17.1 61 HCI 1 3 3. 6

ESW 2 11 12.4 47 HCS 3 8.5 12.3 38

FHS 2 3.5 4.0 7 HVC 1 2 9.8 33

FWS 2 2 6.4 27 IAS 2 20 15.2 30

HCS 12 12.5 12.5 13 LCI 3 11 10.7 21

HPI 1 4 5 19 LCS 1 3 3.7 8

HVC 1 7 9.6 27 MFW 2 4 6.9 21

IAS 1 3 8.6 39 MSS 1 6 10.4 44

ICS 1 2 2.4 4 NSW 1 4 8.6 23

LPI 1 8 7.8 20 RCI 1 2.5 3.1 8

MFW 1 3 4.7 15 RPS 4 4 4.0 4

MSS 1 3 6.6 28 RRS 1 2.5 4.3 17

NSW 1 6 6 11 RWC 1 1 2.4 8

OEP 38 38 38.0 38 SGT 2 7 7 12

RCS 1 4 4.8 13 SLC 1 2 2.1 4

RGW 1 8.5 11.2 24 VSS 2 2 2 2

Acronyms:

AFW auxiliary feedwater

CCW component cooling water

CDS chilled water

CFC containment fan cooler

CHW chilled water

CIS containment isolation system

CRD control rod drive

CSR containment spray 

recirculation

CTS containment spray

CVC chemical volume control

CWS circulating water system

EPS emergency power system

ESW essential service water

FHS fuel handling system

FWS feedwater control system

HCI high pressure coolant injection

HCS high pressure core spray

HPI high-pressure injection

HVC main control room ventilation

IAS instrument air system

ICS integrated control system

LCI low pressure injection

LCS low pressure core spray

LPI low-pressure injection

MFW main feedwater

MSS main steam system

NSW nuclear service water

OEP offsite electrical power

RCI reactor coolant injection

RCS reactor coolant system

RGW radioactive gaseous waste 

system

RPS reactor protection system

SGT standby gas treatment

SLC standby liquid control

VSS vapor suppression
19 

Table 5. Safety, safety relief, and power operated relief valve manufacturers (from EPIX). 

Manufacturer Name PORV SVV SRV Total

Anchor/Darling Valve Co. 8 8

Consolidated Valve Corp./Dresser 119 5 124

Control Components International 109 109

Copes - Vulcan Inc. 137 137

Crosby Valve & Gage Co. 12 714 95 821

Custom fabricated 2 2

Dikkers Valves Canada 90 90

Dresser Industries Inc. 27 27

Dresser Industrial Valve & Instrument Division/

Ashcroft TM

19 626 20 665

Fisher Controls Co. Inc. 53 53

Fisher Governor de Mexico 2 2

Garrett Air Research Mfg. Co. 4 4

Garrett Fluid Comps 3 3

Garrett Pneumatic Sys - Garrett Corp 4 4

Industrial Valves Corp. 6 6

ITT Conoflow/Div. ITT Fluid Tech. Corp. 2 2

Masoneilan International Inc. 42 42

Mesker , George L Co. 3 3

Undetermined 1 1

Schutte and Koerting Co. (Ametek, Inc.) 6 6

Target Rock Corp. 8 5 301 314

W-K-M Division/ACF Industries Inc. 12 12

Total 426 1498 511 2435

3.1.2 LER Data 

LERs provide the transient demand information for the code safety, power-operated and dual-acting 

safety relief valves. While the EPIX reliability database may provide the same demand counts, the type 

of demand and the plant response are only available in the LERs. The relief valve data of interest is 

sought during both operating conditions and shutdown conditions. For the operating condition 

information, this study limited the data review to LERs in the initiating event database (1987–2007). This 

limits the LER based experience to plants that were critical and subsequently tripped. For the shutdown 

LER condition information, the shutdown initiating event database (which is also LER-based, 1990–

2007) is the source of relief valve failures for shutdown conditions. 

LER data reporting as described in NUREG-1022, Event Reporting Guidelines 10 CFR 50.72 and 

50.73 (NRC, 2000) requires licensees to report valid emergency core cooling system signal or critical 

scrams, but does not explicitly require reporting of relief valve actuations. However, NUREG-1022 does 

require the reporting of relief valve failures. Many LERs describing the plant response to the scram or 

trip do report the operation of both the RCS and MSS relief valves. However, a significant portion of the 

LERs use the phrase, ―All systems operated as expected‖ and may reference the plant‘s final safety 

analysis report for the full discussion. This data collection effort did not interpret relief valve actuation 

when not specifically mentioned in the LER. This implies an under-counting of the demands and a 

possible full counting of the failures, which leads to conservative estimates. 
20 
21 

4. OPERATIONAL DATA CHARACTERIZATION 

Once data records are obtained from LERs and EPIX, the data are characterized by the evidence of 

failures, demands, or both. The relief valve data are characterized by the component type, system, 

method of operation, number of components, medium passed, actuation method, failure mode, detection 

method, failure cause, and recovery. For the relevant components, the failure and demand information in 

EPIX and LERs was reviewed and coded. Both types of records are described further below. 

In processing the data for analysis, duplicates in failures or demands arising from information in both 

the LERs and EPIX were resolved. Duplicate records were removed. An overview of the coding 

characterization is discussed below. Appendix A has the specific coding guidance for the relief valve 

study, including database screen shots. 

4.1 Determining Standby Time for Rates 

Standby time for PORVs, SVVs, and SRVs is limited to plant operational periods. Because the 

PORV, SVV, and SRV components are generally required to be available while the plant is operational 

and are assured to be subjected to a full pressure environment, failures and demands that occurred during 

plant shutdown conditions, other than testing, were omitted from this study. Many of the relief valve tests 

are off-line bench tests. Although such tests may occur when the plant is shut down, the test conditions 

are designed to reflect operational conditions. The RVLC components are used during all plant 

conditions and the standby time for these relief valves is based on calendar time. 

For frequency calculations, standby time was estimated by reactor critical years for the PORVs, 

SVVs, and SRVs, and by reactor calendar years for the RVLCs. These data come from monthly 

operating reports and, more recently, from data reported for the Reactor Oversight Process (NRC, 2010b).

4.2 Encoding Demand Information 

For the study period from FY 1988 to FY 2007, the operational data contain 714 instances of one or 

more of the relief valve component types in a system having an unplanned demand. All but 28 of these 

are from the LER data for reactor scrams while critical. The remaining instances were noted during the 

review of EPIX relief valve failures. In addition to describing the LER or EPIX record identifier, plant, 

event date, and component type, the demand records contain: 

 RVsys—a relief-valve oriented system code. It is the actual system if that system is RCS (PWR 

only), MSS, or RHR. Otherwise, it is WATD for a system containing dirty (gray) water, WAT for a 

water system, and GAS for a system containing air or a gas. The RHR, WATD, WAT, and GAS 

designations apply only to RVLC and allow a comparison of mediums. 

RHR is a WAT system but is of special interest because of the risk significance of these relief valves. 

In low power/shutdown conditions, an RHR relief valve failing to open can challenge the piping 

integrity, and failing to reclose can result in loss of coolant. No records are coded as GAS or WATD 

for unplanned demands. 

 Dtype—the type of demand for the valve to open. Possibilities for each relief valve component type 

are shown in Table 6. 

 Ndem—Number of pressure pulses demanding the lifting of the PORV, SVV, or SRV. For the 42 

PORV demands in the study period, 13 SVV demands, and 40 SRV demands, the exact number of 

times a group of valves was demanded was not known exactly. 
22 

Table 6. Number of unplanned demands (different component/RVsys are counted separately). 

Component

Demand type

Electronic

Signal

(Auto)

Manual

Signal

Direct

Acting 

(Pressure

Mechanism)

MSS 

Pressure 

Control 

during Cool 

Down

RCS Pressure 

Control to 

Maintain 

LPOTa

PORV 70 30 — 18 None recorded

SVV — — 29b — —

SRV 40 29 2

c — —

RVLC — — 8 (2 RHR) — —

a. LPOT is ―low pressure over temperature,‖ a ratio that has certain limits during low power conditions. None of 

these demands are recorded among the unplanned demands. 

b. All of these demands are from PWRs. With one exception, the demands come from LERs (rather than 

EPIX), and affect the MSS SVVs (rather than the RCS SVVs).

c. For SRVs, direct acting (pressure mechanism) demands occur fast, in a pressure wave, before the automatic 

mechanism or the plant operator has time to respond. The demands are observed because the valves open 

before an automatic or manual signal has occurred. No failures were observed. These events are studied only 

to determine the relative frequency of this demand type. Both of the demands occurred at the same plant unit. 

 NCompPerD—Number of relief valves responding to the pressure pulse(s). The PORVs, SVVs, or 

SRVs are generally in banks, with staggered setpoints for the individual valves. The number of 

valves in a group lifting is reported. For just one of the eight unplanned RVLC demands (an RHR 

event) two valves were involved. Most multiple relief valve demand information comes just from the 

LER records because each EPIX record describes a single component. Testing data comes from 

EPIX and does not provide information about multiple component responses. 

 Medium—The type of fluid or gas that is passed during the relief opening. This piece of data is to 

gain insight into whether water (as a liquid) rather than steam is passed in the relief valve opening and 

what that does to the failure probabilities. This situation occurred for one SRV demand and for one 

PORV demand. The PORV demand was reported in an LER but was not associated with a scram on 

the day of the relief valve event. 

Two additional attributes are coded but not used extensively in this study. They are 

 RType—reseat demand type. The records are coded the same as the valve opening demand type 

except for four PORV unplanned demands for which the reseat demand is manual rather than 

automatic. 

 RMedium—Medium passed during the reseat demand (steam or liquid, as with the opening). The 

reseat medium was the same as the opening medium for all the demands except for two SRV events 

(one with liquid instead of steam in the open demand, and one with liquid rather than steam in the 

reseat demand). 

4.3 Encoding Failure Information 

For the study period from FY 1988 to FY 2006, the operational data contain 402 instances of one of 

the relief valve component types in a system having a failure. Of these, 130 instances are from the EPIX 

failure data set. The remaining failures were noted during the review of LER initiating event data. In 

addition to describing the LER or EPIX record identifier, plant, event date, and relief valve component 

type, the failure records contain: 

 RVsys—a relief-valve oriented system code (see the definition in Section 4.2) 
23 

 Flmd—failure mode. Five of the failure modes are listed in Table 7. The failure modes refer to 

failure to provide the associated function. Three additional failure modes could occur without 

particular demands: spurious operation (SO), setpoint out-of-specification (SP), and leakage (LK). 

The leakage failure mode applies only to the RVLC. 

 Mtd—Failure discovery method. Discovery method is important because the use of a failure in a 

particular failure probability estimate depends on whether both the failures and associated demands 

can be estimated. For each component type, particular detection methods are applicable, as shown in 

Table 8. 

 Nf—number of failures. 

 nDbeforeF—number of demands before the failure. When this number is greater than one, the 

failure(s) occurred on some pressure pulse (demand) other than the first one. 

 Recvry—Whether recovery occurred, or was judged possible. For PORVs and SRVs, failure of an 

automatic actuation can always be ―recovered‖ by a manual actuation. When the manual actuation 

fails, the failure is recorded in the ―manual demand‖ category. One PORV manual demand failure to 

open was recovered. 

 Plant status—Failures discovered while testing were used, regardless of the plant mode. For PORVs, 

SVVs, and SRVs, failures occurring during plant shutdown modes were excluded. 

Additional attributes that are coded but not used directly in the statistical analysis are the failure cause, 

whether the failure was a common cause failure, and whether there was an operator error of commission 

involved in the event. Support system failures were excluded. See Appendix A for complete coding 

guidance. 

Table 7. Failure modes (functions) that might occur on unplanned and test demands for relief valves. 

Release pressure (open)

Component

Electronic 

Signal

(Auto)

Manual 

Signal

Direct 

Acting 

(Pressure 

Mechanism)

Contain 

Inventory 

(Reseat)a

Control MSS 

Pressure during 

(typically) 4-hr 

Cool Down

Open to 

Maintain 

MPTb

PORV AO OO — CC CT LP

SVV — — OO CC — —

SRV AO OO — CC — —

RVLC — — OO CC — —

a. These data will also be processed separately based on the type of signal.

b. MPT in the PWR primary system is ―minimum pressurization temperature,‖ a parameter that has certain 

limits during low power conditions. One failure was discovered in testing.
24 

Table 8. Use of failure detection methods in computing relief valve estimates. 

Component

Electronic

(E)

Pressure

(P)

(direct acting)

Test/Surveillance 

(S)

Non-Demand

(O)

PORVaFailures to function 

(open or reclose) on an 

automatic or manual 

signal demand. Also 

SO, SP rates.

NA Failures to function 

(open or reclose) on

a testing demand.

Also SO, SP rates.

SO and SP failure

rates.

SVV NA Failures to function 

(open or reclose) on a 

pressure demand. 

Also, SO, SP rates.

Same as for PORV. Same as for 

PORV.

SRV Same as for PORV. Failure to open or 

reclose.

Same as for PORV. Same as for 

PORV.

RVLC NA Same as for SVV. Same as for PORV. Same as for 

PORV.

a. In addition to the open/reseat functions listed above, PORV (E) and (S) detection methods can also show 

failures to control MSS pressure (failure mode CT) and failure to maintain MPT for the RCS. These do not apply to 

the other relief valve types.

4.4 Estimating Test Demands 

Test demands are estimated using EPIX data for the PORVs, SVVs, and SRVs. Five-year, cyclic 

tests are assumed for the RVLC. The testing demands are considered for failure to open and for failure to 

reseat. Estimation methods for the test demands are described below. 

4.4.1 EPIX Data 

The reliability records from EPIX were reviewed to obtain testing demands for relief valve 

components. Relief valves are not typically monitored components for the Mitigating Systems 

Performance Index in the NRC‘s Reactor Oversight Process (NRC, 2010c). The EPIX reliability data for 

relief valves thus relies on estimated values for some plants and systems, rather than monthly or quarterly 

―actual‖ values. 

The EPIX reliability data (for all components) were pre-processed to get a data set that would cover 

quarters contiguously from a component‘s in-service date to the end of the study period or its out-ofservice date, whichever is earlier. The monthly and quarterly actual data are believed to be more accurate 

than the estimated data; however, many of these data are zeros. When 80% of the records for a 

component were zero, the zeros were marked as missing. Then estimates were developed from the actual 

data surrounding the zero data or from associated ―estimated‖ demand rates. 

Another issue in the data processing is that testing demand counts are desired. The older EPIX 

records contain ―total‖ demands rather than separate testing and operational demands. The monthly and 

quarterly ―actual‖ data, on the other hand, generally have testing and operations data and no data in the 

―total‖ field. 

The EPIX reliability demand data for relief valves were analyzed in groups first by plant and system 

(using the system list in Table 4). Then the valves were analyzed by plant and RV system (using the 

RVsys list in Section 4.2). For RVLCs in systems with insufficient reliability data in EPIX, the estimates 

at the level of whether the system carries water, dirty water, or gases were used. Among the quarterly 

data, the median number of quarterly demands for devices of one of the four relief valve types in a given 

system or relief valve system was computed. Medians were also computed across plants. For the 
25 

PORVs, SVVs, or SRVs, separate values were computed for PWRs and BWRs. Medians were used 

instead of means because the EPIX data vary widely. 

Medians were also calculated for the percentage of demands that are testing. These are determined at 

the plant level and plant type level using records in the data set that have demand counts for testing and 

for operations (and no data for ―total,‖ which includes both testing and operations). 

The data were applied to make estimates based on the level of data that was available. Table 9 shows 

the process. In the table, detailed data are specific for a device ID (with a component type, system, and 

plant) and quarter. As explained above, the median data occur at various levels of detail. Most of the 

data fell in Cases 5, 7 and 11. 

Table 9. EPIX relief valve test demand estimate hierarchy. 

Case No. If data provide ... Calculate ...

1 Detailed EPIX test count Test count

2 Detailed test or operations (total) count and a 

plant/system/component-specific estimate of the 

percentage of demands that are testing

Total count × fraction that are testing

3 Test median over devices and quarters Test median

4 Test or operations (total) median and a 

plant/system/component-specific estimate of the 

percentage of demands that are testing

Total count median × fraction that are 

testing

5 Test or operations (total) median and a 

system/component-specific estimate of the percentage of 

demands that are testing

Total count median × industry fraction that 

are testing

6 Like (5) except that the percentage is at the RVsys/ 

component level

Total count median × aggregated industry 

testing fraction 

7 Test median over devices and quarters and plants Industry test median

8 Test or operations (total) median over plants and a 

plant/system-specific estimate of the percentage of 

demands that are testing

Total count industry median × fraction that 

are testing

9 Like (8) except that the percentage is at the system/ 

component level across plants

Total count industry median × industry 

fraction that are testing

10 Like (8) except that the percentage is at the 

RVsys/component level across plants and some systems

Total count industry median × aggregated 

industry fraction that are testing

11-14 Like (7)–(10) except that the median is for the RVsys

rather than the more detailed system

Like (7)–(10)

15 Detailed test or operations (total) count but no estimate of 

the count of demands that are testing

Total count × 0.9 (Note a)

16 Like (15) but total count at plant and system-specific level Total count median × 0.9 (Note a)

17 Like (15) but total count at system-specific level Industry total count median × 0.9 (Note a)

18 Like (15) but total count at RV-system-specific level Aggregated industry total count median 

× 0.9 (Note a)

a. The factor of 0.9 is used to estimate testing demands from total demands when no other information is 

provided and is based on the average proportion shown in the data.

4.4.2 Five-Year Test Data 

Starting from 1987, five-year test dates were estimated for each plant based on its refueling outage 

history. The process described below produced test count estimates that were used with the RVLC test 

failure data to estimate the probability of failing to open or failing to reseat: 

 For each plant and for each refueling outage select the middle date. 

 If operating cycles (from the first operational day at the start of a cycle to the starting day of 

the following refueling outage) exceed 18 months (550 days), assume a mid-cycle outage 
26 

occurred. Assume it occurred in the middle of the cycle. Select a date representing when 

testing would likely occur for each mid-cycle outage. 

 Sort the testing dates in chronological order for each plant. 

 Estimate what fraction of the relief valve populations would be tested on each testing day. 

Select 0.25, 0.33, 0.5, or 1 (all the valves) based on the requirement that each valve must be 

tested at least once every 5 years. This means that testing 25% of the valves is sufficient if the 

differences between test dates and test dates lagging four dates behind on the list are all less 

than 5 years. This criterion is applied for each testing date. 

Testing demands are estimated for a particular calendar year or fiscal year based on the presence of 

testing dates in the period. The test count estimate is the number of testing dates times the number of 

valves present times the testing fraction. 

4.4.3 Overall Test Demand Data 

Table 10 gives an overview of the results of the test demand calculations described above. The total 

number of demands for the period from FY 1998 to FY 2006 is summarized by plant type, component 

type, and system. 

Table 10. EPIX relief valve overview of the results of the test demand calculations. 

RV System

EPIX Demands 5-yr Tests

PORV SVV SRV RVLC

PWR Plants

GAS — — — 1653.7

MSS 14687.0 10788.0 — 738.0

RCS 2690.9 1098.0 — 190.8

RHR — — — 1095.7

WAT — — — 10944.0

WATD — — — 1485.5

BWR Plants

GAS — — — 655.7

MSS — 370.9 2775.4 508.6

RHR — — — 817.0

WAT — — — 4374.5

WATD — — — 440.0
27 

5. CALCULATION METHODS 

Various estimates of occurrence rates, counts, and probabilities were computed from the data. For 

PORVs, SVVs, and SRVs, valve performance is observed during reactor scrams (initiating events) and 

from EPIX non-demand and testing data. Testing demands were also considered, but these apply only to 

the simple failure to open and failure to reseat estimates. The scram data were analyzed for different 

types of demands and for such aspects as failure on pressure pulses other than the initial pulse in an event. 

Because the number of testing demands is quite large, and many estimates are being computed, no 

attempt was made to subtract failures to open from demands to reseat. 

The calculations for industry estimates and bounds follow the methodology described in the 

Handbook of Parameter Estimation for Probabilistic Risk Assessment (Atwood, 2003). The baseline 

period methodology is described by NRC (2005) and Eide et al. (2007a). Industry baseline periods were 

developed, and simple distributions were fit to the data in these periods. For estimates with risk 

significance and sufficient data, trend analyses were performed. 

5.1 Parameter Distributions 

PRAs of U.S. commercial NPPs have used a variety of distributions to model the uncertainty in both 

basic events and initiating event frequencies. Lognormal distributions were used in the WASH-1400 

study (NRC, 1975) in the mid 1970s and have been used in many studies since then. The PRA 

Procedures Guide (NRC, 1983) presented information on modeling component unreliability using 

lognormal, beta, and gamma distributions. In contrast, the Probabilistic Safety Analysis Procedures 

Guide (Bari, 1985) recommended loguniform distributions for component failure rates listed in the 

document. Finally, the more recent data analysis studies (Eide 2007a) performed at the Idaho National 

Laboratory have systematically used beta distributions for probability upon demand data and gamma 

distributions for time-related data. For the present document, beta and gamma distributions are used 

exclusively. (However, with the information presented, other distributions can be fitted to the results if 

desired.) This decision was made based on several factors. The first is the flexibility of such distributions 

in being able to represent component failure data (similar to the flexibility of the lognormal distribution). 

In addition, these distributions are natural choices given the assumptions of demand data following the 

binomial distribution (constant probability of failure per demand) and time-related data following the 

Poisson distribution (constant occurrence rate with time). The beta distribution is bounded by (0, 1), 

matching the bounds for probabilities. The gamma distribution is bounded by (0, ∞), matching the 

bounds for rates. Finally, these distributions are conjugate priors, resulting in simple equations for 

Bayesian updates using these distributions as industry average priors. 

Because the component unreliability data in this report include a high percentage of components 

without any failures (often greater than 90%), insufficient data exist to perform detailed studies to clearly 

identify the most appropriate distribution type (or types) to represent the component failure mode 

distributions. Attempts to fit distributions to the component unreliability data provided inconclusive 

results as to which types of distributions were most appropriate. 

Beta and gamma distributions model uncertainties in the SPAR industry average inputs. The beta 

distribution applies to probability upon demand types of inputs (fail to open/close, etc.), while the gamma 

distribution applies to time-based rates (spurious operation, initiating event frequencies, etc.). The beta 

distribution function for probability upon demand, p, is the following: 

1 1

)1(

)()(

)(

pf )( pp

(1) 

for 0 ≤ p ≤ 1 and α and β > 0. This distribution is denoted beta (α, β). 
28 

The mean of this distribution is 

mean p

(2) 

and the variance is 

)1()(

variance 2

p

(3) 

Additional information on the beta distribution is presented in Handbook of Parameter Estimation for 

Probabilistic Risk Assessment (Atwood, 2003). 

The gamma probability distribution function for the failure or initiating event rate, λ (units of 

events/time), is the following: 

)exp(

)(

)(

)(

1

f

(4) 

where 

λ, α, and β > 0. 

The mean of this distribution is 

mean

(5) 

and the variance is 

variance 2

(6) 

Additional information on the gamma distribution is also presented in Atwood (2003). Alternative 

definitions of the gamma distribution (such as those in the Excel software) define β as the inverse of the β

used in this report. The β used in this report has units of hours or reactor critical year (depending upon 

the application). 

Details concerning the estimation of α and β are presented in the appendices. In general, if sufficient 

data were available such that an empirical Bayes (EB) analysis provided results (Atwood, 2003), then α

and β estimates from that analysis were used. (The definition of ―sufficient‖ is not clear cut. However, in 

general if there were only several failure events, the EB analysis failed to produce results.) 

The EB method can be applied at the plant or component level. At the plant level, failure data (fi/di) 

for a given component failure mode (combining data from similar component types at the plant) are 

considered a group. The beta distribution (parameters α and β) is estimated directly from the data, 

modeling variation between groups. Each group is assumed to have its own failure probability (pi) 

obtained from this beta distribution. Failures (fi) are assumed to have a binomial distribution governed by 

pi. The likelihood function for the data is based on the observed number of failures and successes and this 
29 

beta-binomial model. The likelihood function is then maximized based on an iterative search of the 

parameters α and β. For time-based failures, a similar process is used based on a gamma-Poisson model. 

The EB method is similar at the component level except each component‘s data are considered a group. 

EB analysis results at the plant level were used in this report to determine the beta and gamma distribution 

parameters α and β. Plant level results were used rather than component level results to estimate 

uncertainties based on several considerations: 

 Because of the limited number of components with failures, data grouped at the component level 

often result in a high percentage of component groups with no failures. This results in cases in which 

the EB analysis fails to generate results. In contrast, at the plant level, significantly fewer plant level 

groups have no failures. This results in fewer cases in which the EB analysis fails to generate results. 

 Because of the limited number of components with failures, EB results obtained at the component 

level do not always appear to be realistic (very low estimates for α can result, leading to extremely 

low 5th percentile estimates). In contrast, the results obtained at the plant level generally appear to be 

better behaved. 

 In several cases, even with many failure events (typically greater than ten), EB analysis results were 

degenerate, indicating little variation between plants. For these few cases, the assumption of 

homogeneity in the data resulted in the use of α estimates obtained from the Bayesian update of the 

Jeffreys noninformative prior distribution (JNID). 

 In all cases, a simplified version of the constrained noninformative distribution (CNID) was also 

generated (Atwood, 2003). However, those results were used only if the EB analyses did not produce 

results. The CNID for gamma distributions uses α = 0.5 and the industry mean to calculate β

(Equation 5). However, the CNID for beta distributions uses an α that is a function of the industry 

mean and ranges from 0.32 to approximately 0.5. For this report, a simplified CNID was used for 

beta distributions in which α was always set to 0.5. In cases where the simplified CNID was used, the 

industry mean was calculated using a maximum likelihood estimate (failures divided by demands or 

hours). If there were no failures, then a Bayesian update of the JNID was used (Atwood, 2003). In 

these cases, the industry mean is 

1

5.0

D

Pmean

(7) 

for beta distributions and 

T

mean

5.0

(8) 

for gamma distributions 

where 

D = number of industry demands 

T = number of industry hours or reactor critical years. 
30 
31 

6. RISK-BASED ANALYSIS OF THE EXPERIENCE 

Estimates for the high-capacity relief valves follow in Section 6.1. Reliability data for the lowcapacity relief valves are in Section 6.2. Final selected data partitions and uncertainty distributions are 

shown in Subsection 6.3. 

6.1 High-Capacity Relief Valves 

To review, the high-capacity relief valves are the PWR PORVs and SVVs and the dual-action BWR 

SRVs. PORVs and SVVs are found in both the MSS and RCS in PWRs, but the most frequent use is 

noted in the MSS. The PWR MSS PORVs are atmospheric dump valves and release steam to the 

atmosphere, which means water is lost from the inventory. The PWR RCS PORVs release pressure from 

the pressurizer to a tank. The PORVs are electronically actuated, while the SVVs act only from direct 

pressure. The SVVs are designed to protect the piping and to be a backup for pressure release when the 

PORV pressure release is not adequate. In addition, PWR pressure release from the MSS occurs more 

often than release from the RCS. The SVVs have some use in BWR plants, but the use is limited and is 

not discussed here. All the SRVs are in the BWR MSS. 

Four random processes are at work in the operational data for the high-capacity relief valve: 

 First, an event (need for pressure release) occurs. Operational data exists for scram events, and many 

of them lead to demands for one or more of the high-capacity relief valves. 

 In an event, a random number of pressure pulses occur for a particular type of valve in either the MSS 

or the RCS. 

 The number of valves that need to lift given one pulse depends on the system pressure and the 

number of valves set at that pressure. In this study, the range of the setpoint settings is not known and 

is different from plant to plant, so that the fraction of valves needing to lift is assumed to be 

proportional to the strength of the pressure pulse. All the relief valves of a particular type in a 

particular system at a unit are treated equally (equal chance of being demanded to lift). 

 Finally, the demanded valves may behave as designed or may fail. 

The probabilities for failure to open and failure to close/reseat (sticking open) are given in 

Section 6.1.2. These estimates are conditioned on the number of individual valves demanded. For use in 

the SPAR models, estimates are provided based on whether manual demands succeeded after automatic 

demand failures. The pattern of failures with regard to the first pulse in an event compared to subsequent 

pulses is also studied. 

The relief valves also receive periodic testing. These data from EPIX are also cited for failure to open 

and failure to close. Each test is assumed to consist of a single pressure pulse for a valve. 

Special failure modes for PORVs include pressure control during MSS cooldown and RCS pressure 

control during low power operations where a specified minimum pressure/temperature ratio needs to be 

maintained. 

In Section 6.1.3 rates for spurious operation and setpoint-out-of-specification are given. These 

failures are tabulated per valve per reactor critical year for the high capacity relief valves without regard 

for the method of detection. 

6.1.1 High-Capacity Demands 

The total number of valve demands in an event is the sum, over events, of the sum, over pulses in an 

event, of the fraction of valves demanded in a pulse multiplied by the number of valves present to respond 
32 

to the demand. This last number is not random. Instead, it is plant-specific. The high-capacity relief 

valve population counts at the plants are fairly well known. 

In the risk-based analysis, the probability of various relief valve demands given various types of 

scram (initiating) events is given as well as the overall probability given any scram. The data include 

information about the number of pressure pulses per event and the fraction of valves lifting per pulse. 

These are attributes of the operating profiles of the valves and the energy to the relief valves of the 

initiating event. 

The operating profile is also characterized by the nature of the demand. The demand may be 

automatic or manual for PORVs and SRVs; SRVs may also have direct pressure demands. The SVVs 

have only direct pressure demands. Details of the demand patterns are in the second subsection. 

The SPAR models use estimates for the probability of relief valves being demanded during particular 

initiating events. The frequencies of initiating events, as used in the SPAR models, are based on the 

grouping known as ―Functional Impacts‖ by Poloski (1999). Events are counted at the plant, unit, and 

date levels. For PWRs, MSS events are counted separately from RCS events. Table 11—which uses 

functional impacts—has a row for each type of initiating event, with columns describing the involvement 

of PWR PORVs and SVVs for the MSS and RCS and BWR SRVs. 

Table 11 shows that reported BWR SRV demands occur most often during LOOP initiators. Among 

PWRs, MSS PORV demands are reported 26% of the time for loss of condenser heat sink; however, this 

number is likely based on an undercount because the valves could operate in these events and not be 

specifically called out in the LER (but rather included in a statement about all systems operating as 

required). The table shows the lower usage of the MSS SVVs (16%), and shows even lower use of RCS 

PORVs (8%) and SVVs (0.8%). Among the more rare initiators, little can be inferred because there are 

few operational events. 

When RCS PORVs are demanded in losses of condenser heat sink, the number of pressure pulses on 

the valves tends to be fairly high. Table 11 also shows that BWR SRVs tend to experience multiple 

pressure pulses. The exact number of such pulses is often not known. In such cases, an estimated range 

is used in the data analysis. Table 12 shows the ranges for the uncertain events. For the first two sets of 

initiators, the spread tends to be around two. There is less variation with the more rare initiators. 

The initiators in the first three sections of Table 11 and Table 12 correspond to the initiators used in 

the NRC‘s Baseline Risk Index of Initiating Events (BRIIE) (Eide et al., 2007b). The events listed in the 

last section of Table 11 (Fire, HELB, PLOSW, and PLOCCW) are rare and do not occur in the 1998–

2002 data set used to develop the BRIIE. 

In the stuck open relief valve (SORV) initiating event category, note that there are 15 SORV events at 

BWRs and no SRV demands that correlate to these SORV events in the data collection. This study does 

not consider a spurious operation of a relief valve a ―demand‖ so it appears that all of the BWR SORV 

events are due to spurious operation. In contrast, the PWR SORV data shows two SORV events (these 

are actually functional impacts) and eight demands. In these cases, the transient required the opening of 

more than one relief valve and the relief valve did not reseat as expected. 

Table 13 is similar to Table 11, showing only the fraction of scrams with RV demands. Here, the 

scrams were tallied according to the initial plant fault instead of the functional impact groupings, which 

results in a single initiating event count for each event. 
33

Table 11. Relief valve demands on initiating events grouped by functional impact, 1988-2007. 

Scrams RV Events

PWR BWR

MSS RCS MSS

PORV SVV PORV SVV SRV

Initiatora PWR BWR PWR BWR

% 

Scrams 

with 

Demands

Avg. 

Pulses 

per 

Event

% Valves 

Demanded 

per Pulse

% Scrams 

with 

Demandsb

Avg. 

Pulses 

per 

Event

% Valves 

Demanded 

per Pulse

% 

Scrams 

with 

Demands

Avg. 

Pulses 

per 

Event

% Valves 

Demanded 

per Pulse

% 

Scrams 

with 

Demands

Avg. 

Pulses 

per 

Event

% Valves 

Demanded 

per Pulse

% 

Scrams 

with 

Demands

Avg. 

Pulses 

per 

Event

% Valves 

Demanded 

per Pulse

Initiators That Occur More Often

TRAN 1744 860 351 173 9.9 2.09 67. 6.5 1.46 24.1 3.5 4.16 68.8 0.2 1 50 20.0 2.78 34.6

LOMFW 167 81 31 18 9.0 2.73 62.5 7.8 1.46 25.9 1.8 1 85.7 0 — — 22.2 4.11 41.7

LOCHS 128 189 65 73 25.8 2.61 88.7 16.4 1.33 24.9 7.8 8.9 71.4 0.8 1 50 38.6 4.78 32.7

Infrequent Initiators

LOOP 42 21 19 18 19.0 1.75 100 9.5 1 13.5 16.7 5.14 54.5 0 — — 85.7 4.83 38.9

LOIA 17 13 4 2 17.6 3 87.5 0 — — 5.9 2 33.3 0 — — 15.4 4.5 19.6

Rare Initiators

SGTR 4 0 2 0 50.0 1 37.5 0 — — 0 — — 0 — — NA NA NA

VSLOCA 4 2 1 0 0 — — 25.0 1 25. 0 — — 0 — — 0 — —

LOAC 3 7 2 2 33.3 1 100 33.3 1 50. 0 — — 0 — — 28.6 4 29.4

SORV 2 15 8 0 100 1 100 100 1 41.7 100 1 100 100 1 50 0 — —

LODC 1 1 2 0 0 — — 100 7 5 100 1 50 0 — — — — —

Initiators with Data Pooled Across Plant Type (Non-BRIIE)

Fire 30 4 6.7 1 100 3.3 1 33.3 0 — — 0 — — 12.5 7 28.6

HELB 11 3 18.2 1 100 9.1 1 6.3 0 — — 0 — — — — —

PLOSW 2 2 100 1 100 0 — — 0 — — 0 — — — — —

PLOCCW 1 0 0 — — 0 — — 0 — — 0 — — — — —

Overall 1922 1022 — 212 11.1 — — 7.0 — — 4.0 — — 0.2 — — 20.7 — —

a. Initiators: 

TRAN general transient

LOMFW loss of main feedwater

LOCHS loss of condenser heat sink

LOOP loss of offsite power

LOIA loss of instrument air

SGTR steam generator tube rupture

VSLOCA very small loss of coolant accident

LOAC loss of vital AC bus

SORV stuck open relief valve

LODC loss of vital DC bus

HELB high energy line break

PLOSW partial loss of service water

PLOCCW partial loss of component cooling water

The categories refer to functional impacts, so one scram event can contribute to more than one initiator category. No RVLC data are presented because the RVLCs are rarely 

demanded in scram events.

b. Among scrams at plants with MSS SVV, 1931 were at PWR plants and 331 were at BWR plants with SVVs. However, no BWR SVV demands were noted in the operational 

data.
34

Table 12. Minimum, nominal, and maximum numbers of pulses per scram for various initiating events grouped by functional impact. 

Initiator

PWR BWR

MSS RCS MSS

PORV SVV PORV SVV SRV

Minimum Nominal Maximum Minimum Nominal Maximum Minimum Nominal Maximum Minimum Nominal Maximum Minimum Nominal Maximum

Initiators that occur more often

TRAN 1.6 2.1 2.8 1.3 1.5 1.8 3.7 4.2 5.4 1 1 1 2.0 2.8 3.7

LOMFW 1.9 2.7 3.8 1.2 1.5 2.1 1 1 1 — — — 2.7 4.1 5.7

LOCHS 1.9 2.6 3.6 1.2 1.3 1.7 8 8.9 9.8 1 1 1 3.1 4.8 6.6

Infrequent initiators

LOOP 1.5 1.9 2.5 1 1 1.35 3.4 5.1 7 — — — 3.1 4.8 6.8

LOIA 2 3 4.3 — — — 2 2 2 — — — 3 4.5 6

Rare initiator

SGTR 1 1 1 — — — — — — — — — NA NA NA

VSLOCA — — — 1 1 1 — — — — — — — — —

LOAC 1 1 2 1 1 2 — — — — — — 2.5 4 6

SORV 1 1 1 1 1 1 1 1 1 1 1 1 — — —

LODC — — — 4 7 10 1 1 1 — — — — — —

Initiators with data pooled across plant type

Fire 1 1 1 1 1 1 — — — — — — 4 7 10

HELB 1 1 1 1 1 1 — — — — — — — — —

PLOSW 1 1 1 — — — — — — — — — — — —

PLOCCW — — — — — — — — — — — — — — —

a. Initiators: 

TRAN general transient

LOMFW loss of main feedwater

LOCHS loss of condenser heat sink

LOOP loss of offsite power

LOIA loss of instrument air

SGTR steam generator tube rupture

VSLOCA very small loss of coolant accident

LOAC loss of vital AC bus

SORV stuck open relief valve

LODC loss of vital DC bus

HELB high energy line break

PLOSW partial loss of service water

PLOCCW partial loss of component cooling water
35 

Table 13. Relief valve demands on scrams, with scram classification based on the initial plant fault. 

Initial Plant 

Faulta

PWR BWR

MSS RCS MSS

PORV SVV PORV SVV SRV

Fire 8.00E−02 4.00E−02 4.00E−02 0.00E+00 2.00E−01

Flood — — — — 1.00E+00

FWLB 0.00E+00 0.00E+00 5.00E−01 0.00E+00 —

LOAC 1.00E+00 1.00E+00 0.00E+00 0.00E+00 1.43E−01

LOCHS 1.54E−01 1.79E−01 2.56E−02 2.56E−02 2.41E−01

LOIA 1.33E−01 0.00E+00 6.67E−02 0.00E+00 9.09E−02

LOMFW 1.11E−01 6.67E−02 1.11E−02 0.00E+00 7.32E−02

LOOP 2.22E−01 1.11E−01 1.48E−01 0.00E+00 8.00E−01

LOSWS 0.00E+00 0.00E+00 0.00E+00 0.00E+00 —

PLOCCW — — — — 0.00E+00

PLOSWS 6.67E−01 0.00E+00 0.00E+00 0.00E+00 —

SGTR 5.00E−01 0.00E+00 0.00E+00 0.00E+00 —

SLB 1.82E−01 9.09E−02 0.00E+00 0.00E+00 3.33E−01

SORV — — — — 0.00E+00

TRAN 1.00E−01 6.10E−02 3.55E−02 1.18E−03 2.07E−01

VSLOCA 0.00+00 5.00E−01 0.00E+00 0.00E+00 0.00E+00

a. Acronyms:

FWLB feedwater line break

LOAC loss of vital AC bus

LOCHS loss of condenser heat sink

LOIA loss of instrument air

LOMFW loss of main feedwater

LOOP loss of offsite power

LOSWS loss of service water system

PLOCCW partial loss of component cooling water

PLOSWS partial loss of service water

SGTR steam generator tube rupture

SLB steam line break

SORV stuck open relief valve

TRAN general transient

VSLOCA very small loss-of-coolant accident

The data tables in this section and Appendix C contain a field labeled ―Abbreviation.‖ These 

abbreviations provide the user with a coded description of what specific results are displayed in that row 

of the table. The coded descriptions are made up of the component type acronym and any of the suffixes 

necessary to describe the variable. Table 14 shows the list of possible suffixes that are used in this section 

and Appendix C and an explanation of what that suffix means. 

Table 14. Listing of data element extensions. 

Suffix Suffix Description

(none) Count of the variable, for example, SRV components in a particular RV system at a plant 

unit. 

_Ev Failures are counted based on all the information for the component type, system, and date 

combination characterizing an event.

_Scram Failures and demands are counted based on scrams.

_Pulse Relates to a pressure pulse (system demand).

_CperD Relates to the number of components responding to a pressure pulse demand.

_O The results apply to the opening of valve.

_C The results apply to the closing of valve.

_S The results apply to the spurious operation of the valve.

_D, _Dr Setpoint drift--setpoint out of specification.

_LK Leakage past the valve seat.

_LP The results apply to the valves ability to maintain minimum pressure/temperature at low 

power (RCS PORV only).

_CT The results apply to the valves ability to control pressure/temperature in automatic 

cooldown mode through the atmospheric dump valves during cool-down (MSS PORV only).

_1 Relates to initial pulse, or to whether an event has just one pulse. 
Table 14. (continued) 

36 

Suffix Suffix Description

_2 Relates to subsequent demands or pressure pulses rather than the initial demand or 

pressure pulse.

_A Automatic – The results apply to automatic demands of the component.

_M Manual – The results apply to a manual demand of the component.

_N The data are counted for each event; an event is the required demand of the relief valve(s) 

as reported in either an LER or an EPIX report.

_P Pressure demand of a dual acting relief valve (SRV only)

_V Valve (not just the actuation circuitry).

_All The results include all failures (recovered and non-recovered).

_NR The results include only those failures that were not recovered.

_PR The probability that the failure was recovered. 

Table 15 through Table 17 provide further details about the demands from scram events for PORVs, 

SVVs, and SRVs, respectively. The data are representative of a non-specific scram event and include all 

of the initial plant faults from Table 13. 

In PWRs, PORVs are in the MSS and RCS. Table 15 shows the demand profile of the MSS and RCS 

PORV components. The MSS and RCS PORVs are most likely demanded automatically immediately 

following a scram. 

Table 15 through Table 17 provide estimates of probabilities of events and the number of pulses per 

event. The probabilities use the Bayesian update of the JNID for beta distributions (see Section 5.1).

The Poisson distribution is used in modeling the number of pulses given an event. There is always 

one pulse, but the number of additional pulses is treated as a random quantity with a Poisson distribution. 

The expected number of pulses per event is 1 + {expected number of extra pulses}. Each pulse creates an 

opportunity to see these extra pulses, so the expected total number of extra pulses is proportional to the 

number of original pulses. 

Suppose M is the number of total pulses, given n observed events. Let λ be the mean of the Poisson 

distribution for the number of extra pulses given one pressure event. The expected value of M is 

E[M] = n + λ * n. 

Solve this expression for λ. The MLE estimate of λ would be 

λ = [ E[M] - {observed events} ] / n = [ (observed pulses - n) ] / n. 

The update of a Jeffreys noninformative prior gamma distribution would produce 

[ (observed pulses - n) + 0.5 ] / n 

as the estimate for λ. 

To compute the total number of pulses, we add the n initial event pulses back into the expression 

(alternately, you could say that we add 1 initial pulse to λ), and get 

[ {observed pulses} + 0.5 ] / n 

as the expected number of pulses for one event. 

The reason that these situations differ from the other rows in the table is that they are not estimates of 

probabilities. Probabilities must always be less than or equal to 1.0, while the number of pulses given an 

event can easily exceed 1.0. The other rows in the table are labeled directly as probabilities, or are 

"fractions" which again are probabilities. 
37 

Table 15. Demand profile details for PWR power-operated relief valves. 

Failure Mode Abbreviation Numerator Denominator Value

Main Steam System

Number of pulses with auto demand/PORV 

event

PORV_Pulse_A 248 206 1.21E+00

Number of pulses with manual 

demand/PORV event

PORV_Pulse_M 161 206 7.84E−01

Number of pulses/PORV event PORV_Pulse 409 206 1.99E+00

Prob PORV demand is automatic PORV_FrcPulse_A 248 409 6.08E−01

P[PORV auto pulses per event=1] PORV_P_A_N1 145 206 7.03E−01

P[PORV pulses per event=1] PORV_P_V_N1 164 206 7.95E−01

PORV fraction demanded/initial pulse (auto) PORV_FrcDem_1_A 515 900 5.72E−01

PORV fraction demanded/initial pulse 

(manual) 

PORV_FrcDem_1_M 105 900 1.17E−01

PORV fraction demanded/initial pulse PORV_FrcDem_1 620 900 6.89E−01

PORV fraction demanded/any pulse (auto) PORV_FrcDem_A 744 1279 5.82E−01

PORV fraction demanded/any pulse 

(manual)

PORV_FrcDem_M 475 517 9.18E−01

PORV fraction demanded/any pulse PORV_FrcDem 1219 1796 6.79E−01

Reactor Coolant System

Number of pulses with auto demand/PORV 

event 

PORV_Pulse_A 227 70 3.25E+00

Number of pulses with manual

demand/PORV event 

PORV_Pulse_M 55 70 7.93E−01

Number of pulses/PORV event PORV_Pulse 282 70 4.04E+00

Prob PORV demand is automatic PORV_FrcPulse_A 227 282 8.07E−01

P[PORV auto pulses per event=1] PORV_P_A_N1 52 70 7.39E−01

P[PORV pulses per event=1] PORV_P_V_N1 51 70 7.25E−01

PORV fraction demanded/initial pulse (auto) PORV_FrcDem_1_A 104 158 6.57E−01

PORV fraction demanded/initial pulse 

(manual)

PORV_FrcDem_1_M 2 158 1.57E−02

PORV fraction demanded/initial pulse PORV_FrcDem_1 106 158 6.70E−01

PORV fraction demanded/any pulse (auto) PORV_FrcDem_ 285 556 5.13E−01

PORV fraction demanded/any pulse 

(manual)

PORV_FrcDem_M 55 116 4.74E−01

PORV fraction demanded/any pulse PORV_FrcDem 340 672 5.06E−01

The SVVs are in the MSS and RCS. Table 16 shows that the SVV component is frequently 

demanded in the MSS. The phenomena is the result of a pressure pulse, similar to a water-hammer that 

runs back up the main steam piping after a turbine stop or MSIV closure that opens the SVVs 

momentarily and is then gone before the PORVs can respond. The phenomenon occurs in plants with 

certain geometry of piping and does not happen in other plants. Some final safety analysis reports address 

the issue and may report the opening of the SVV as a ―normal‖ expected response. 
38 

Table 16. Demand profile details for PWR code safety valves. 

Failure Mode Abbreviation Numerator Denominator Value

Main Steam System

Number of pulses/SVV event SVV_Pulse 199 135 1.48E+00

P[SVV pulses per event=1] SVV_P_N1 121 135 8.93E−01

SVV fraction demanded/initial pulse SVV_FrcDem_1 569 2295 2.48E−01

SVV fraction demanded/any pulse SVV_FrcDem 769 3353 2.29E−01

Reactor Coolant System

Number of pulses/SVV event SVV_Pulse 4 4 1.13E+00

P[SVV pulses per event=1] SVV_P_N1 4 4 9.00E−01

SVV fraction demanded/initial pulse SVV_FrcDem_1 4 8 5.00E−01

SVV fraction demanded/any pulse SVV_FrcDem 4 8 5.00E−01

SRVs are in the MSS of BWR plants. Table 17 shows the SRV demand data profile. These relief 

valves are usually demanded multiple times and more than one SRV is demanded at a time. SRV manual 

demands are twice as prevalent as automatic demands. Only approximately 1% of the SRV demands are 

found to be from direct pressure. When manual demands are part of an event, the number of pressure 

pulses tends to be larger than when the event is handled through automatic demands alone. A single 

pressure pulse suffices for 62% of the events. 

Table 17. Demand profile details for BWR (main steam system) safety relief valves. 

Failure Mode Abbreviation Numerator Denominator Value

Number of pulses with auto 

demand/SRV event 

SRV_Pulse_A 260 212 1.23E+00

Number of pulses with man. 

demand/SRV event 

SRV_Pulse_M 439 212 2.07E+00

Number of pulses/SRV event SRV_Pulse 699 212 3.30E+00

Prob. SRV demand is automatic SRV_FrcPulse_A 260 699 3.73E−01

P[SRV auto pulses per event=1] SRV_P_A_N1 136 212 6.41E−01

P[SRV pulses per event=1] SRV_P_V_N1 131 212 6.17E−01

Prob. SRV demand from direct pressure SRV_P_P 35 3172 1.12E−02

SRV fraction demanded/initial pulse 

(auto)

SRV_FrcDem_1_A 705 2649 2.66E−01

SRV fraction demanded/initial pulse 

(manual)

SRV_FrcDem_1_M 223 2649 8.43E−02

SRV fraction demanded/initial pulse SRV_FrcDem_1 928 2649 3.50E−01

SRV fraction demanded/any pulse 

(auto)

SRV_FrcDem_A 1394 3035 4.59E−01

SRV fraction demanded given any pulse 

(manual) 

SRV_FrcDem_M 1743 6409 2.72E−01

SRV fraction demanded/any pulse SRV_FrcDem 3137 9444 3.32E−01

6.1.2 High-Capacity Failure Probabilities 

Most of the failure probability estimates for the three types of high-capacity relief valves are 

associated with reactor transients. This is the set of events where the number of relief valve demands and 

failures could be reasonably estimated. Failures from other types of demands are in the EPIX records but 

the associated number of demands is clear only from the transients. 

Recovery was considered as an action the operator could take in an expeditious manner to correct the 

failed state of the relief valve. The most common recovery is the manual operation of either an SRV or 

PORV to close the valve. However, the only ―recovery‖ available for the direct acting relief valves is to 

reduce system pressure until the relief valve reseats. This was not considered an expeditious recovery 
39 

action and was not counted as such. However, in every case of these relief valves not reseating, the 

reduction in pressure eventually led to relief valve closure. 

Relief valve failure estimates are partitioned into the initial demand (init) and any subsequent 

demand(s) (after). These estimates are provided to help the user estimate the probability of relief valve 

failure after many demands. Note that there are very few failures when multiple demands occur and the 

results are based on a Bayesian update of the JNID (see Section 5.1).

Table 18 provides point estimates (or Bayesian update of the JNID for zero failures) of the failure 

data for the PWR PORV component. The MSS PORVs are used to mitigate the effects of high steam line 

pressures that occur when the condenser is lost (i.e., when steam dump to the condenser does not occur or 

MSIVs are closed). The table lists subsets of the collected data including: 

 Opening and closing 

 Recovery and non-recovery 

 Initial and subsequent operation 

 Automatic and manual actuation 

 RCS PORV response to relieving liquid 

Table 18 introduces data collected on the RCS PORV response to relieving liquid instead of steam. 

In this data collection, there were no instances of the RCS PORV failure to open or close during the relief 

of liquid. The data presented here is based on four separate liquid relief events at four PWR plants. The 

RCS PORVs include three manufacturers. When a PWR pressurizer goes solid (generally during a safety 

injection), the PORV relief valves respond to relieve pressure as with steam (since the actuator of the 

PORV is a pressure switch), and the pressure quickly decreases and the PORV closes. The pressure then 

subsequently, increases rapidly demanding the PORV to reopen. The result of these phenomena is that 

the RCS PORV subsequent demand count is a much larger proportion of the overall demands than 

observed during the normal (steam) demands. The estimate for the failure probability of the initial liquid 

demand is only slightly larger than the estimate for the initial steam demand. The estimate for the failure 

probability of the subsequent demand(s) is three times smaller than the estimate for the subsequent steam 

demands. Note that both of the subsequent estimates are based on zero failures recorded and 

approximately three times more demands for the liquid data, which is due to the above discussed 

phenomena.
40 

Table 18. Failure probabilities for PWR power-operated relief valves (behavior after scrams). 

Failure Mode and Demand Grouping Abbreviation Failures Demands Probability

Main Steam System PORVs

Open All failures and 

demands (per 

RV)

All failures (recovered and 

non-recovered).

PORV_O 14 1219 1.19E−02

Non recovery probability PORV_O_NR 10 1219 8.61E−03

Recovery probability PORV_O_PR 4 14 3.00E−01

Initial RV demand PORV_O_1 14 620 2.33E−02

Subsequent demand(s) PORV_O_2 0 599 8.33E−04

Automatic failures and 

demands

PORV_O_A 14 744 1.95E−02

Automatic Initial RV 

demand

PORV_O_1_A 14 515 2.81E−02

Automatic Subsequent 

demand(s)

PORV_O_2_A 0 229 2.17E−03

Close All failures and 

demands

All failures (recovered and 

non-recovered).

PORV_C 10 1219 8.61E−03

Non recovery probability PORV_C_NR 4 1219 3.69E−03

Recovery probability PORV_C_PR 6 10 5.91E−01

Initial RV demand PORV_C_1 10 620 1.69E−02

Subsequent demand(s) PORV_C_2 0 599 8.33E−04

Automatic failures and 

demands

PORV_C_A 3 736 4.75E−03

Automatic Initial RV 

demand

PORV_C_1_A 1 507 2.95E−03

Automatic Subsequent 

demand(s)

PORV_C_2_A 2 229 1.09E−02

Reactor Coolant System PORVs

Open All failures and 

demands (per 

RV)

All failures (recovered and 

non-recovered).

PORV_O 2 340 7.33E−03

Non recovery probability PORV_O_NR 2 340 7.33E−03

Recovery probability PORV_O_PR 0 2 1.67E−01

Initial RV demand PORV_O_1 2 106 2.34E−02

Subsequent demand(s) PORV_O_2 0 234 2.13E−03

Automatic failures and 

demands

PORV_O_A 0 285 1.75E−03

Automatic Initial RV 

demand

PORV_O_1_A 0 104 4.76E−03

Automatic Subsequent 

demand(s)

PORV_O_2_A 0 181 2.75E−03

Close All failures and 

demands (per 

RV)

All failures (recovered and 

non-recovered).

PORV_C 1 340 4.40E−03

Non recovery probability PORV_C_NR 1 340 4.40E−03

Recovery probability PORV_C_PR 0 1 2.50E−01

Initial RV demand PORV_C_1 1 106 1.40E−02

Subsequent demand(s) PORV_C_2 0 234 2.13E−03

Automatic failures and 

demands

PORV_C_A 0 281 1.77E−03

Automatic Initial RV 

demand

PORV_C_1_A 0 100 4.95E−03

Automatic Subsequent 

demand(s)

PORV_C_2_A 0 181 2.75E−03

Liquid Open Initial RV demand PORV_O_L_1 0 7 6.25E-02

Subsequent demand(s) PORV_O_L_2 0 698 7.15E-04

Close Initial RV demand PORV_C_L_1 0 7 6.25E-02

Subsequent demand(s) PORV_C_L_2 0 698 7.15E-04

The MSS PORVs are used in a cooldown rate control mode while shutting down after a scram. In 

addition, the RCS PORVs are used in a minimum pressurization temperature (MPT) function where the 
41 

setpoint is changed to approximately 300 psig while the RCS is cold. Failures during these modes of 

operation are described in Table 19. The shutdown initiating events database was used to look for MPT 

data; no data were found except in the testing of the MPT function. 

Table 19. Additional failure probabilities for PWR power-operated relief valves (behavior after scrams). 

Failure Mode Abbreviation

Data from scram events Data from testing

Failures Demands Probability Failures Demands Probability

Main steam system: control pressure during cool-down (behavior after scrams)

PORV control function 

failed (only) 

PORV_CT 4 104 4.29E−02 2 10653 2.35E−04

PORV control function 

failed (only)

(not recovered) 

PORV_CT_NR 3 104 3.33E−02 2 10653 2.35E−04

P[Recov. PORV control 

function failed (only)] 

PORV_CT_PR 1 4 3.00E−01 0 2 1.67E−01

Reactor coolant system: Maintain minimum pressure/temperature (testing data)

PORV low-pressure 

control function failed

PORV_LP — — — 1 2070 7.24E−04

Table 20 provides data for the PWR SVVs. The SVVs are in the MSS and RCS. MSS SVVs that fail 

to reseat after opening are eventually closed by reducing pressure either by the PORVs or re-establishing 

steam dump to the condenser. This means that all events were eventually recovered. Table 20 provides 

point estimates (or Bayesian update of the JNID for zero failures) of the failure data for the PWR SVV 

component. The table lists subsets of the collected data including 

 Opening and closing 

 Recovery and non-recovery 

 Initial and subsequent operation 
42 

Table 21 provides point estimates (or Bayesian update of the JNID for zero failures) of the failure 

data for the BWR SRV component. The table lists subsets of the collected data including 

 Opening and closing 

 Recovery and non-recovery 

 Initial and subsequent operation 

 Automatic and manual actuation 

 Initiating event demand and any demand (including testing) 

 Pressure demand (for the pressure actuation mode of the SRV). 

Table 20. Failure probabilities for PWR code safety valves (behavior after scrams). 

Failure Mode and Demand Grouping Abbreviation Failures Demands Probability

Main Steam System Code Safety Valves

Open All failures 

and 

demands

All failures (recovered and 

non-recovered).

SVV_O 0 769 6.49E−04

Non recovery probability SVV_O_NR 0 769 6.49E−04

Initial RV demand SVV_O_1 0 769 6.49E−04

Subsequent demand(s) SVV_O_2 0 196 2.54E−03

Close All failures 

and 

demands

All failures (recovered and 

non-recovered).

SVV_C 15 769 2.01E−02

Non recovery probability SVV_C_NR 5 769 7.14E−03

Recovery probability SVV_C_PR 10 15 6.56E−01

Initial RV demand SVV_C_1 15 573 2.70E−02

Subsequent demand(s) SVV_C_2 0 196 2.54E−03

Reactor Coolant System Code Safety Valves

Open All failures 

and 

demands

All failures (recovered and 

non-recovered).

SVV_O 0 4 1.00E−01

Non recovery probability SVV_O_NR 0 4 1.00E−01

Initial RV demand SVV_O_1 0 4 1.00E−01

The data 

are 

counted for 

each plant 

pressure 

demand

All failures (recovered and 

non-recovered).

SVV_O_N 0 4 1.00E−01

Non recovery probability SVV_O_N_NR 0 4 1.00E−01

Close All failures 

and 

demands

All failures (recovered and 

non-recovered).

SVV_C 2 4 5.00E−01

Non recovery probability SVV_C_NR 2 4 5.00E−01

Recovery probability SVV_C_PR 0 2 1.67E−01

Initial RV demand SVV_C_1 2 4 5.00E−01

Table 22 provides data for the three valve types based on testing. The data are from EPIX and were 

collected for the 1998–2007 period. Testing demands were used for simple failure to open and failure to 

close or reseat. The possibility of complicated demands involving multiple pressure pulses or multiple 

components per pressure pulse was not a part of the testing demands. 

The estimates from test data tend to be much lower than the corresponding estimates from the scram 

data. The test for similar results from transients and testing failed for PORV failure to open, PORV 

failure to close on an automatic demand, and SVV failure to close. 
43 

Table 21. Failure probabilities for BWR (main steam system) safety relief valves. 

Failure Mode and Demand Grouping Abbreviation Failures Demands Probability

Open All failures and 

demands

All failures (recovered 

and non-recovered).

SRV_O 5 3137 1.75E−03

Non recovery 

probability

SRV_O_NR 5 3137 1.75E−03

Recovery probability SRV_O_PR 0 5 8.33E−02

Initial RV demand SRV_O_1 4 929 4.84E−03

Subsequent demand(s) SRV_O_2 1 2209 6.79E−04

Pressure demand 

of a SRV

All failures (recovered 

and non-recovered).

SRV_O_P 0 35 1.39E−02

Automatic 

Demand

All failures (recovered 

and non-recovered).

SRV_O_A 2 1394 1.79E−03

Initial RV demand SRV_O_1_A 2 705 3.54E−03

Subsequent demand(s) SRV_O_2_A 0 689 7.25E−04

Close All failures and 

demands

All failures (recovered 

and non-recovered).

SRV_C 1 3137 4.78E−04

Non recovery 

probability

SRV_C_NR 1 3137 4.78E−04

Recovery probability SRV_C_PR 0 1 2.50E−01

Initial RV demand SRV_C_1 1 929 1.61E−03

Subsequent demand(s) SRV_C_2 0 2209 3.26E−04

Pressure demand 

of a SRV

All failures (recovered 

and non-recovered).

SRV_C_P 0 35 1.39E−02

Automatic 

Demand

All failures (recovered 

and non-recovered).

SRV_C_A 0 1394 3.58E−04

Initial RV demand SRV_C_1_A 0 705 7.08E−04

Subsequent demand(s) SRV_C_2_A 0 689 7.25E−04

Liquid Open Initial RV demand SRV_O_1_L 0 56 8.77E-03

Subsequent demand(s) SRV_O_2_L 0 56 8.77E-03

Close Initial RV demand SRV_C_1_L 0 56 8.77E-03

Subsequent demand(s) SRV_C_2_L 0 56 8.77E-03

Table 22. Failure probabilities based on testing (EPIX). 

Failure Mode Abbreviation Failures

Test 

Demands Probability

PWR main steam system 

PORV fail to auto. open PORV_O_A 3 10653 3.29E−04

PORV fail to open PORV_O 34 10653 3.24E−03

PORV fail to auto. close PORV_C_A 0 10653 4.69E−05

PORV fail to close PORV_C 10 10653 9.86E−04

PWR reactor coolant system

PORV fail to auto open PORV_O_A 1 2070 7.24E−04

PORV fail to open PORV_O 4 2070 2.17E−03

PORV fail to auto. close PORV_C_A 0 2070 2.41E−04

PORV fail to close PORV_C 2 2070 1.21E−03

PWR main steam system 

SVV fail to open SVV_O 3 9571 3.66E−04

SVV fail to close/reseat SVV_C 2 9571 2.61E−04

PWR reactor coolant system

SVV fail to open SVV_O 0 1805 2.77E−04

SVV fail to close/reseat SVV_C 0 1805 2.77E−04

BWR main steam system 

SRV fail to auto. open SRV_O_A 0 6343 7.88E−05

SRV fail to open SRV_O 7 6343 1.18E−03

SRV fail to auto. close SRV_C_A 0 6343 7.88E−05

SRV fail to close/reseat SRV_C 4 6343 7.09E−04
44 

6.1.3 High Capacity Failure Rates 

The failure modes modeled as rates are spurious operation and setpoint out-of-calibration. The rates 

are based on per valve reactor critical time. Table 23 shows the failure rates for the three valve types. 

The SVV setpoint out-of-specification was most often noted in the event report as the plant personnel 

reported that the post-trip analysis of data indicated that the SVV lifted either slightly early or slightly 

late. Neither of these was interpreted as a failure to open or a failure to reseat. 

6.2 Low Capacity Relief Valves 

This section provides data for the RVLCs used in many systems throughout a nuclear power plant. 

These valves are generally not used on scrams, so only testing data are available. The number of tests is 

estimated from the number of valves, assuming a 5-year testing interval. The failures to open and failures 

to close/reseat events from EPIX that are cited as occurring on testing demands are used to estimate 

failure probabilities. Data for both plant types were combined. The data are in Table 24. 

Failure rates for RVLC are summarized in Table 25. Rates are estimated for spurious operation and 

setpoint-out-of-specification per valve per calendar year. The method of failure detection is not restricted 

for these estimates. The RVLC also have leakage data. 

The residual heat removal (RHR) RVLC data are studied in detail for use in shutdown risk 

assessments. RV performance in other systems is compared based on the medium (water, dirty [gray] 

water, or gas) for the pressure being released. Some of the valves are in systems with gas (nitrogen, 

control air, etc.), some are in water systems, and some are in systems with raw or dirty water. The 

incidence of spurious operation occurred somewhat more frequently in the gaseous systems (4 in 7000 

reactor years, compared with 6 in approximately 52,000 valve years for clean water systems). The 

p-value for the test of differences was 0.016. 
45 

Table 23. Failure rates, per valve per reactor critical year. 

Failure Mode Abbreviation Failures

Valve 

Standby 

Years Rate

PWR Main Steam System 

PORV spurious operation PORV_S 13 2821 4.79E−03

PORV spurious operation (not recovered) PORV_S_NR 9 2821 3.37E−03

P[Recov. PORV spurious operation] PORV_S_PR 4 13 3.46E−01

PORV setpoint out of specification PORV_D 6 2821 2.30E−03

PWR Reactor Coolant System

PORV spurious operation PORV_S 6 1221 5.32E−03

PORV spurious operation (not recovered) PORV_S_NR 3 1221 2.87E−03

P[Recov. PORV spurious operation] PORV_S_PR 3 6 5.83E−01

PORV setpoint out of specification PORV_D 0 1221 4.10E−04

PWR Main Steam System 

SVV spurious operation SVV_S 2 11148 2.24E−04

SVV spurious operation (not recovered) SVV_S_NR 2 11148 2.24E−04

P[Recov. SVV spurious operation] SVV_S_PR 0 2 2.50E−01

SVV setpoint out of specification SVV_D 89 11148 8.03E−03

PWR Reactor Coolant System

SVV spurious operation SVV_S 0 1806 2.77E−04

SVV spurious operation (not recovered) SVV_S_NR 0 1806 2.77E−04

SVV setpoint out of specification SVV_D 2 1806 1.38E−03

BWR Main Steam System 

SRV spurious operation SRV_S 10 3904 2.69E−03

SRV spurious operation (not recovered) SRV_S_NR 6 3904 1.66E−03

P[Recov. SRV spurious operation] SRV_S_PR 4 10 4.50E−01

SRV setpoint out of specification SRV_D 115 3904 2.96E−02
46 

Table 24. RVLC failure probabilities (5-year testing) for both PWRs and BWRs. 

Failure Mode Abbreviation Failures

Test

Demands Probability

Main Steam System

RVLC fail to open RVLC_O 0 1690 2.96E−04

RVLC fail to open (not recovered) RVLC_O_NR 0 1690 2.96E−04

RVLC fail to close/reseat RVLC_C 0 1690 2.96E−04

RVLC fail to close/reseat (not recovered) RVLC_C_NR 0 1690 2.96E−04

Reactor Coolant System (PWR)

RVLC fail to open RVLC_O 0 224 2.23E−03

RVLC fail to open (not recovered) RVLC_O_NR 0 224 2.23E−03

RVLC fail to close/reseat RVLC_C 0 224 2.23E−03

RVLC fail to close/reseat (not recovered) RVLC_C_NR 0 224 2.23E−03

Residual Heat Removal System

RVLC fail to open RVLC_O 0 2378 2.10E−04

RVLC fail to open (not recovered) RVLC_O_NR 0 2378 2.10E−04

RVLC fail to close/reseat RVLC_C 2 2378 1.05E−03

RVLC fail to close/reseat (not recovered) RVLC_C_NR 2 2378 1.05E−03

P[Recov. RVLC fail to close/reseat] RVLC_C_PR 0 2 1.67E−01

Water Systems (other than RCS and RHR)

RVLC fail to open RVLC_O 6 16292 3.99E−04

RVLC fail to open (not recovered) RVLC_O_NR 6 16292 3.99E−04

P[Recov. RVLC fail to open] RVLC_O_PR 0 6 7.14E−02

RVLC fail to close/reseat RVLC_C 6 16292 3.99E−04

RVLC fail to close/reseat (not recovered) RVLC_C_NR 5 16292 3.38E−04

P[Recov. RVLC fail to close/reseat] RVLC_C_PR 1 6 2.14E−01

Dirty Water Systems

RVLC fail to open RVLC_O 4 6985 6.44E−04

RVLC fail to open (not recovered) RVLC_O_NR 4 6985 6.44E−04

P[Recov. RVLC fail to open] RVLC_O_PR 0 4 1.00E−01

RVLC fail to close/reseat RVLC_C 0 6985 7.16E−05

RVLC fail to close/reseat (not recovered) RVLC_C_NR 0 6985 7.16E−05

Gas Systems (other than MSS)

RVLC fail to open RVLC_O 0 718 6.96E−04

RVLC fail to open (not recovered) RVLC_O_NR 0 718 6.96E−04

RVLC fail to close/reseat RVLC_C 0 718 6.96E−04

RVLC fail to close/reseat (not recovered) RVLC_C_NR 0 718 6.96E−04
47 

Table 25. RVLC failure rates, per valve per calendar year for both PWRs and BWRs. 

Failure Mode Abbreviation Failures

Valve

Standby

Years Rate

Main Steam System

RVLC spurious operation RVLC_S 0 6461 7.74E−05

RVLC spurious operation (not recovered) RVLC_S_NR 0 6461 7.74E−05

RVLC setpoint out of spec. RVLC_D 0 6461 7.74E−05

RVLC leakage RVLC_LK 0 6461 7.74E−05

Reactor Coolant System (PWR)

RVLC spurious operation RVLC_S 0 925 5.41E−04

RVLC spurious operation (not recovered) RVLC_S_NR 0 925 5.41E−04

RVLC setpoint out of spec. RVLC_D 0 925 5.41E−04

RVLC leakage RVLC_LK 0 925 5.41E−04

Residual Heat Removal System

RVLC spurious operation RVLC_S 6 9041 7.19E−04

RVLC spurious operation (not recovered) RVLC_S_NR 5 9041 6.08E−04

P[Recov. RVLC spurious operation] RVLC_S_PR 1 6 2.50E−01

RVLC setpoint out of spec. RVLC_D 4 9041 4.98E−04

RVLC leakage RVLC_LK 3 9041 3.87E−04

Water Systems (other than RCS and RHR)

RVLC spurious operation RVLC_S 5 63651 8.64E−05

RVLC spurious operation (not recovered) RVLC_S_NR 5 63651 8.64E−05

P[Recov. RVLC spurious operation] RVLC_S_PR 0 5 1.00E−01

RVLC setpoint out of spec. RVLC_D 3 63651 5.50E−05

RVLC leakage RVLC_LK 17 63651 2.75E−04

Dirty Water Systems

RVLC spurious operation RVLC_S 0 27025 1.85E−05

RVLC spurious operation (not recovered) RVLC_S_NR 0 27025 1.85E−05

RVLC setpoint out of spec. RVLC_D 0 27025 1.85E−05

RVLC leakage RVLC_LK 2 27025 9.25E−05

Gas Systems (other than MSS)

RVLC spurious operation RVLC_S 2 2935 8.52E−04

RVLC spurious operation (not recovered) RVLC_S_NR 2 2935 8.52E−04

P[Recov. RVLC spurious operation] RVLC_S_PR 0 2 2.50E−01

RVLC setpoint out of spec. RVLC_D 2 2935 8.52E−04

RVLC leakage RVLC_LK 0 2935 1.70E−04
48 

6.3 Uncertainty Distributions 

Appendix B contains tables with results from possible industry distributions for the RV estimates 

generated in this report. For each estimate, a distribution was selected from the list for recommended use 

in uncertainty analyses and regulatory assessments. The recommended distributions can be treated as 

prior distributions for plant-specific updates or special analyses. The selection of these distributions is 

described below. 

The distributions are ―conjugate‖ distributions for the related data. Therefore, beta distributions are 

considered for probabilities and gamma distributions are considered for rates. In each of these cases, 

three possible distributions are considered: 

 An update of the JNID, using overall industry data. The mean of the resulting distribution is 

(n+0.5)/(D+1) for probabilities, where n events are observed in D demands. For rates, the mean is 

(n+0.5)/T, where T is the event exposure time. 

 The constrained noninformative distribution (CNID): This distribution is constrained to have a mean 

equal to the JNID distribution but is a wider distribution reflecting greater uncertainty. Like the JNID 

distribution, the calculation is based on the total number of events and demands or time. 

 As applicable, a distribution reflecting variation across different levels of an attribute of interest, such 

as different plants or years. Here, the method uses data pooled within each level of the attribute under 

study, rather than the overall data. A distribution is sought that maximizes the likelihood of seeing 

the observed data. These distributions are used in the EB method. Several distributions may be 

obtained corresponding to several ways of grouping the data. Sometimes, however, no distribution is 

fitted because the parameter values (e.g., the alpha and beta for either the beta or the gamma 

distribution) that would maximize the likelihood are at zero or infinity. In these cases, the data may 

be fairly homogeneous with little variation with regard to the grouping levels. 

A test for such differences accompanies each EB analysis. Three possibilities for the test exist—

either it shows differences and the EB distribution characterizes the differences, or an EB distribution is 

found in spite of the fact that the statistical test does not show differences, or, conversely, the statistical 

test shows differences but the EB procedure does not converge to a meaningful set of parameters. 

When the statistical test shows little evidence in the data for differences in the rates or probabilities 

between the groupings, the use of the EB distribution is questionable. In this study, the p-value for the 

test of differences had to be 0.2 or lower before an EB distribution was considered for use in risk 

assessments. 

When no EB distribution is found, but the statistical test shows significant differences in the grouped 

data, the most common scenario is that one of the levels of the grouping variable contains higher 

probabilities than the other levels. The table showing all the distributions gives the p-values, so that this 

situation can be identified. 

A final consideration for the use of EB distributions, when they appear at all, deals with the shape of 

the fitted distributions. When the alpha parameter is very small, the beta or gamma distribution is Jshaped and very skewed. The lower bounds tend to be orders of magnitude lower than the mean, yet the 

distributions support relatively large values as well. All of the distributions that were identified appear in 

the distribution tables, but the highly skewed distributions are not recommended for use in risk 

assessments at this time. 

The following rules were used to select the recommended distributions: 

 If less than three events were observed, the CNID distribution was selected. 
49 

 If no EB distributions were found, or none were found that satisfy the criteria of alpha greater than 

0.3 and p-value for test of differences less than 0.2, then the JNID distribution was selected. 

 If more than one eligible EB distribution was identified, then the one with the lowest p-value for the 

test of differences in the data groupings was selected. 

When an EB distribution was selected to represent the industry variation, the Kass-Steffey correction 

was applied to inflate the variance to accommodate for the fact that the parameters were estimated from 

the data. This correction preserves the identified mean but changes the alpha and beta parameters to 

allow the overall variance to include variation in the parameters as well as variation in groupings. 

For the total population of relief valve data, two considerations regarding pooling were evaluated: 

1. Engineering consideration—the engineering consideration that was applied to the relief valve 

component reliability analysis is whether the RV is in a BWR or PWR plant and what type of 

relief valve is considered. No statistical tests were applied to make these pooling decisions; these 

pooling were based on engineering judgment. 

2. Statistical consideration—the pooled groups from item 1 were evaluated for statistical differences 

in systems, plants, years, and data source (pressure demands or testing demands), as applicable. 

These tests either confirmed the hypothesis that the group was homogeneous or did not. Two 

possible outcomes of the statistical pooling tests are possible: 

a. Further divide the group based on the identified difference, e.g., the test identifies that the 

data are not pool-able by system and the data are broken up by system. 

b. Use the variability of the differences to model the uncertainty, e.g., the test identifies that 

the data are different by plant and an EB analysis is performed. 

6.4 Uncertainty Results 

The following tables show the results of the uncertainty analyses using the methods described in the 

preceding paragraphs. Only the final selected distribution and variability types are shown. 

Demand Profiles. Table 26, Table 27, Table 28, and Table 29 show distributions and selected 

baseline years for the high-capacity relief valve demand profiles. The most common selected source of 

variation is between plants. These demand profiles are based on a generic scram event. For demand 

probabilities specific to a particular initiating event, see Table 11 and Table 12. 

Failure Probabilities. Table 30, Table 31, and Table 32 show the distributions and selected baseline 

years for the high-capacity relief valve failure on demand estimates. Most of the estimates are not based 

on any observed variation in the data; rather a constrained non-informative estimate of variation is used. 

Failure Rates. Table 33 shows the estimated failure rate distributions per reactor critical year for 

high-capacity relief valves. Demand and testing data are pooled in most of the cases. 

RVLC Rates and Probabilities. Table 34 and Table 35 show the distributions and selected baseline 

years for the RVLC components. 
50

Table 26. Relief valve demands on scrams, 1988-2007. 

Failure Mode Abbreviation

Baseline

Period

Start Year

RV

Demands

Scram

Count

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

Prob. MSS PORV demand given 

PWR scram

PORV_Scram_MSS 1998 72 493 EB 0.032 0.150 0.324 2.144 Plant 0.0039

Prob. RCS PORV demand given 

PWR scram

PORV_Scram_RCS 2001 19 312 EB 0.001 0.069 0.239 0.605 Plant 0.0008

Prob. MSS SVV demand given 

PWR scram

SVV_Scram_MSS 2001 12 416 NI 0.018 0.030 0.045 12.5 — —

Prob. RCS SVV demand given 

PWR scram

SVV_Scram_RCS 1987 4 1922 NI 0.001 0.002 0.004 4.5 — —

Prob. SRV demand given BWR 

scram

SRV_Scram 1996 85 391 EB 0.068 0.215 0.408 3.098 Plant 0.0040

a. EB = maximum likelihood distribution (prior for empirical Bayes updates); NI = update of Jeffreys noninformative prior.
51

Table 27. Demand profile details from scram data for PWR power-operated relief valves. 

Failure Mode Abbreviation

Baseline

Period

Start Year Numerator Denominator

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

Pvalue for

Diff.

Fraction of MSS PORV events PORV_Ev_MSS 1992 129 181 EB 0.441 0.711 0.921 6.054 Plant 0.0414

Fraction of RCS PORV events PORV_Ev_RCS 1992 52 181 EB 0.079 0.289 0.559 2.466 Plant 0.0422

Prob PORV demand is automatic PORV_FrcPulse_A 1997 215 268 EB 0.474 0.844 0.999 2.889 System 

(MSS, 

RCS)

<1.E−05

P[PORV auto pulses per event=1] PORV_P_A_N1 2000 47 76 EB 0.271 0.618 0.909 3.212 Plant 0.1425

P[PORV pulses per event=1] PORV_P_V_N1 1995 100 134 EB 0.490 0.750 0.942 6.453 Year 0.0100

PORV fraction demanded/initial 

pulse (auto) 

PORV_FrcDem_1_A 2003 116 149 EB 0.051 0.744 1.000 0.595 Plant <1.E−05

PORV fraction demanded/initial 

pulse (manual) 

PORV_FrcDem_1_M 1997 50 370 EB 0.017 0.135 0.328 1.481 Year <1.E−05

PORV fraction demanded/initial 

pulse

PORV_FrcDem_1 1999 243 297 EB 0.519 0.840 0.996 3.886 Plant <1.E−05

PORV fraction demanded/any 

pulse (auto) 

PORV_FrcDem_A 1999 343 466 EB 0.446 0.727 0.937 5.585 System 

(MSS, 

RCS)

<1.E−05

PORV fraction demanded/any 

pulse (manual) 

PORV_FrcDem_M 1987 530 633 EB 0.308 0.704 0.972 2.714 System 

(MSS, 

RCS)

<1.E−05

PORV fraction demanded/any 

pulse

PORV_FrcDem 1999 471 608 EB 0.440 0.732 0.945 5.179 System 

(MSS, 

RCS)

<1.E−05

a. EB = maximum likelihood distribution (prior for empirical Bayes updates).
52

Table 28. Demand profile details from scram data for PWR code safety valves. 

Failure Mode Abbreviation

Baseline

Period

Start

Year Numerator Denominator

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

Pvalue

for

Diff.

Fraction of MSS SVV events SVV_Ev_MSS 1987 135 139 EB 0.789 0.965 1.000 3.165 Plant 0.0688

Fraction of RCS SVV events SVV_Ev_RCS 1987 4 139 NI 0.012 0.032 0.060 4.500 — —

P[SVV pulses per event=1] SVV_P_N1 1990 93 104 NI 0.837 0.890 0.936 93.500 — —

SVV fraction demanded/initial pulse SVV_FrcDem_1 1987 573 2303 EB 0.074 0.230 0.433 3.134 Plant <1.E−05

SVV fraction demanded/any pulse SVV_FrcDem 1991 560 2527 EB 0.060 0.221 0.438 2.571 Plant <1.E−05

a. EB = maximum likelihood distribution (prior for empirical Bayes updates); NI = update of Jeffreys noninformative prior.
53

Table 29. Demand profile details from scram data for BWR (main steam system) safety relief valves. 

Failure Mode Abbreviation

Baseline 

Period 

Start Year Numerator Denominator

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

Pvalue

for

Diff.

Prob. SRV demand is automatic SRV_FrcPulse_A 1988 249 631 EB 0.042 0.464 0.927 0.986 Plant <1.E−05

P[SRV auto pulses per event=1] SRV_P_A_N1 2000 29 55 NI 0.417 0.527 0.635 29.5 — —

P[SRV pulses per event=1] SRV_P_V_N1 2000 33 55 NI 0.489 0.598 0.703 33.5 — —

Prob. SRV demand from direct 

pressure 

SRV_P_P 1999 6 1369 NI 0.002 0.005 0.008 6.5 — —

SRV fraction demanded/initial 

pulse (auto)

SRV_FrcDem_1_A 1999 255 847 EB 0.015 0.308 0.768 0.848 — —

SRV fraction demanded/initial 

pulse (manual)

SRV_FrcDem_1_M 2003 52 424 EB 0.000 0.097 0.422 0.306 Plant <1.E−05

SRV fraction demanded/initial 

pulse

SRV_FrcDem_1 1999 358 847 EB 0.170 0.440 0.729 3.310 Plant <1.E−05

SRV fraction demanded/any pulse 

(auto)

SRV_FrcDem_A 1995 856 1604 EB 0.148 0.491 0.838 2.266 Plant <1.E−05

SRV fraction demanded/any pulse 

(manual) 

SRV_FrcDem_M 1996 842 2666 EB 0.142 0.343 0.577 4.075 Plant <1.E−05

SRV fraction demanded/any pulse SRV_FrcDem 1996 1655 4115 EB 0.183 0.436 0.707 3.815 Plant —

a. EB = maximum likelihood distribution (prior for empirical Bayes updates); NI = update of Jeffreys noninformative prior.
54

Table 30. Failure probabilities for PWR power-operated relief valves. 

Failure Mode Abbreviation Discovery

Baseline 

Period 

Start 

Year Failure Demand

Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.b

Open

All failures and demands

All failures 

(recovered and 

non-recovered).

PORV_O Scram & 

Tests b

1994 44 13530.9 EB 2.39E−06 6.40E−03 2.79E−02 0.347 Plant 8.00E-38

Non recovery 

probability

PORV_O_NR Scram 2002 1 351 CNID 1.58E−05 4.26E−03 1.64E−02 0.494 — —

Recovery 

probability

PORV_O_PR Failures 1990 0 11 CNID 7.70E−05 4.17E−02 1.65E−01 0.433 — —

Initial RV demand PORV_O_1 Scram 2003 1 133 CNID 3.72E−05 1.12E−02 4.33E−02 0.483 — —

Subsequent 

demand(s)

PORV_O_2 Scram 1987 0 833 CNID 2.34E−06 6.00E−04 2.30E−03 0.499 — —

Automatic Demand

All failures 

(recovered and 

non-recovered).

PORV_O_A Scram & 

Tests

2001 2 8547.9 CNID 1.15E−06 2.92E−04 1.12E−03 0.5 — —

Initial RV demand PORV_O_1_A Scram 1990 4 472 NI 3.53E−03 9.51E−03 1.78E−02 4.5 — —

Subsequent 

demand(s)

PORV_O_2_A Scram 1987 0 410 CNID 4.70E−06 1.22E−03 4.68E−03 0.498 — —

Close

All failures and demands

All failures 

(recovered and 

non-recovered).

PORV_C Scram & 

Tests

1990 18 13897.9 EB 2.61E−04 1.46E−03 3.45E−03 2.009 Year 3.75E-05

Non recovery 

probability

PORV_C_NR Scram 1987 5 1559 EB 8.19E−05 3.41E−03 1.12E−02 0.767 Year 0.1321

Recovery 

probability

PORV_C_PR Failures 1988 6 11 NI 3.10E−01 5.42E−01 7.65E−01 6.5 — —

Initial RV demand PORV_C_1 Scram 1990 6 547 NI 5.40E−03 1.19E−02 2.03E−02 6.5 — —

Subsequent 

demand(s)

PORV_C_2 Scram 1987 0 833 CNID 2.34E−06 6.00E−04 2.30E−03 0.499 — —
Table 30. (continued) 

55

Failure Mode Abbreviation Discovery

Baseline 

Period 

Start 

Year Failure Demand

Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.b

Automatic Demand

All failures 

(recovered and 

non-recovered).

PORV_C_A Scram & 

Tests

2000 3 9742.7 EB 7.51E−06 3.06E−04 1.01E−03 0.773 Year 0.1837

Initial RV demand PORV_C_1_A Scram 1999 1 188 CNID 2.77E−05 7.94E−03 3.06E−02 0.488 — —

Subsequent 

demand(s)

PORV_C_2_A Scram 1998 2 149 CNID 5.06E−05 1.67E−02 6.48E−02 0.474 — —

Cooldown Mode

All failures and 

demands

All failures 

(recovered and 

non-recovered).

PORV_CT Scram & 

Tests

2002 2 7156.1 CNID 1.37E−06 3.49E−04 1.34E−03 0.499 — —

Non recovery 

probability

PORV_CT_NR Scram & 

Tests

2002 2 7156.1 CNID 1.37E−06 3.49E−04 1.34E−03 0.499 — —

Recovery 

probability

PORV_CT_PR Failures 1987 1 6 CNID 8.37E−05 2.14E−01 7.88E−01 0.327 — —

Low 

Pressure 

Mode

All failures 

and 

demands

All failures 

(recovered and 

non-recovered).

PORV_LP Testing 1987 1 12,723 CNID 4.56E−07 1.69E−04 6.67E−04 0.467 System 

(MSS, 

RCS)

0.0233

Liquid

Open

Initial RV demand PORV_O_1_L Scram 1987 0 7 CNID 6.52E-05 6.25E-02 2.54E-01 0.393 — —

Close

Subsequent 

demand(s)

PORV_O_2_L Scram 1987 0 698 CNID 2.78E-06 7.15E-04 2.75E-03 0.498 — —

a. CNID = constrained noninformative distribution; EB = maximum likelihood distribution (prior for empirical Bayes updates); NI = update of Jeffreys noninformative prior.

b. The scram and test data differ (p-value =0.0053 for failure to open, <1.E−05 for failure to close on an automatic demand, and =0.0001 for failure to close on any demand). 
56

Table 31. Failure probabilities for PWR code safety valves. 

Failure Mode Abbreviation Discovery

Baseline 

Period Start 

Year Failure Demand

Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.

Open

All failures and demands

All failures 

(recovered and 

non-recovered).

SVV_O Scram & 

Tests

1999 0 9980.6 CNID 1.97E−07 5.01E−05 1.92E−04 0.5 — —

Non recovery 

probability

SVV_O_NR Scram 1987 0 773 CNID 2.52E−06 6.46E−04 2.48E−03 0.499 — —

Initial RV demand SVV_O_1 Scram 1987 0 773 CNID 2.52E−06 6.46E−04 2.48E−03 0.499 — —

Subsequent 

demand(s)

SVV_O_2 Scram 1987 0 196 CNID 9.62E−06 2.54E−03 9.77E−03 0.496 — —

Close

All failures and demands

All failures 

(recovered and 

non-recovered).

SVV_C Scram & 

Tests b

2000 3 8835.9 EB 7.27E−06 3.39E−04 1.13E−03 0.743 Year 0.1725

Non recovery 

probability

SVV_C_NR Scram 1995 1 368 CNID 1.51E−05 4.07E−03 1.57E−02 0.494 — —

Recovery 

probability

SVV_C_PR Failures 1987 10 17 NI 3.92E−01 5.83E−01 7.64E−01 10.5 — —

Initial RV demand SVV_C_1 Scram 2001 3 77 EB 4.85E−05 4.63E−02 1.89E−01 0.396 Plant 0.1038

Subsequent 

demand(s)

SVV_C_2 Scram 1987 0 196 CNID 9.62E−06 2.54E−03 9.77E−03 0.496 — —

a. CNID = constrained noninformative distribution; EB = maximum likelihood distribution (prior for empirical Bayes updates); NI = update of Jeffreys noninformative prior.

b. The scram and test data differ (p-value <1.E−05). 
57

Table 32. Failure probabilities for BWR safety relief valves. 

Failure Mode Abbreviation Discovery

Baseline 

Period 

Start Year Failure Demand

Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.

Open

All failures and demands

All failures 

(recovered and 

non-recovered).

SRV_O Scram & Tests 1989 11 9054.1 EB 1.68E−04 1.27E−03 3.22E−03 1.616 Year 0.148

Non recovery 

probability

SRV_O_NR Scram 2001 1 1122 CNID 5.15E−06 1.34E−03 5.14E−03 0.498 — —

Recovery 

probability

SRV_O_PR Failures 1987 0 5 CNID 4.88E−05 8.33E−02 3.45E−01 0.361 — —

Pressure demand 

of a SRV

SRV_O_P Scram 1987 0 35 CNID 4.41E−05 1.39E−02 5.39E−02 0.479 — —

Initial RV demand SRV_O_1 Scram 1988 3 855 NI 1.27E−03 4.09E−03 8.20E−03 3.5 — —

Subsequent 

demand(s)

SRV_O_2 Scram 2001 1 841 CNID 6.83E−06 1.78E−03 6.85E−03 0.497 — —

Automatic 

Demand

All failures 

(recovered and 

non-recovered).

SRV_O_A Scram & Tests 1991 0 7495.1 CNID 2.62E−07 6.67E−05 2.56E−04 0.5 — —

Initial RV demand SRV_O_1_A Scram 1987 2 705 CNID 1.32E−05 3.54E−03 1.36E−02 0.495 — —

Subsequent 

demand(s)

SRV_O_2_A Scram 1987 0 689 CNID 2.82E−06 7.25E−04 2.78E−03 0.499 — —

Close

All failures and demands

All failures 

(recovered and 

non-recovered).

SRV_C Scram & Tests 2003 2 3536.6 CNID 2.75E−06 7.07E−04 2.72E−03 0.499 — —

Non recovery 

probability

SRV_C_NR Scram 2001 1 1122 CNID 5.15E−06 1.34E−03 5.14E−03 0.498 — —

Recovery 

probability

SRV_C_PR Failures 1987 0 1 CNID 1.40E−04 2.50E−01 8.54E−01 0.338 — —

Pressure demand 

of a SRV

SRV_C_P Scram 1987 0 35 CNID 4.41E−05 1.39E−02 5.39E−02 0.479 — —

Initial RV demand SRV_C_1 Scram 2000 1 311 CNID 1.76E−05 4.81E−03 1.85E−02 0.493 — —
Table 32. (continued) 

58

Failure Mode Abbreviation Discovery

Baseline 

Period 

Start Year Failure Demand

Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.

Subsequent 

demand(s)

SRV_C_2 Scram 1987 0 928 CNID 2.10E−06 5.38E−04 2.07E−03 0.499 — —

Automatic 

Demand

All failures 

(recovered and 

non-recovered).

SRV_C_A Scram & Tests 1987 0 7737.1 CNID 2.54E−07 6.46E−05 2.48E−04 0.5 — —

Initial RV demand SRV_C_1_A Scram 1987 0 705 CNID 2.76E−06 7.08E−04 2.72E−03 0.499 — —

Subsequent 

demand(s)

SRV_C_2_A Scram 1987 0 689 CNID 2.82E−06 7.25E−04 2.78E−03 0.499 — —

Open

Liquid

Initial RV demand SRV_O_1_L Scram 1987 0 56 CNID 3.02E-05 8.77E-03 3.39E-02 0.486 — —

Close

Initial RV demand SRV_C_1_L Scram 1987 0 56 CNID 3.02E-05 8.77E-03 3.39E-02 0.486 — —

a. CNID = constrained noninformative distribution; EB = maximum likelihood distribution (prior for empirical Bayes updates); NI = update of Jeffreys noninformative prior.
59

Table 33. Failure rates, per valve per reactor critical year. 

Failure Mode Abbreviation Discovery

Baseline

Period

Start

Year Failure

Valve

Standby

Years

Gamma Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

PWR power-operated relief valves

PORV spurious operation PORV_S Any 

method

2003 8 1928.8 NI 2.25E−03 4.41E−03 7.15E−03 8.5 — —

PORV spurious operation (not 

recovered) 

PORV_S_NR Any 

method

1998 12 3788.1 EB 7.92E−04 3.16E−03 6.81E−03 2.739 Year 0.0666

P[Recov. PORV spurious 

operation] 

PORV_S_PR Failures 2001 5 15 NI 1.66E−01 3.44E−01 5.45E−01 5.5 — —

PORV setpoint out of specification PORV_D Any 

method

1999 2 3445.2 CNID 2.85E−06 7.26E−04 2.79E−03 0.5 — —

PWR code safety valves

SVV spurious operation SVV_S Any 

method

2003 2 6483.4 CNID 1.52E−06 3.86E−04 1.48E−03 0.5 — —

SVV spurious operation (not 

recovered)

SVV_S_NR Any 

method

2003 2 6483.4 CNID 1.52E−06 3.86E−04 1.48E−03 0.5 — —

P[Recov. SVV spurious operation] SVV_S_PR Failures 1987 0 2 CNID 4.78E−05 1.67E−01 6.63E−01 0.321 — —

SVV setpoint out of specification SVV_D Any 

method

2001 23 9061.8 EB 4.59E−04 2.54E−03 6.00E−03 2.027 Year 0.0199

BWR safety relief valves

SRV spurious operation SRV_S Any 

method

1998 10 3673.5 EB 3.64E−04 2.71E−03 6.85E−03 1.637 Year 0.1562

SRV spurious operation (not 

recovered)

SRV_S_NR Any 

method

2003 2 1888.4 CNID 5.21E−06 1.32E−03 5.09E−03 0.5 — —

P[Recov. SRV spurious operation] SRV_S_PR Failures b1987 4 10 NI 1.85E−01 4.09E−01 6.53E−01 4.5 — —

SRV setpoint out of specification SRV_D Any 

method

1999 115 3365.6 EB 2.31E−03 3.45E−02 9.94E−02 1.119 Year <1.E−05

a. CNID = constrained noninformative distribution; EB = maximum likelihood distribution (prior for empirical Bayes updates); NI = update of Jeffreys noninformative prior.

b. Probabilities of recovery, based on the failure data, are all beta distributions rather than gamma distributions.
60

Table 34. RVLC failure probabilities (5-year testing) (both plant types). 

Failure Mode Abbreviation Discovery

Baseline

Period

Start

Year Failure Demand

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value for

Diff.

RVLC fail to open RVLC_O Testing 2000 5 21460.5 EB 2.46E−05 2.35E−04 6.26E−04 1.403 Year 0.1903

RVLC fail to open (not recovered) RVLC_O_NR Testing 2000 5 21460.5 EB 2.46E−05 2.35E−04 6.26E−04 1.403 Year 0.1903

P[Recov. RVLC fail to open] RVLC_O_PR Failures 1987 0 10 CNID 7.63E−05 4.55E−02 1.81E−01 0.426 — —

RVLC fail to close/reseat RVLC_C Testing 2002 1 15791.2 CNID 3.73E−07 9.50E−05 3.65E−04 0.5 — —

RVLC fail to close/reseat (not 

recovered) 

RVLC_C_NR Testing 2002 1 15791.2 CNID 3.73E−07 9.50E−05 3.65E−04 0.5 — —

P[Recov. RVLC fail to 

close/reseat] 

RVLC_C_PR Failures 1987 1 8 CNID 4.78E−05 1.67E−01 6.63E−01 0.321 — —

RVLC fail to open (RHR) RVLC_O_RHR Testing 1987 0 2378.1 CNID 8.24E−07 2.10E−04 8.07E−04 0.5 — —

RVLC fail to close/reseat (RHR) RVLC_C_RHR Testing 1987 2 2378.1 CNID 4.07E−06 1.05E−03 4.04E−03 0.498 — —

a. CNID = constrained noninformative distribution; EB = maximum likelihood distribution (prior for empirical Bayes updates); NI = update of Jeffreys noninformative prior.
61

Table 35. RVLC failure rates, per valve per calendar year. 

Failure Mode Abbreviation Discovery

Baseline

Period

Start

Year Failure

Valve

Standby

Years

Gamma Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value for

Diff.

RVLC spurious operation RVLC_S Any 

method

2002 4 61,416 NI 2.71E−05 7.33E−05 1.38E−04 4.5 — —

RVLC spurious operation (not 

recovered) 

RVLC_S_NR Any 

method

2002 4 61,416 NI 2.71E−05 7.33E−05 1.38E−04 4.5 — —

P[Recov. RVLC spurious 

operation] 

RVLC_S_PR Failuresb1987 1 13 CNID 3.95E−05 1.07E−01 4.47E−01 0.337 — —

RVLC setpoint out of spec. RVLC_D Any 

method

2002 3 61,416 NI 1.76E−05 5.70E−05 1.15E−04 3.5 — —

RVLC leakage RVLC_LK Any 

method

1988 22 110,037 EB 1.18E−07 2.20E−04 9.44E−04 0.364 Plant 0.0016

RVLC spurious operation (RHR) RVLC_S_RHR Any 

method

2001 2 5,887 CNID 1.67E−06 4.25E−04 1.63E−03 0.5 — —

RVLC setpoint out of 

specification (RHR)

RVLC_D_RHR Any 

method

1987 4 9,040.7 NI 1.84E−04 4.98E−04 9.36E−04 4.5 — —

a. CNID = constrained noninformative distribution; EB = maximum likelihood distribution (prior for empirical Bayes updates); NI = update of Jeffreys noninformative prior.

b. Probabilities of recovery, based on the failure data, are all beta distributions rather than gamma distributions.
62
63

7. ENGINEERING ANALYSIS OF THE EXPERIENCE 

7.1 Industry Trends 

The RV estimates were reviewed for trends across the study period from 1987 to 2007. To be part of 

the trend analysis, a failure mode had to be flagged for summary analysis, have at least four events, and 

be based on either Poisson or binomial counts. No BWR data for SVVs were included because there 

were no reported failures or reported uses in scrams. Generalized loglinear regression was used to find 

linear models for simple functions of the mean of the probability or rate in each year. The models 

identified slope and intercept parameters maximizing the likelihood of the observed data, which was 

assumed to be Poisson- or binomially-distributed. The methods are described in Sections 7.2.2.2 and 

7.4.2.2, respectively, of NUREG/CR-6823, Handbook of Parameter Estimation for Probabilistic Risk 

Assessment (Atwood, 2003). 

Table 36 provides an overview of the trend analysis. It shows where statistically significant trends 

were found in the RV data. These are cases where the p-value for a statistical test of whether the slope 

could be zero was less than or equal to 0.05. The only instance of increasing trends in failures pertains to 

setpoint problems in BWR SRVs, where a higher incidence of events was observed in FY 2007. 

There is no column for RVLCs in Table 36 because the overall RVLC data did not show any failure 

trends. The profile of RVLC use was not studied in detail because of a lack of data. The demands during 

scrams are very infrequent (two instances in the data). Also, the number of pressure pulses per event was 

greater than one in only one instance. The fact that multiple valves provide pressure relief in most cases 

means that single failures are not reportable by LER. Data from various failure modes come from RVLC 

testing, and no trends were found in those data. 

Table 36. Overview of statistically significant RV trend findings. 

Estimate

PWR PORV

(p-value) a

PWR MSS SVV

(p-value)

BWR SRV

(p-value)

Operating Profile Analysis (use of valves)

Demand given scram MSS PORV demands increasing (0.0037)

and RCS PORV demands increasing 

(0.0018)

— —

Automatic rather than manual 

demands in scrams

MSS PORV automatic demands increasing 

(more often automatic) (0.0007) and RCS 

PORV demands more often automatic 

(<5.E−05)

— —

Risk-based Analysis

Failure to automatically open in a 

scram (successful manual 

opening)

MSS PORV, decreasing 

(0.0042)

— —

Failure to close/reseat (per 

scram event)

— Somewhat 

decreasing (0.047)

—

Setpoint out of specification Decreasing (<1.E−05)

(underfit)

Decreasing 

(<1.E−05) (underfit)

Increasing 

(0.008)

(underfit)

a. The p-value is stated in parentheses. Statistically significant findings have a p-value for the slope less than or 

equal to 0.05. However, one in twenty regressions is expected to show such a low p-value even when no trend is 

present.
64 

Table 37 provides a more detailed view of the trend results. A section appears for each of the four 

RV component types. One line summarizes each data set analyzed. The overall totals are given, along 

with whether a statistically significant trend was observed. An evaluation of the fit of the trend models is 

also presented. Small p-values for both of these tests are flagged in the table. In the case of ―overfit,‖ the 

data are generally sparse and mostly zeros. The underfit cases could be analyzed treating the likelihood 

function as negative binomial instead of Poisson. In the comments column, Table 37 contains general 

remarks about the findings. The table is followed by plots of the trend data; the first column indicates the 

figure number for each analysis. 
65

Table 37. Overview summary of RV trend analyses. 

Figure No. Estimate Events

Demands

or Years

Trend

(slope p-value)

Goodness

of Fit Comments

Figure 10 Probability of MSS 

PORV demand given 

PWR scram

206 1854.00 Increasing 

(0.0037)

OK More MSS PORVs tend to get demanded in a 

scram than RCS PORVs. For both, the number of 

reported demands remains fairly constant but the 

incidence of scrams at PWR plants has 

decreased.

Figure 11 Probability of RCS 

PORV demand given 

PWR scram

70 1765.00 Increasing 

(0.0018)

OK See comment for Figure 10.

Figure 12 Probability MSS PORV 

demand is automatic 

248 409.00 Increasing

(0.0007)

Underfit

(p-val 0.0000)

The fraction of MSS PORV demands that are 

automatic rather than manual has varied over the 

years. Before 1992, however, it was consistently 

less than 0.6. In most of the recent years, it has 

been near 1. 

Figure 13 Probability RCS PORV 

demand is automatic 

227 282.00 Increasing

(0.0000)

Underfit

(p-val 0.0000)

Since 1995, nearly all RCS PORV demands from 

scrams have been automatic.

Figure 14 MSS PORV fail to open 

(event)

13 206.00 Not statistically

significant

OK —

Figure 15 MSS PORV fail to open 

automatic (scrams)

14 744.00 Decreasing

(0.0042)

Underfit

(p-val 0.0131)

No failures to automatically open have been 

reported on scrams since FY 1999.

Figure 16 MSS PORV fail to open 

(scrams)

14 1219.00 Not statistically

significant

Underfit

(p-val 0.0351)

The uncertainty in 2002 was high because there 

were only 3 demands (other years had more than 

20 and the average in other years exceeds 60).

Figure 17 MSS PORV fail to open 

(testing)

34 10653.17 Not statistically

significant

OK Testing estimates are lower than estimates 

developed from failures on scrams.

Figure 18 MSS PORV fail to 

close/reseat (event)

11 206.00 Not statistically

significant

OK —

Figure 19 MSS PORV fail to close 

(scrams)

10 1219.00 Not statistically

significant

OK See comment for Figure 16.

Figure 20 MSS PORV fail to close 

(testing)

10 10653.17 Not statistically

significant

OK Lower estimates than for Figure 19. Data from 

EPIX.

Figure 21 MSS PORV spurious 

operation

13 2821.01 Not statistically

significant

Underfit

(p-val 0.0294)

Per MSS valve per reactor critical year. Data from 

EPIX.

Figure 22 RCS PORV spurious 

operation

6 1220.91 Not statistically

significant

OK Per RCS valve per reactor critical year. Data from 

EPIX.

Figure 23 MSS PORV setpoint out 

of specification

6 2821.01 Decreasing

(0.0180)

OK Per MSS valve per reactor critical year. Data from 

EPIX.
Table 37. (continued). 

66

Figure No. Estimate Events

Demands

or Years

Trend

(slope p-value)

Goodness

of Fit Comments

Figure 24 Probability of MSS SVV 

demand given PWR 

scram 

135 2252.00 Not statistically

significant

Underfit

(p-val 0.0028)

Both scrams and SVV actuations on scrams are 

lower since 1997.

Figure 25 Probability of RCS SVV 

demand given PWR 

scram 

4 1922.00 Not statistically

significant

OK The scram data show fewer demands for RCS 

SVVs than MSS SVVs.

Figure 26 MSS SVV fail to 

close/reseat (event) 

13 135.00 Decreasing

(0.0467)

Underfit

(p-val 0.0030)

Per scram event using MSS SVVs. The number of 

events is decreasing.

Figure 27 MSS SVV fail to 

close/reseat (scrams)

15 769.00 Not statistically

significant

Underfit

(p-val 0.0424)

Per demanded valve. Since FY 2000, all SVV 

scram events have been single-pulse events.

Figure 28 MSS SVV setpoint out 

of specification

89 11148.24 Decreasing

(0.0000)

Underfit

(p-val 0.0002)

Per valve per reactor critical year. Data from

EPIX.

Figure 29 Probability of SRV 

demand given BWR 

scram

212 1022 Not statistically 

significant

OK 10–40% of BWR scram LERs cite SRV demands.

Figure 30 Probability SRV 

demand is automatic 

260 699 Not statistically 

significant

Underfit

(pval 0.0000)

The probability that an SRV demand from a scram 

is automatic (rather than manual) varies 

tremendously.

Figure 31 Probability SRV 

demand from direct 

pressure 

35 3172 Not statistically 

significant

Underfit

(p-val 0.0000)

Just five turbine trip events were reported with 

these demands. 16 demands occurred in one 

1997 event (LER 4581997005).

Figure 32 SRV fail to open (event) 6 212 Not statistically 

significant

Overfit

(p-val 0.98)

Per event. Includes failure just to automatically 

open.

Figure 33 SRV fail to open 

(scrams)

5 3137 Not statistically 

significant

OK Per demand.

Figure 34 SRV fail to open 

(testing)

7 6343.09 Not statistically 

significant

OK Per demand. Testing estimates are lower than 

estimates developed from failures on scrams.

Figure 35 SRV spurious operation 10 3904.24 Not statistically 

significant

OK Per reactor critical year.

Figure 36 SRV setpoint out of 

specification

115 3904.24 Increasing 

(0.0078)

Underfit

(p-val 0.0000)

29 failures among 8 events in FY 2007. Most drift 

events were discovered in testing.

Figure 37 RVLC fail to open 10 28286.08 Not statistically 

significant

OK Based on testing. A decreasing trend is almost 

statistically significant (p-value 0.051). Data from 

EPIX.

Figure 38 RVLC fail to 8 28286.08 Not statistically OK Per valve test. Data from EPIX.
Table 37. (continued). 

67

Figure No. Estimate Events

Demands

or Years

Trend

(slope p-value)

Goodness

of Fit Comments

close/reseat significant

Figure 39 RVLC spurious 

operation

13 110037.0 Not statistically 

significant

OK Per valve year. Data from EPIX.

Figure 40 RVLC setpoint out of 

specification

9 110037.0 Not statistically 

significant

OK Per valve year. Data from EPIX.

Figure 41 RVLC leakage 22 110037.0 Not statistically 

significant

Underfit

(p-val 0.0079)

Per valve year. Data from EPIX.
68 

Figure 10. Probability of MSS PORV demand given PWR scram. 

Figure 11. Probability of RCS PORV demand given PWR scram. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.08

0.16

0.24

0.32

0.40

0.48 Fraction of PWR scrams with MSS PORV demands

Prob. of MSS PORV demand given PWR scram

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.0037 PORV_Scram_MSS-02-May-2008

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.05

0.10

0.15

0.20

0.25 Fraction of PWR scrams with RCS PORV demands

Prob. of RCS PORV demand given PWR scram

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.0018 PORV_Scram_RCS-02-May-2008
69 

Figure 12. Probability MSS PORV demand is automatic. 

Figure 13. Probability RCS PORV demand is automatic. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Fraction of MSS PORV demands that are automatic

Prob. MSS PORV demand is automatic

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.00075 PORV_FrcPulse_A_MSS-02-May-2008

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.0

0.2

0.4

0.6

0.8

1.0

1.2 MSS PORV failures per automatic demand

Prob. RCS PORV demand is automatic

Fitted model

90% confidence band on probability

Binomial logit model p-value <= 0.00005 PORV_FrcPulse_A_RCS-02-May-2008
70 

Figure 14. MSS PORV fail to open (event). 

Figure 15. MSS PORV fail to open automatic (scrams). 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.15

0.30

0.45

0.60

0.75

0.90 Failures per MSS PORV event

Prob. PWR RV event includes MSS PORV failure to open

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.25 PORV_O_N_MSS-02-May-2008

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.08

0.16

0.24

0.32 Failures per automatic MSS PORV demand

MSS PORV fail to auto. open (during PWR scram)

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.0042 PORV_O_A_MSS_Unpl-02-May-2008
71 

Figure 16. MSS PORV fail to open (scrams). 

Figure 17. MSS PORV fail to open (testing). 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.15

0.30

0.45

0.60

0.75 Failures per MSS PORV demand

MSS PORV fail to open (during PWR scram)

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.45 PORV_O_MSS_Unpl-02-May-2008

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.000

0.003

0.006

0.009

0.012

0.015

0.018 Failures per MSS PORV demand

MSS PORV fail to open (testing)

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.092 PORV_O_MSS_Test-02-May-2008

(No EPIX data prior to 1997)
72 

Figure 18. MSS PORV fail to close/reseat (event). 

Figure 19. MSS PORV fail to close (scrams). 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.15

0.30

0.45

0.60

0.75

0.90 Failures per MSS PORV event

Prob. PWR RV event includes MSS PORV failure to close

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.53 PORV_C_N_MSS-02-May-2008

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.15

0.30

0.45

0.60

0.75 Failures per MSS PORV demand

MSS PORV fail to close (during PWR scram)

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.14 PORV_C_MSS_Unpl-02-May-2008
73 

Figure 20. MSS PORV fail to close (testing). 

Figure 21. MSS PORV spurious operation. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.0000

0.0015

0.0030

0.0045

0.0060

0.0075

0.0090 Failures per MSS PORV demand

MSS PORV fail to close (testing)

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.099 PORV_C_MSS_Test-02-May-2008

(No EPIX data prior to 1997)

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.000

0.008

0.016

0.024

0.032

0.040

0.048 Failures per MSS PORV per reactor critical year

MSS PORV spurious operation

Fitted model

90% confidence band on frequency

Poisson log model p-value = 0.24 PORV_S_MSS-02-May-2008

(No EPIX data prior to 1997)
74 

Figure 22. RCS PORV spurious operation. 

Figure 23. MSS PORV setpoint out of specification. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.000

0.015

0.030

0.045

0.060

0.075 Failures per RCS PORV per reactor critical year

RCS PORV spurious operation

Fitted model

90% confidence band on frequency

Poisson log model p-value = 0.11 PORV_S_RCS-02-May-2008

(No EPIX data prior to 1997)

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.01

0.02

0.03

0.04

0.05 Failures per MSS PORV per reactor critical year

MSS PORV setpoint out of specification

Fitted model

90% confidence band on frequency

Poisson log model p-value = 0.018 PORV_D_MSS-02-May-2008

(No EPIX data prior to 1997)
75 

Figure 24. Probability of MSS SVV demand given PWR scram. 

Figure 25. Probability of RCS SVV demand given PWR scram. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.05

0.10

0.15

0.20

0.25 Fraction of PWR scrams with MSS SVV demands

Prob. of MSS SVV demand given PWR scram

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.69 SVV_Scram_MSS-02-May-2008

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.000

0.015

0.030

0.045

0.060

0.075

0.090 Fraction of PWR scrams with RCS SVV demands

Prob. of RCS SVV demand given PWR scram

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.52 SVV_Scram_RCS-02-May-2008
76 

Figure 26. MSS SVV fail to close/reseat (per event). 

Figure 27. MSS SVV fail to close/reseat (per valve demanded in a scram). 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Failures per MSS SVV event

Prob. PWR RV event includes MSS SVV failure to close

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.047 SVV_C_N_MSS-02-May-2008

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.0

0.2

0.4

0.6

0.8

1.0 Failures per MSS SVV demand

MSS SVV fail to close (during PWR scram)

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.073 SVV_C_MSS_Unpl-02-May-2008
77 

Figure 28. MSS SVV setpoint out of specification. 

Figure 29. Probability of SRV demand given BWR scram.

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.000

0.008

0.016

0.024

0.032

0.040 Failures per SVV per reactor critical year

MSS SVV setpoint out of specification

Fitted model

90% confidence band on frequency

Poisson log model p-value <= 0.00005 SVV_D_MSS-02-May-2008

(No EPIX data prior to 1997)

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.0

0.1

0.2

0.3

0.4

0.5

0.6 Fraction of PWR scrams with SRV demands

Prob. of SRV demand given BWR scram

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.30 SRV_Scram-02-May-2008
78 

Figure 30. Probability SRV demand is automatic. 

Figure 31. Probability SRV demand from direct pressure. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Fraction of SRV demands that are automatic

Prob. SRV demand is automatic

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.070 SRV_FrcPulse_A-02-May-2008

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.04

0.08

0.12

0.16

0.20 Fraction SRV demands from pressure

Prob. SRV demand from direct pressure

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.19 SRV_P_P-02-May-2008
79 

Figure 32. Probability SRV failure to open given one or more demands in a BWR scram (per event). 

Figure 33. Probability of SRV failure to open, per demand (data from BWR scrams). 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.15

0.30

0.45

0.60

0.75 Prob. BWR RV event includes SRV failure to open

Prob. BWR RV event includes SRV failure to open

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.26 SRV_O_N-02-May-2008

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.000

0.015

0.030

0.045

0.060

0.075

0.090 Failures per SRV demand

SRV fail to open (during BWR scram)

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.36 SRV_O_Unpl-02-May-2008
80 

Figure 34. SRV fail to open (data from testing). 

Figure 35. SRV spurious operation. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.000

0.003

0.006

0.009

0.012

0.015

0.018 Failures per SRV demand

SRV fail to open (testing)

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.15 SRV_O_Test-02-May-2008

(No EPIX data prior to 1997)

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.000

0.005

0.010

0.015

0.020

0.025

0.030 Failures per SRV per reactor critical year

SRV spurious operation

Fitted model

90% confidence band on frequency

Poisson log model p-value = 0.75 SRV_S-02-May-2008

(No EPIX data prior to 1997)
81 

Figure 36. SRV setpoint out of specification. 

Figure 37. RVLC fail to open. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00

0.03

0.06

0.09

0.12 Failures per SRV per reactor critical year

SRV setpoint out of specification

Fitted model

90% confidence band on frequency

Poisson log model p-value = 0.0078 SRV_D-02-May-2008

(No EPIX data prior to 1997)

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.0000

0.0008

0.0016

0.0024

0.0032

0.0040 Failures per RVLC demand

RVLC fail to open

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.051 RVLC_O-02-May-2008

(No EPIX data prior to 1997)
82 

Figure 38. RVLC fail to close/reseat. 

Figure 39. RVLC spurious operation. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

-0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035 Failures per RVLC demand

RVLC fail to close/reseat

Fitted model

90% confidence band on probability

Binomial logit model p-value = 0.13 RVLC_C-02-May-2008

(No EPIX data prior to 1997)

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00000

0.00015

0.00030

0.00045

0.00060

0.00075

0.00090 Failures per RVLC per reactor year

RVLC spurious operation

Fitted model

90% confidence band on frequency

Poisson log model p-value = 0.13 RVLC_S-02-May-2008

(No EPIX data prior to 1997)
83 

Figure 40. RVLC setpoint out of specification. 

Figure 41. RVLC leakage. 

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.00000

0.00015

0.00030

0.00045

0.00060

0.00075

0.00090 Failures per RVLC per reactor year

RVLC setpoint out of specification

Fitted model

90% confidence band on frequency

Poisson log model p-value = 0.12 RVLC_D-02-May-2008

(No EPIX data prior to 1997)

19871988198919901991199219931994199519961997199819992000200120022003200420052006

Fiscal Year

0.0000

0.0003

0.0006

0.0009

0.0012

0.0015 Failures per RVLC per reactor year

RVLC leakage

Fitted model

90% confidence band on frequency

Poisson log model p-value = 0.14 RVLC_LK-02-May-2008

(No EPIX data prior to 1997)
84 

7.2 Factors Affecting Relief Valve Reliability 

7.2.1 Method of Detection 

The distribution charts for the methods of failure detection are shown in Figure 42 to Figure 45. 

These figures group the relief valves by system and relief valve type. 

Figure 42 shows the PWR MSS relief valves detection distribution. The PORVs experience most of 

their failures during automatic or manual switch demands, whereas most of the SVV failures are detected 

during testing. The SVVs do not experience any demands through electronic actuation; the PORVs do 

not see any demands directly from pressure, which explains the single bars in those two categories. The 

non-demand detection is the method by which either spurious operation or leakage is observed. 

Figure 42. PWR MSS relief valve failure detection methods. 

Figure 43 shows the PWR RCS relief valves detection distribution. The RCS PORVs experience 

most of their failures during non-demand situations, whereas the RCS SVVs see most failures detected 

during an observed pressure transient (it should be noted that the total number of SVV failures is 9). The 

RCS SVVs do not experience any demands through electronic actuation and the RCS PORVs do not see 

any demands directly from pressure, which explains the single bars in those two categories. The nondemand detection is the method by which either the spurious operation or leakage is observed. 

0%

10%

20%

30%

40%

50%

60%

70%

80%

Electronic Non-Demand Pressure Test

PORV

SVV

Percent of Failures

System
85 

Figure 43. PWR RCS relief valve detection methods. 

Figure 44 shows the BWR SRV dual acting relief valve detection distribution. SRVs experience most 

failure detection during testing. The most likely failure mode here is setpoint out-of-specification. These 

valves are especially subject to the corrosion bonding issue and repeatedly are flagged as failing the 

pressure setpoint testing. 

Figure 45 shows the RVLC failure events in the RHR and generic water systems for both PWRs and 

BWRs. RVLCs experience most failure detections during testing. It is rare for the RHR RVLCs to 

experience a failure while under a pressure demand (a single event observed). The non-demand detection 

is the method by which either the spurious operation or leakage is observed. 

Electronic Non-Demand Pressure Test

60%

50%

40%

30%

20%

10%

PORV

SVV

System

0%

Percent of Failures
86 

Figure 44. BWR SRV failure detection methods. 

Figure 45. RVLC detection methods. 

0%

10%

20%

30%

40%

50%

60%

Non-Demand Pressure Test

Electronic Non-Demand Pressure Test

0%

10%

20%

30%

40%

50%

60%

70%

80%

SRV

System

Percent of Failures

System

RHR

WAT

Percent of Failures
87 

7.2.2 Relief Valve Failure Causes 

Failure cause codes are denoted here by two-letter abbreviations. These abbreviations are listed in 

Table 38. Figure 46 to Figure 49 show the distributions of the failure causes for the groups of relief 

valves in this study. Figure 46 shows the PWR MSS relief valve cause distribution. The largest 

contributor to the MSS PORV failures is the age/wear cause. The largest contributor to the MSS SVV 

failures is the dirt/contamination/corrosion cause. Figure 47 shows the PWR RCS relief valve cause 

distribution. The largest contributor to the MSS PORV and SVV failures is the age/wear cause. Figure 

48 shows the BWR SRV relief valve cause distribution. The largest contributor to the MSS SRV failures 

is the dirt/contamination/corrosion cause. Figure 49 shows the cause distribution to the RVLC valves for 

the RHR system and all other systems. The RVLC and RHR failures are due to age/wear, 

dirt/contamination/corrosion, and design deficiency causes. 

The failures due to dirt/contamination/corrosion causes were reviewed for any further insights. There 

were no repeated dirt/contamination/corrosion related causes observed in the data except the corrosion 

bonding failure mechanism. 

Table 38. Failure cause code descriptions. 

Fail Cause 

Code Fail Cause Description

AW Age/Wear

DC Dirt/Contamination/Corrosion

DD Design Deficiency

DF Debris/Foreign Material

II Initial Installation

MF Manufacturing Defect

MP Maintenance/Procedure 

Deficiencies

OA Out-of-Adjustment

OD Other devices

OT Other

SD Setpoint Drift

UK Unknown
88 

Figure 46. PWR MSS relief valve failure causes distribution. 

Figure 47. PWR RCS relief valve failure causes distribution. 

0 %

10%

20%

30%

40%

50%

60%

70%

AW DC DD DF II MF MP OA OD OT SD UK

Percent of Failures

Failure Cause

PORV

SVV

0 %

5 %

10%

15%

20%

25%

30%

35%

AW DC DD DF II MF MP OA OD OT SD UK

Percent of Failures

Failure Cause

PORV

SVV
89 

Figure 48. BWR SRV failure causes distribution. 

Figure 49. RVLC failure causes distribution. 

0 %

10%

20%

30%

40%

50%

60%

70%

AW DC DD DF II MF MP OA OD OT SD UK

Percent of Failures

Failure Cause

SRV

0 %

5 %

10%

15%

20%

25%

30%

AW DC DD DF II MF MP OA OD OT SD UK

Percent of Failures

Failure Cause

RHR

WAT
90 

7.2.3 Relief Valve Type 

Section 2.1.7 discusses different types of BWR SRV valves. These SRVs are identified and grouped into 

 ̳Direct Acting‘ and  ̳Pilot Actuated‘ sub-types in the failure data collection. Figure 50 shows the 

weighted failure count (between direct acting and pilot actuated) for the open and close failure modes. 

Figure 50. Failure comparison of SRV sub-types. 

0

2

4

6

8

1 0

1 2

Fail to Close Fail to Open

Weighteed Failures

Direct 

Acting

Pilot 

Actuated
91 

8. COMPARISON OF CURRENT RESULTS WITH HISTORICAL 

ESTIMATES 

This section compares the reliability estimates with historical estimates for similar 

component/system/failure mode combinations. Four sources of relevant available relief valve reliability 

estimates were identified to include in an evaluation of historical estimates: 

1. NUREG/CR-6928, Industry-Average Performance for Components and Initiating Events at 

U.S. Commercial Nuclear Power Plants (Eide 2007a). The data in this document are 

currently in use in the SPAR models (Version 3.45). These estimates are the most recent 

estimates in use as of the date this document was published. 

2. NUREG/CR-1363, Data Summaries of Licensee Event Reports of Valves at U.S. Commercial 

Nuclear Power Plants, January 1, 1976 to December 31, 1987 (NRC, 1982). The data in this 

document were compiled from the LER reports from 1976 to 1980. 

3. NUREG/CR-4550: 

a. Vol. 3, Analysis of Core Damage Frequency: Surry Unit 1 Internal Events (NRC 

1990a). The data in this document are from the Surry internal event data tables. The 

PWR relief valve historical comparison data are from this document. 

b. Vol. 4, Analysis of Core Damage Frequency: Peach Bottom Unit 2 Internal Events

(NRC 1989). The data in this document are from the Peach Bottom internal event 

data tables, which reference the ASEP study (Kolaczkowski 1983) and plant specific 

data. The BWR relief valve historical comparison data are from this document. 

Figure 51 and Table 39 show the results of the data review from the above listed sources. Several of 

the compared estimates show differences greater than 100 percent. It needs to be noted that the estimates 

in NUREG/CR-6928 are always based on a combination of EPIX test, non-demand, and actual demand 

data. Most of the estimates in this report are based on only actual demand data (following scrams) and 

come from a mixture of LERs and EPIX documents. In addition, each document was reviewed and 

classified to a PRA failure mode, which was not a part of the NUREG/CR-6928 effort. 

The following are the estimates from this report with significant differences to the estimates from 

NUREG/CR-6928. All of these entries are for the SVV component: 

1. BWR SVV Fails to Reclose—the estimate in this report is a factor of approximately 4 larger 

than the estimate in NUREG/CR-6928. Since the use of SVVs in BWRs is rare, the value 

used for this comparison is based on the pooled data from the PWR MSS and RCS SVV data. 

Table 31, item SVV_C, shows that the estimate in this report is based on three failures in 

8836 demands. NUREG/CR-6928, Table A.2.45-3, shows that the fail to close of the SVV is 

based on zero failures in 7393 demands and is also pooled across the MSS and RCS systems. 

2. RCS SVV Fails to Open—the estimate in this report is approximately two orders of 

magnitude smaller than the estimate in NUREG/CR-6928. Table 31, item SVV_O, shows 

that the estimate in this report is based on zero failures in 9981 demands. NUREG/CR-6928, 

Table A.2.45-3, shows that the fail to open of the SVV is based on 18 failures in 7393 

demands and is also pooled across the MSS and RCS systems. This report added the Setpoint 

Out-of-Specification failure mode to the data collection taxonomy. Most of the previously 

classified Fail-to-Open events were classified as Setpoint Out-of-Specification. See Table 33

item SVV_D, which shows 23 setpoint events in the data (these were previously counted as 

Fail to Close, Fail to Open, and Spurious Operation in NUREG/CR-6928). 
92 

3. RCS SVV Fails to Reclose—the estimate in this report is a factor of approximately 4 larger 

than the estimate in NUREG/CR-6928. The value used for this comparison is based on the 

pooled data from the PWR MSS and RCS SVV data. Table 31, item SVV_C, shows that the 

estimate in this report is based on three failures in 8836 demands. NUREG/CR-6928, Table 

A.2.45-3, shows that the fail to close of the SVV is based on 0 failures in 7393 demands and 

is also pooled across the MSS and RCS systems. 

4. RCS SVV Spurious Operation—the estimate in this report is approximately one order of 

magnitude smaller than the estimate in NUREG/CR-6928. Table 33, item SVV_S, shows 

that the estimate in this report is based on two failures in 6483 valve standby years. 

NUREG/CR-6928, Table A.2.45-3, shows that the fail to open of the SVV is based on 11 

failures in 43,668,600 hours and is also pooled across the MSS and RCS systems. 

Figure 51. Comparison of historical relief valve reliability estimates. 

1.00E-0 8

1.00E-0 7

1.00E-0 6

1.00E-0 5

1.00E-0 4

1.00E-0 3

1.00E-0 2

1.00E-0 1

1.00E+00

Event Probability

NUREG/CR-6928

This Report

NUREG/CR-1363

NUREG/CR-4550
93

Table 39. Comparison of historical estimates with this report. 

Basic Event 

Description

NUREG/CR-6928 This Report NUREG/CR-1363 NUREG/CR-4550

BetaAlphaMeanDistribution TypeBetaAlphaMeanDistribution TypeEFMeanDistribution TypeEFMeanDistribution Type

BWR SRV Fail to 

Close 

624.5 0.50 8.00E-04 Beta 705.30 0.50 7.07E-04 Beta 1.50 3.10E-03 Log Normal - 9.60E-02 Point 

Estimate

BWR SRV Fails to 

Open Actuation

37.2 0.30 8.00E-03 Beta 1270.82 1.62 1.27E-03 Beta 1.25 8.90E-03 Log Normal - - -

BWR SRV Fails to 

Open Pressure

37.2 0.30 8.00E-03 Beta 33.98 0.48 1.39E-02 Beta 1.20 1.10E-02 Log Normal - - -

BWR SVV Fails to 

Reclose

7142.4 0.50 7.00E-05 Beta 2191.00 0.74 3.39E-04 Beta - - - - - -

RCS One PORV Fails 

to Reclose

499.5 0.50 1.00E-03 Beta 1432.99 2.01 1.40E-03 Beta - - - 10.00 3.00E-02 Log Normal

RCS PORV Fail to 

Open

56.7 0.40 7.00E-03 Beta 53.87 0.35 6.40E-03 Beta - - - 3.00 1.00E-03 Log Normal

RCS PORVs Fail to 

Close After Passing 

Liquid

5.0 0.56 1.00E-01 Beta 5.90 0.39 6.25E-02 Beta - - - - - -

RCS PORVs Open 

During LOOP

5.0 0.95 1.60E-01

(Note 1)

Beta - - 1.48E-01 Beta - - - - - -

RCS PORVS Open 

During Transient 

12.0 0.50 4.00E-02

(Note 1)

Beta - - 1.18E-01 Beta - - - - 4.10E-02 Max Entropy

RCS SVV Fail to 

Open

37.2 0.30 8.00E-03 Beta 9999.50 0.50 5.00E-05 Beta 2.00 3.90E-03 Log Normal 3.00 1.00E-03 Log Normal

RCS SVV Fails to 

Reclose

7142.4 0.50 7.00E-05 Beta 2191.00 0.74 3.39E-04 Beta - - - - - -

RCS SVV Spurious 

Operation (hr-1)

6.00E-05 0.30 5.00E-07 Gamma 1.13E+07 0.50 4.41E-08 Gamma 2.00 1.70E-06 Log Normal - - -

SG PORV Fail to 

Close

499.5 0.50 1.00E-03 Beta 1374.02 2.01 1.46E-03 Beta - - - - - -

SG PORV Fail to 

Open

56.7 0.40 7.00E-03 Beta 53.87 0.35 6.40E-03 Beta - - - 3.00 1.00E-03 Log Normal

Note 1 Estimate is not from NUREG/CR-6928. These values are used in the current SPAR models.
94 
95 

9. SUMMARY 

In risk assessments, relief valves are important because energy must be removed in the decay heat 

removal function (which protects the reactor core) and pressure must be released in the overpressure 

function (which protects piping and components). Therefore, it is important that the SPAR models reflect 

current relief valve performance. This report documents the work performed to generate SPAR model 

inputs that represent current industry relief valve performance. 

The data sources for this study were EPIX and LERs. EPIX data from INPO were reviewed to 

characterize the relief valve component performance . The EPIX operational data describe relief valve 

performance (full fiscal years) between October 1, 1997, and September 30, 2007. Four types of relief 

valves are considered in this report: safety relief valves (SRVs), power-operated relief valves (PORVs), 

American Society of Mechanical Engineers (ASME) code safety valves (SVVs), and low-capacity relief 

valves (RVLCs).

The authors evaluated relief valve data to determine 

1. The probability of relief valves and safety valves lifting given specific transients. 

2. The probability of relief valves and safety valves reseating after opening. 

3. Given multiple relief valve and safety valve cycles, is a relief valve more or less likely to reseat. 

4. The probability of relief valves and safety valves failing to lift. 

5. Spurious operation of relief valves and safety valves. 

Section 6 presents results from the analysis of the relief valve experience. This study identified 

several pieces of previously unknown information (e.g., the fraction of initiating events where the relief 

valves are demanded, expected number of total demands, and the separation of the failure to open on the 

initial and subsequent demands). 

Section 7 presents an engineering analysis of the data to identify trends in demands and failures. In 

addition, factors affecting relief valve reliability were examined and charts presenting detection and cause 

comparisons are included. 

Section 8 presents a comparison of the estimates in this report to selected historical estimates. 

Appendix A provides the coding guidance for creating and maintaining the relief valve study 

database. The goal of the database is to collect failure and actuation data for MSS and RCS safety-related 

relief valves. In addition, data are collected on RVLCs in water and gas systems. 

Appendix B contains tables listing the results for possible industry distributions for the relief valve 

estimates. The tables deal with the estimates as follows: 

 High-capacity relief valves 

Probabilities of demands on scrams (Table B-1) 

Demand-related estimates for PWR PORVs (Table B-2) 

Demand-related estimates for PWR SVVs (Table B-3) 

Demand-related estimates for BWR SRVs (Table B-4) 

Failure probabilities for PWR PORVs (Table B-5) 

Failure probabilities for PWR SVVs (Table B-6) 
96 

Failure probabilities for BWR SRVs (Table B-7) 

Failure rates (all three valve types) (Table B-8) 

 Low-capacity relief valves 

Failure probabilities (Table B-9) 

Failure rates (Table B-10). 

Appendix C provides a demonstration of the use of the results in generic BWR and PWR relief valve 

response models. 
97 

10. REFERENCES 

Atwood, C.L., et al., 2003,, Handbook of Parameter Estimation for Probabilistic Risk Assessment, 

Nuclear Regulatory Commission, NUREG/CR-6823, September 2003. 

Bari, R. A., et al., 1985, Probabilistic Safety Analysis Procedures Guide, NRC, NUREG/CR-2815, 

August. 

Eide, S. A., et al., 2007a, Industry-Average Performance for Components and Initiating Events at U.S. 

Commercial Nuclear Power Plants, NUREG/CR-6928 (INL/EXT-06-11119), February 2007. 

Eide, S. A., et. al., 2007b, Baseline Risk Index for Initiating Events (BRIIE), NUREG/CR/6932 

(INL/EXT-06-11950), June 2007. 

NRC, 2010a, Reactor Operational Experience Results and Databases, 

http://nrcoe.inel.gov/results/index.cfm. 

NRC, 2010b, Reactor Oversight Process, http://www.nrc.gov/reactors/operating/oversight/ropdescription.html. 

NRC, 2010c, Mitigating Systems Performance Index (MSPI),

http://www.nrc.gov/NRR/OVERSIGHT/ASSESS/mspi.html. 

NRC, 2005, Memorandum of Agreement between the Institute of Nuclear Power Operations and the U.S. 

Nuclear Regulatory Commission, November 14, ML060060035. 

NRC, 2000, Event Reporting Guidelines 10 CFR 50.72 and 50.73, NUREG-1022, October. 

NRC, 1990, Severe Accident Risks: An Assessment for Five U.S. Nuclear Power Plants, NUREG-1150, 

Final Report, December. 

NRC, 1990a, Analysis of Core Damage Frequency: Surry Unit 1 Internal Events, NUREG/CR-4550, Vol. 

3, Rev. 1, Part 1, April 1990. 

NRC, 1989, Analysis of Core Damage Frequency: Peach Bottom Unit 2 Internal Events, NUREG/CR4550, Vol. 4, Rev. 1, Part 1, August 1989. 

NRC, 1983, PRA Procedures Guide, NUREG/CR-2300, January. 

NRC, 1982, Data Summaries of Licensee Event Reports of Valves at U.S. Commercial Nuclear Power 

Plants, January 1, 1976 to December 31, 1987, NUREG/CR-1363, Rev 1, October 1982. 

NRC, 1975, Reactor Safety Study: An Assessment of Accident Risks in US Commercial Nuclear Power 

Plants, WASH-1400 (NUREG 75/014). 

O‘Reilly, P. et al., 2005, The NRC’s SPAR Model Enhancement Program: Objectives, Status, 

Implications, International Topical Meeting on Probabilistic Safety Analysis PSA’05, American 

Nuclear Society, Inc. 
98 

Poloski, J. P. et al., 1999, Rates of Initiating Events at U.S. Nuclear Power Plants, U.S. Nuclear 

Regulatory Commission, NUREG/CR-5750 (INEEL/EXT-98-00401), February 1999. 
Appendix A 

Relief Valve Study Coding Guidance 
A-1

Appendix A 

Relief Valve Study Coding Guidance 

This appendix provides the coding guidance for creating and maintaining the relief valve (RV) study 

databases. The goal of the RV study is to collect failure and actuation data for main steam system (MSS) 

and reactor coolant system (RCS) safety-related relief valves. In addition, data are collected on lowcapacity relief valves (RVLCs) in water and gas systems. 

The Integrated Data Collection and Coding System (IDCCS) has been modified to assist the data 

collection effort. To create the backfit of RV data from 1997 to present, the Master Documents table has 

been modified to include fields that identify licensee event report (LER) and Equipment Performance and 

Information Exchange (EPIX) records deemed interesting to the RV study. LERs are selected based on 

being in either the initiating event or the shutdown initiating event data sets from 1997 to present. Coders 

look at LERs to determine various demand parameters and identify failures detected during those 

demands. The EPIX device database has been reviewed to determine the components of interest to the 

RV study. These include power-operated relief valves (PORVs), RCS and MSS code safety valves 

(SVVs), safety relief valves (SRVs), and RVLCs in various systems. Many of the EPIX failure records 

have already been reviewed for the Common Cause Failure study; the rest have not yet been reviewed. 

Regardless, all records identified as potential RVs will be reviewed anew for this study. Information 

already at hand will be made available to the coders. 
A-2

A-1. IDCCS EXPLORER 

A-1.1 Initial Coding 

The IDCSS Explorer window has been modified to accommodate the RV study. Figure A-1 shows 

the modified Explorer form with the RV ―New‖ option selected and the results of right-clicking on the 

LER number. Notice the last two items listed in the Option Select window. ―Relief Valve‖ adds a record 

to the RV study and opens the data input form. The ―Relief Valve N/A‖ option works similar to the 

general N/A option but is designed for the RV backfit effort to keep track of the records that do not meet 

RV study criteria. 

For an LER or EPIX record to be identified as N/A, the record must not meet any of the criteria 

included in this coding guidance for the system, component, or failure mode. Failures of the accumulator 

on PORVs do not fail the RV if they do not fail the air/nitrogen line. Example: If the accumulator failure 

only affects the ability of the RV to actuate when loss of instrument air, then it is not a failure. 

A-1.2 Review 

When the ―Initial‖ option under RVs is selected, only those RV and RV N/A records that the current 

user can review will show up. The coder can double-click the event number to open the RV study record 

or right-click the record to open the Option Select window to view the record or to agree with the RV N/A 

designation. 
A-3

Figure A-1. IDCCS Explorer view. 
A-4

A-2. RELIEF VALVE STUDY WINDOW 

The RV Study window includes the failure and actuation data collection input views in one form. 

Figure A-2 shows the RV Study window with a right-click on the Sub-Record section of the Failures tab. 

The user can add a failure sub-record or delete the current failure sub record. The same is true for the 

Demand tab. 

The coder should add as many sub-records (failure or demand) as necessary to explicitly describe the 

event. Different systems, components, failure modes, number of actuation/failures, etc. all indicate that 

there should be multiple sub-records. 

Figure A-2. Relief Valve Study main form. 
A-5

A-2.1 Relief Valve Study Failure Sub-Records 

When a new failure record is added, the RV Study form will look like Figure A-3. Figure A-4 shows 

the new failure record partially filled out. The fields are described below. 

Figure A-3. Relief Valve Study main form with new failure record. 

Figure A-4. Relief valve study failure record partially filled out. 
A-6

System—the system that the failure event occurred in. The system list is limited to RCS, MSS, 

residual heat removal (RHR), WAT, WATD, and GAS. WAT is a clean water system, WATD is a 

dirty (gray) water system, and GAS is an air, nitrogen, etc. system. 

Component—the component applicable to the failure record. The component list is limited to the 

RVs of interest for the selected system. 

Number of Inoperabilities—the number of times the component failed. Generally, this should be ―1.‖ 

Double-clicking will increment the value by one. If the component failed due to the same reasons 

more than once in a failure record and was repaired between failures, then there may be a reason for 

indicating more than one for this field. 

Failure Mode—the failure mode appropriate to the event (see Table A-1). The failure modes are 

limited based on the component selected. The failure modes have been broken down to capture 

failures in the automatic and manual modes for PORVs and SRVs. Spurious operation and setpoint 

drift are also valid failure modes. 

Cause—the cause of the failure most appropriate to the description (see Table A-2). 

Method of Detection—the method of failure detection. Non-demand inspection is included to count 

those failures not detected during testing or a real pressure or electronic signal demand. Examples are 

the discovery of internal leakage by a downstream sensor or an RV selector switch in ―Bypass,‖ etc. 

Number of Demands to Failure—the number of demands to the failure of the RV. Mostly applicable 

to the PORV, SVVs, and SRVs. The question is after multiple demands (pressure cycles, manual 

cycles), do the RVs fail? This does not generally apply to the LCRVs although it is possible. All 

failures will get at least one demand, even testing. 

Recovery—Mutually exclusive option boxes signify either that the RV failure is not recoverable, is 

capable of being recovered (in the judgment of the reviewer), or is actually recovered. The default is 

―Non-Recoverable.‖ Typically, if a failure occurs on test demands, the plant operators do not attempt 

recovery. The purpose of the ―Recoverable‖ label is to identify those failures that could quickly and 

easily be recovered from (usually within 5–10 minutes) if they occurred during an actual unplanned 

(emergency) situation. These option buttons apply only to component failures (not faults or 

administrative inoperabilities). By definition, the event is not recovered or recoverable if 

maintenance is required to restore operability. Minor maintenance actions such as fuse replacement, 

resetting of breakers, or changing out a light bulb are allowed to support a recoverable situation. 

Special Information Group—These check-boxes record variables within the failure. 

 Error of Commission—Checked when the cause of the failure is intentional but inappropriate 

action by personnel (for example, a mis-positioned valve, control switch, or circuit breaker). 

 Support System Failure—Checked when the safety function failure of the RV being studied is 

caused by a failure of a support system outside the RV boundaries identified for the study. 

Although support system failures are not used in calculating the RV unreliability, they are 

included in the engineering assessment of the unplanned demands. This does include failures that 

are explicitly modeled in the probabilistic risk assessment (for example, multiple components fail 

to operate due to the loss of a vital electrical bus). 

 Common Cause Failure—Checked when there are failures of multiple similar RVs due to a 

shared cause. For example, multiple RVs failed to open due to the same design or installation 

error. This does not include failures that are explicitly modeled in the probabilistic risk 

assessment (for example, multiple components fail to operate due to the loss of a vital electrical 

bus). 
A-7

Table A-1. Failure mode descriptions. 

Failure 

Mode Description Comments

PORVs

AC Failure of automatic close function only The manual function would have succeeded.

AO Failure of automatic open function only The manual function would have succeeded.

CC Fail to close (reseat) on demand (auto 

and manual)

The RV was demanded open and subsequently did not 

reseat. Independent of the method of demand.

OO Fail to open on demand (auto and 

manual)

The RV was demanded open and did not open. Independent 

of the method of demand.

SO Spurious operation open or close The RV transferred open or close without a valid demand.

SP Setpoint out of specification Collect all setpoint problems.

SVVs

CC Fail to close (reseat) on demand The RV was demanded open and subsequently did not 

reseat. These only get demanded open by system pressure 

above setpoint.

OO Fail to open on demand The RV was demanded open and did not open. These only 

get demanded open by system pressure above setpoint.

SO Spurious operation open or close The RV transferred open or close without a valid demand.

SP Setpoint out of specification Collect all setpoint problems.

SRVs

AC Failure of automatic close function only Failure of the pilot close actuation by signal. The pressure 

function would have succeeded.

AO Failure of automatic open function only Failure of the pilot open actuation by signal. The pressure 

function would have succeeded.

CC Fail to close (reseat) on demand The RV was demanded open and subsequently did not 

reseat. Independent of the method of demand.

OO Fail to open on demand The RV was demanded open and did not open. Independent 

of the method of demand.

SO Spurious operation open or close The RV transferred open or close without a valid demand.

SP Setpoint out of specification Collect all setpoint problems.

LCRVs

CC Fail to close (reseat) on demand The RV was demanded open and subsequently did not 

reseat. These only get demanded open by system pressure 

above setpoint.

LK Leakage past seat The RV leaked past set.

OO Fail to open on demand The RV was demanded open and did not open. These only 

get demanded open by system pressure above setpoint.

SO Spurious operation open or close The RV transferred open or close without a valid demand.

SP Setpoint out of specification Collect all setpoint problems.
A-8

Table A-2. Failure cause. 

Fail Cause Description

AW Age/Wear

DC Dirt/Contamination/Corrosion

DD Design Deficiency

DF Debris/Foreign Material

II Initial Installation

MF Manufacturing Defect

MP Maintenance/Procedure Deficiencies

OA Out-of-Adjustment

OD Other devices

OT Other

SD Setpoint Drift

UK Unknown

A-2.2 Relief Valve Study Demand Sub-Records 

After a new demand record is added, the RV study window will look like Figure A-5. Figure A-6 

shows the demand record filled out. The fields are described below. 

System—the system where the failure event occurred. The system list is limited to RCS, MSS, RHR, 

WAT, WATD, and GAS. WAT is a clean water system, WATD is a dirty (gray) water system, and 

GAS is an air, nitrogen, etc. system. 

Component—the component applicable to the failure record. The component list will be limited to 

the RVs of interest for the selected system. 

Demand Type (Open)—the type of open demand for the group of relief valves demanded: pressure, 

automatic signal, or manual signal. The PORVs and SRVs may use any of the three; SVVs and 

LCRVs will only use the pressure option. Records whether the demand was due to system pressure 

actuating the valve (SVVs and the pressure mode of the SRVs), the automatic setpoint signal (SRVs 

and PORVs), or a manual switch demand (SRVs and PORVs). The demand type must apply to all 

demands counted in the Demand Count field. 

Demand Count (est)—the estimated demands applicable to the event. If the demand count is known 

(indicated in the LER or EPIX record), then ―Known‖ is selected and the ―Open Demand Count 

(known)‖ field is filled in. Otherwise, the total number of demands to the group of relief valves is 

estimated in the ―Demand Count (est)‖ area of the screen. 

Open Demand Count (known)—the number of demands if the LER or EPIX report specifies such. 

This field is grayed out until the ―Known‖ option is selected under ―Demand Count (est).‖

Open Medium Passed—indicates whether steam or liquid was passed during the open demand. This 

must apply to the total number of demands the record is describing. If the medium changes, add 

another record to continue the description. 

RVs Demanded—the count of RVs that were demanded out of the known population (e.g., 2 of 3) 

during each Open demand. The form will automatically enter the known population of the type of 

RV in the selected system to the right of ―of.‖ The program will not allow a value greater than the 

known population. 
A-9

Figure A-5. Relief valve demand sub-record. 

Figure A-6. Relief valve demand sub-record filled out. 
A-10

Demand Type (Reseat)— the type of reseat demand: pressure, automatic signal, or manual signal. 

The PORVs and SRVs may use any of the three; SVVs and LCRVs will only use the pressure option. 

Record whether the demand was due to system pressure actuating the valve (SVVs and the pressure 

mode of the SRVs), the automatic setpoint signal (SRVs and PORVs), or a manual switch demand 

(SRVs and PORVs). The demand type must apply to all demands counted in the Demand Count 

field. 

Reseat Medium Passed—records whether steam or liquid was passed during the reseat demand. This 

must apply to the total number of demands the record is describing. If the medium changes, add 

another record to continue the description. 

Assume a Pressure Spike?—indicates whether there is enough knowledge to assume that the 

phenomena of a pressure pulse due to the rapid closure of the turbine throttle valve caused the main 

steam PORVs and/or SVVs to lift during the transient. 

A-2.3 Relief Valve Population 

The RV Counts tab shows the number of each type of RV that has been identified in each system at 

the plant. The information in this table is used when filling in the demand sub-record ―RVs Demanded‖

field. Figure A-7 shows the ―RV Counts‖ tab. If there appears to be a conflict between the counts in this 

table and new information, the RV team will investigate and correct the table as appropriate. 

Figure A-7. Relief valve population as known. 
A-11

A-2.4 Comments 

The Comments tab is used to record a synopsis of the event and reasons for coding the event, 

including any assumptions. Figure A-8 shows the Comments tab. The comment block is required to be 

filled in before the program will allow an exit. 

Figure A-8. Relief valve comment block. 
A-12
Appendix B 

Distributions for Relief Valve Estimates 

B-1

Appendix B 

Distributions for Relief Valve Estimates 

This appendix contains ten tables listing the results for possible industry distributions for the relief 

valve estimates. The tables deal with the estimates as follows: 

 High-capacity relief valves 

− Probabilities of demands on scrams (Table B-1) 

− Demand-related estimates for PWR PORVs (Table B-2) 

− Demand-related estimates for PWR SVVs (Table B-3) 

− Demand-related estimates for BWR SRVs (Table B-4) 

− Failure probabilities for PWR PORVs (Table B-5) 

− Failure probabilities for PWR SVVs (Table B-6) 

− Failure probabilities for BWR SRVs (Table B-7) 

− Failure rates (all three valve types) (Table B-8) 

 Low-capacity relief valves 

− Failure probabilities (Table B-9) 

− Failure rates (Table B-10). 

For each estimate, the baseline period methodology used in NUREG/CR-6928 was applied to identify 

a baseline period that would be relevant for current risk assessments (Eide et al., 2007). The method 

involves considering candidate baseline periods starting in 1987, 1988, 1989, etc. All of the periods are at 

least 5 years long and end with the most recent data (FY-2007). For each period, a Poisson regression or 

binomial regression analysis is performed to identify trends, if any, in the data as the years increase. The 

type of regression corresponds to the data (binomial for probabilities and Poisson for rates). Generally, 

the period with least evidence of a trend was selected as the baseline period. This period has the largest 

p-value for the evaluation of the significance of the slope. When no events were found in the data, or just 

one, the entire period (1987–2007) was used. When two events occurred, the whole period was used 

unless they were both in the first years, such that the conditional probability of the events occurring so 

early in the study period with random data was less than 0.05. In this last case, the period following the 

events was selected. 

The baseline period methodology is expected to undergo further review, so future versions of this 

report may show different periods. Another aspect of the methodology that will be reviewed is whether to 

keep the period the same for pairs of events, such as an occurrence with or without recovery. In the 

current assessment, each estimate was treated independently. 

For each estimate, the following entities are listed in the tables, as applicable: 

 The update of the Jeffreys noninformative distribution (NI). This distribution has an alpha parameter 

equal to the number of events plus 0.5, and a beta equal to the number of demands plus 1 for 

probabilities. The second distribution parameter for rates is equal to the exposure time. 

 A constrained noninformative distribution (CNID). The mean is constrained to equal the NI 

distribution mean, but these distributions are wider (Atwood et al., 2003). 

 The results of tests of differences with regard to attributes such as years, plants, systems, scram data 

vs. testing data, and other conditions as applicable. For each of these analyses, a maximum likelihood 

distribution is given if one was found in the data. This is the distribution that would be used for 
B-2

empirical Bayes (EB) estimates. If no maximum was found, the distribution type is characterized as 

“NA.” Information for the evaluation remains in the table, however, because the right-most column 

shows whether significant differences were seen in the data when grouped according to the attribute 

under study. The p-values correspond to a chi-square test evaluation based on simulations. Thus the 

tests are meaningful even when the sample sizes are small and asymptotic distributions might not 

apply. 

For each estimate, one row in the following tables was selected as the best representation for the 

variation present in the industry data and was listed in the tables in Section 6 of the main body of this 

report. 
B-3

Table B-1. Possible distributions for the probability of relief valve demands on scrams, 1988–2007. 

Failure Mode Abbreviation

Baseline

Period

Start Year

RV

Demand

Scram

Count

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value for

Diff.

PWR MSS power-operated relief valves

Prob of MSS PORV demand given PWR 

scram 

PORV_Scram_MSS 1998 72 493 NI 0.121 0.147 0.174 72.5 — —

CNID 0.000 0.147 0.598 0.322 — —

EB 0.117 0.147 0.179 50.266 Year 0.1903

EB 0.032 0.150 0.324 2.144 Plant 0.0039

PWR RCS power-operated relief valves

Prob of RCS PORV demand given PWR 

scram 

PORV_Scram_RCS 2001 19 312 NI 0.042 0.062 0.086 19.5 — —

CNID 0.000 0.062 0.253 0.394 — —

NA — — — — Year 0.2251

EB 0.001 0.069 0.239 0.605 Plant 0.0008

PWR MSS code safety valves

Prob of MSS SVV demand given PWR 

scram

SVV_Scram_MSS 2001 12 416 NI 0.018 0.030 0.045 12.5 — —

CNID 0.000 0.030 0.118 0.453 — —

NA — — — — Year 0.8136

EB 0.000 0.034 0.204 0.128 Plant 0.0004

PWR RCS code safety valves

Prob of RCS SVV demand given PWR 

scram

SVV_Scram_RCS 1987 4 1922 NI 0.001 0.002 0.004 4.5 — —

CNID 0.000 0.002 0.009 0.496 — —

EB 0.000 0.002 0.007 0.820 Year 0.3686

EB 0.000 0.003 0.014 0.042 Plant —

BWR MSS safety-relief valves

Prob of SRV demand given BWR scram SRV_Scram 1996 85 391 NI 0.185 0.218 0.253 85.5 — —

CNID 0.000 0.218 0.796 0.328 — —

EB 0.134 0.217 0.311 12.458 Year 0.0644

EB 0.068 0.215 0.408 3.098 Plant 0.0040

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood 

estimate found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.
B-4

Table B-2. Possible distributions for demands for PWR power-operated relief valves. 

Failure Mode Abbreviation

Baseline

Period

Start

Year Numerator Denominator

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

Fraction of MSS PORV events PORV_Ev_MSS 1992 129 181 NI 0.655 0.712 0.765 129.5 — —

CNID 0.095 0.712 1.000 0.873 — —

NA — — — — Year 0.2334

EB 0.441 0.711 0.921 6.054 Plant 0.0414

Fraction of RCS PORV events PORV_Ev_RCS 1992 52 181 NI 0.235 0.288 0.345 52.5 — —

CNID 0.000 0.288 0.905 0.354 — —

NA — — — — Year 0.2321

EB 0.079 0.289 0.559 2.466 Plant 0.0422

Prob PORV demand is 

automatic 

PORV_FrcPulse_A 1997 215 268 NI 0.760 0.801 0.840 215.5 — —

CNID 0.248 0.801 1.000 1.305 — —

EB 0.452 0.797 0.990 3.601 Year <1.E−05

EB 0.130 0.785 1.000 0.826 Plant <1.E−05

EB 0.474 0.844 0.999 2.889 System 

(MSS/ 

RCS)

<1.E−05

P[PORV auto pulses per 

event=1] 

PORV_P_A_N1 2000 47 76 NI 0.525 0.617 0.706 47.5 — —

CNID 0.030 0.617 0.999 0.653 — —

EB 0.447 0.618 0.777 13.889 Year 0.1660

EB 0.271 0.618 0.909 3.212 Plant 0.1425

NA — — — — System 

(MSS/ 

RCS)

0.3084

P[PORV pulses per event=1] PORV_P_V_N1 1995 100 134 NI 0.681 0.744 0.804 100.5 — —

CNID 0.137 0.744 1.000 0.991 — —

EB 0.490 0.750 0.942 6.453 Year 0.0100

EB 0.626 0.745 0.850 29.607 Plant 0.3561

NA — — — — System 

(MSS/ 

RCS)

0.5093

PORV fraction demanded/initial 

pulse (auto) 

PORV_FrcDem_1_A 2003 116 149 NI 0.719 0.777 0.830 116.5 — —

CNID 0.193 0.777 1.000 1.147 — —

EB 0.669 0.779 0.875 33.094 Year 0.0767

EB 0.051 0.744 1.000 0.595 Plant <1.E−05

NA — — — — System 

(MSS/ 

0.6022
Table B-2. (continued). 

B-5

Failure Mode Abbreviation

Baseline

Period

Start

Year Numerator Denominator

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

RCS)

PORV fraction demanded/initial 

pulse (manual) 

PORV_FrcDem_1_M 1997 50 370 NI 0.108 0.136 0.166 50.5 — —

CNID 0.000 0.136 0.560 0.324 — —

EB 0.017 0.135 0.328 1.481 Year <1.E−05

EB 0.000 0.175 0.892 0.131 Plant <1.E−05

EB 0.000 0.077 0.355 0.272 System 

(MSS/ 

RCS)

<1.E−05

PORV fraction demanded/initial 

pulse

PORV_FrcDem_1 1999 243 297 NI 0.779 0.817 0.853 243.5 — —

CNID 0.290 0.817 1.000 1.437 — —

EB 0.561 0.803 0.966 7.167 Year <1.E−05

EB 0.519 0.840 0.996 3.886 Plant <1.E−05

EB 0.621 0.773 0.898 18.131 System 

(MSS/ 

RCS)

0.0010

PORV fraction demanded/any 

pulse (auto) 

PORV_FrcDem_A 1999 343 466 NI 0.701 0.736 0.769 343.5 — —

CNID 0.124 0.736 1.000 0.956 — —

EB 0.464 0.763 0.965 4.895 Year <1.E−05

EB 0.418 0.818 0.998 2.614 Plant <1.E−05

EB 0.446 0.727 0.937 5.585 System 

(MSS/ 

RCS)

<1.E−05

PORV fraction demanded/any 

pulse (manual) 

PORV_FrcDem_M 1987 530 633 NI 0.812 0.837 0.860 530.5 — —

CNID 0.347 0.837 1.000 1.643 — —

EB 0.355 0.825 1.000 1.835 Year <1.E−05

EB 0.258 0.855 1.000 0.986 Plant <1.E−05

EB 0.308 0.704 0.972 2.714 System 

(MSS/ 

RCS)

<1.E−05
Table B-2. (continued). 

B-6

Failure Mode Abbreviation

Baseline

Period

Start

Year Numerator Denominator

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

PORV fraction demanded/any 

pulse

PORV_FrcDem 1999 471 608 NI 0.746 0.774 0.802 471.5 — —

CNID 0.189 0.774 1.000 1.133 — —

EB 0.422 0.768 0.981 3.671 Year <1.E−05

EB 0.400 0.831 1.000 2.180 Plant <1.E−05

EB 0.440 0.732 0.945 5.179 System 

(MSS/ 

RCS)

<1.E−05

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood 

estimate found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.
B-7

Table B-3. Possible distributions for demands for PWR code safety valves. 

Failure Mode Abbreviation

Baseline

Period

Start

Year Numerator Denominator

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

Fraction of MSS SVV events SVV_Ev_MSS 1987 135 139 NI 0.940 0.968 0.988 135.5 — —

CNID 0.874 0.968 1.000 13.532 — —

EB 0.922 0.972 0.998 40.490 Year 0.4724

EB 0.789 0.965 1.000 3.165 Plant 0.0688

Fraction of RCS SVV events SVV_Ev_RCS 1987 4 139 NI 0.012 0.032 0.060 4.5 — —

CNID 0.000 0.032 0.126 0.449 — —

EB 0.002 0.028 0.078 1.165 Year 0.4712

EB 0.000 0.035 0.211 0.113 Plant 0.0675

P[SVV pulses per event=1] SVV_P_N1 1990 93 104 NI 0.837 0.890 0.936 93.5 — —

CNID 0.543 0.890 1.000 2.726 — —

EB 0.809 0.896 0.962 36.177 Year 0.3842

EB 0.720 0.900 0.994 9.280 Plant 0.2457

NA — — — — System 

(MSS/ 

RCS)

0.6894

SVV fraction demanded/initial pulse SVV_FrcDem_1 1987 573 2303 NI 0.234 0.249 0.264 573.5 — —

CNID 0.000 0.249 0.853 0.338 — —

EB 0.116 0.270 0.456 4.681 Year <1.E−05

EB 0.074 0.230 0.433 3.134 Plant <1.E−05

NA — — — — System 

(MSS/ 

RCS)

0.1128

SVV fraction demanded/any pulse SVV_FrcDem 1991 560 2527 NI 0.208 0.222 0.235 560.5 — —

CNID 0.000 0.222 0.803 0.329 — —

EB 0.102 0.273 0.483 3.727 Year <1.E−05

EB 0.060 0.221 0.438 2.571 Plant <1.E−05

NA — — — — System 

(MSS/ 

RCS)

0.1269

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood estimate

found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.
B-8

Table B-4. Possible distributions for demands of BWR (main steam system) safety-relief valves. 

Failure Mode Abbreviation

Baseline 

Period 

Start 

Year Numerator Denominator

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.

Prob. SRV demand is automatic SRV_FrcPulse_A 1988 249 631 NI 0.363 0.395 0.427 249.5 — —

CNID 0.001 0.395 0.974 0.413 — —

EB 0.098 0.417 0.780 1.908 Year <1.E−05

EB 0.042 0.464 0.927 0.986 Plant <1.E−05

P[SRV auto pulses per event=1] SRV_P_A_N1 2000 29 55 NI 0.417 0.527 0.635 29.5 — —

CNID 0.009 0.527 0.996 0.528 — —

NA — — — — Year 0.7896

NA — — — — Plant 0.5532

P[SRV pulses per event=1] SRV_P_V_N1 2000 33 55 NI 0.489 0.598 0.703 33.5 — —

CNID 0.023 0.598 0.999 0.622 — —

NA — — — — Year 0.9077

NA — — — — Plant 0.5358

Prob. SRV demand from direct 

pressure 

SRV_P_P 1999 6 1369 NI 0.002 0.005 0.008 6.5 — —

CNID 0.000 0.005 0.018 0.493 — —

EB 0.000 0.006 0.031 0.151 Year 0.0004

NA — — — — Plant <1.E−05

SRV fraction demanded/initial 

pulse (auto)

SRV_FrcDem_1_A 1999 255 847 NI 0.276 0.301 0.327 255.5 — —

CNID 0.000 0.301 0.919 0.360 — —

EB 0.144 0.313 0.508 5.144 Year <1.E−05

EB 0.015 0.308 0.768 0.848 Plant <1.E−05

SRV fraction demanded/initial 

pulse (manual)

SRV_FrcDem_1_M 2003 52 424 NI 0.098 0.124 0.151 52.5 — —

CNID 0.000 0.124 0.513 0.328 — —

EB 0.018 0.114 0.268 1.745 Year 0.0005

EB 0.000 0.097 0.422 0.306 Plant <1.E−05

SRV fraction demanded/initial 

pulse 

SRV_FrcDem_1 1999 358 847 NI 0.395 0.423 0.451 358.5 — —

CNID 0.002 0.423 0.982 0.433 — —

EB 0.315 0.430 0.548 20.724 Year 0.0008

EB 0.170 0.440 0.729 3.310 Plant <1.E−05
Table B-4. (continued). 

B-9

Failure Mode Abbreviation

Baseline 

Period 

Start 

Year Numerator Denominator

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.

SRV fraction demanded/any pulse 

(auto)

SRV_FrcDem_A 1995 856 1604 NI 0.513 0.534 0.554 856.5 — —

CNID 0.010 0.534 0.996 0.536 — —

EB 0.164 0.486 0.815 2.613 Year <1.E−05

EB 0.148 0.491 0.838 2.266 Plant <1.E−05

SRV fraction demanded/any pulse 

(manual)

SRV_FrcDem_M 1996 842 2666 NI 0.301 0.316 0.331 842.5 — —

CNID 0.000 0.316 0.931 0.367 — —

EB 0.182 0.328 0.490 7.878 Year <1.E−05

EB 0.142 0.343 0.577 4.075 Plant <1.E−05

SRV fraction demanded/any pulse SRV_FrcDem 1996 1655 4115 NI 0.390 0.402 0.415 1656 — —

CNID 0.001 0.402 0.977 0.418 — —

EB 0.206 0.387 0.584 6.596 Year <1.E−05

EB 0.183 0.436 0.707 3.815 Plant —

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood 

estimate found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.
B-10

Table B-5. Failure probabilities for PWR power-operated relief valves. 

Failure Mode Abbreviation Discovery Baseline

Period

Start Year

Failure Demand Beta Distribution Variation

Typea5

th Mean 95th Alpha Source P-value

for Diff.

PORV fail to open (event) PORV_O_N Scram 2003 1 49 NI 3.60E−03 3.00E−02 7.70E−02 1.5 — —

CNID 7.16E−05 3.00E−02 1.18E−01 0.453 — —

PORV fail to open (event) (not 

recovered)

PORV_O_N_NR Scram 1987 8 276 NI 1.58E−02 3.07E−02 4.94E−02 85 —

CNID 7.22E−05 3.07E−02 1.21E−01 0.452 — —

NA — — — — Year 0.6859

EB 8.89E−04 2.94E−02 9.31E−02 0.818 Plant 0.3111

NA — — — — System 

(MSS/ 

RCS)

0.4693

P[Recov. PORV fail to open (event)] PORV_O_N_PR Failures 1995 1 5 NI 3.64E−02 2.50E−01 5.63E−01 1.5 — —

CNID 1.40E−04 2.50E−01 8.54E−01 0.338 — —

PORV fail to auto open PORV_O_A Scram & 

Tests

2001 2 8547.9 NI 6.70E−05 2.92E−04 6.47E−04 2.5 — —

CNID 1.15E−06 2.92E−04 1.12E−03 0.500 — —

NA — — — — Scram/ 

test

0.8003

EB 1.75E−12 2.39E−04 1.32E−03 0.148 Year 0.0528

EB 1.71E−05 2.44E−04 6.98E−04 1.142 Plant 0.9553

NA — — — — System 

(MSS/ 

RCS)

0.2153

PORV fail to open PORV_O Scram & 

Tests

1994 44 13530.9 NI 2.52E−03 3.29E−03 4.14E−03 44.5 — —

CNID 1.23E−05 3.29E−03 1.27E−02 0.495 — —

EB 2.02E−03 4.59E−03 8.01E−03 6.095 Scram/ 

test

0.0053

EB 1.02E−03 3.45E−03 7.04E−03 3.296 Year <1.E−05

EB 2.39E−06 6.40E−03 2.79E−02 0.347 Plant <1.E−05

NA — — — — System 

(MSS/ 

RCS)

0.3152
Table B-5. (continued). 

B-11

Failure Mode Abbreviation Discovery Baseline

Period

Start Year

Failure Demand Beta Distribution Variation

Typea5

th Mean 95th Alpha Source P-value

for Diff.

PORV fail to open (not recovered) PORV_O_NR Scram 2002 1 351 NI 5.01E−04 4.26E−03 1.11E−02 1.5 — —

CNID 1.58E−05 4.26E−03 1.64E−02 0.494 — —

P[Recov. PORV fail to open] PORV_O_PR Failures 1990 0 11 NI 1.75E−04 4.17E−02 1.57E−01 0.5 — —

CNID 7.70E−05 4.17E−02 1.65E−01 0.433 — —

PORV fail to auto open (init) PORV_O_1_A Scram 1990 4 472 NI 3.53E−03 9.51E−03 1.78E−02 4.5 — —

CNID 3.24E−05 9.51E−03 3.68E−02 0.486 — —

EB 3.24E−09 6.92E−03 3.63E−02 0.189 Year 0.1010

NA — — — — Plant <1.E−05

NA — — — — System 

(MSS/ 

RCS)

0.6023

PORV fail to open (init) PORV_O_1 Scram 2003 1 133 NI 1.32E−03 1.12E−02 2.90E−02 1.5 — —

CNID 3.72E−05 1.12E−02 4.33E−02 0.483 — —

PORV fail to auto open (after) PORV_O_2_A Scram 1987 0 410 NI 4.79E−06 1.22E−03 4.67E−03 0.5 — —

CNID 4.70E−06 1.22E−03 4.68E−03 0.498 — —

PORV fail to open (after) PORV_O_2 Scram 1987 0 833 NI 2.36E−06 6.00E−04 2.30E−03 0.5 — —

CNID 2.34E−06 6.00E−04 2.30E−03 0.499 — —

PORV fail to close/reseat (event) PORV_C_N Scram 1987 12 276 NI 2.67E−02 4.51E−02 6.73E−02 12.5 — —

CNID 7.64E−05 4.51E−02 1.80E−01 0.426 — —

NA — — — — Year 0.5442

EB 5.24E−08 4.40E−02 2.29E−01 0.200 Plant 0.0239

NA — — — — System 

(MSS/ 

RCS)

0.1980

PORV fail to close (event) (not 

recovered)

PORV_C_N_NR Scram 1987 5 276 NI 8.32E−03 1.99E−02 3.53E−02 5.5 — —

CNID 5.71E−05 1.99E−02 7.73E−02 0.470 — —

EB 1.70E−03 1.81E−02 4.88E−02 1.313 Year 0.2401

EB 2.89E−10 1.89E−02 1.05E−01 0.154 Plant 0.1475

NA — — — — System 

(MSS/ 

RCS)

1.0000
Table B-5. (continued). 

B-12

Failure Mode Abbreviation Discovery Baseline

Period

Start Year

Failure Demand Beta Distribution Variation

Typea5

th Mean 95th Alpha Source P-value

for Diff.

P[Recov. PORV fail to close (event)] PORV_C_N_PR Failures 1987 7 12 NI 3.52E−01 5.77E−01 7.88E−01 7.5 — —

CNID 1.77E−02 5.77E−01 9.98E−01 0.591 — —

NA — — — — Year 1.0000

NA — — — — Plant 1.0000

NA — — — — System 

(MSS/ 

RCS)

0.4168

PORV fail to auto close PORV_C_A Scram & 

Tests

2000 3 9742.7 NI 1.11E−04 3.59E−04 7.22E−04 3.5 — —

CNID 1.41E−06 3.59E−04 1.38E−03 0.499 — —

EB 2.64E−11 5.07E−03 2.82E−02 0.146 Scram/ 

test

<1.E−05

EB 7.51E−06 3.06E−04 1.01E−03 0.773 Year 0.1837

EB 2.15E−77 9.28E−04 1.67E−03 0.017 Plant <1.E−05

NA — — — — System 

(MSS/ 

RCS)

0.4343

PORV fail to close PORV_C Scram & 

Tests

1990 18 13897.9 NI 8.66E−04 1.33E−03 1.88E−03 18.5 — —

5.13E−06 1.33E−03 5.12E−03 0.498 — —

4.59E−04 2.56E−03 6.05E−03 2.013 Scram/ 

test

0.0001

2.61E−04 1.46E−03 3.45E−03 2.009 Year <1.E−05

1.39E−09 2.94E−03 1.54E−02 0.190 Plant <1.E−05

— — — — System 

(MSS/ 

RCS)

0.9609

PORV fail to close (not recovered) PORV_C_NR Scram 1987 5 1559 NI 1.47E−03 3.53E−03 6.30E−03 5.5 — —

CNID 1.32E−05 3.53E−03 1.36E−02 0.495 — —

EB 8.19E−05 3.41E−03 1.12E−02 0.767 Year 0.1321

EB 6.28E−10 3.67E−03 1.95E−02 0.177 Plant 0.0797

NA — — — — System 

(MSS/ 

RCS)

1.0000
Table B-5. (continued). 

B-13

Failure Mode Abbreviation Discovery Baseline

Period

Start Year

Failure Demand Beta Distribution Variation

Typea5

th Mean 95th Alpha Source P-value

for Diff.

P[Recov. PORV fail to close] PORV_C_PR Failures 1988 6 11 NI 3.10E−01 5.42E−01 7.65E−01 6.5 — —

CNID 1.10E−02 5.42E−01 9.97E−01 0.546 — —

NA — — — — Year 0.7383

EB 7.17E−02 5.53E−01 9.69E−01 1.088 Plant 0.4349

NA — — — — System 

(MSS/ 

RCS)

0.4533

PORV fail to auto close (init) PORV_C_1_A Scram 1999 1 188 NI 9.37E−04 7.94E−03 2.06E−02 1.5 — —

CNID 2.77E−05 7.94E−03 3.06E−02 0.488 — —

PORV fail to close (init) PORV_C_1 Scram 1990 6 547 NI 5.40E−03 1.19E−02 2.03E−02 6.5 — —

CNID 3.90E−05 1.19E−02 4.59E−02 0.482 — —

NA — — — — Year 0.5491

NA — — — — Plant 0.1849

NA — — — — System 

(MSS/ 

RCS)

1.0000

PORV fail to auto close (after) PORV_C_2_A Scram 1998 2 149 NI 3.86E−03 1.67E−02 3.66E−02 2.5 — —

CNID 5.06E−05 1.67E−02 6.48E−02 0.474 — —

NA — — — — Year 0.2460

NA — — — — Plant 0.1253

NA — — — — System 

(MSS/ 

RCS)

0.2055

PORV fail to close/reseat (after) PORV_C_2 Scram 1987 0 833 NI 2.36E−06 6.00E−04 2.30E−03 0.5 — —

CNID 2.34E−06 6.00E−04 2.30E−03 0.499 — —

PORV low-pressure control function 

fail

PORV_LP Testing 1987 1 12722.9 NI 1.38E−05 1.18E−04 3.07E−04 1.5 — —

CNID 4.63E−07 1.18E−04 4.53E−04 0.500 — —

NA — — — — Year 0.4501

EB 8.73E−35 1.25E−04 6.11E−04 0.042 Plant 0.0036

EB 4.56E−07 1.69E−04 6.67E−04 0.467 System 

(MSS/ 

RCS)

0.0233
Table B-5. (continued). 

B-14

Failure Mode Abbreviation Discovery Baseline

Period

Start Year

Failure Demand Beta Distribution Variation

Typea5

th Mean 95th Alpha Source P-value

for Diff.

PORV control function fail (only) PORV_CT Scram & 

Tests

2002 2 7156.1 NI 8.00E−05 3.49E−04 7.73E−04 2.5 — —

CNID 1.37E−06 3.49E−04 1.34E−03 0.499 — —

NA — — — — Scram/ 

test

0.9333

NA — — — — Year 0.5438

EB 2.10E−12 3.74E−04 2.07E−03 0.146 Plant 0.2214

NA — — — — System 

(MSS/ 

RCS)

0.5336

PORV control function fail (only) (not 

recovered)

PORV_CT_NR Scram & 

Tests

2002 2 7156.1 NI 8.00E−05 3.49E−04 7.73E−04 2.5 — —

CNID 1.37E−06 3.49E−04 1.34E−03 0.499 — —

NA — — — — Scram/ 

test

0.9333

NA — — — — Year 0.5438

EB 2.10E−12 3.74E−04 2.07E−03 0.146 Plant 0.2214

NA — — — — System 

(MSS/ 

RCS)

0.5336

P[Recov. PORV control function fail 

(only)]

PORV_CT_PR Failures 1987 1 6 NI 3.02E−02 2.14E−01 4.95E−01 1.5 — —

CNID 8.37E−05 2.14E−01 7.88E−01 0.327 — —

PORV fail to close/reseat (liquid) (init) PORV_C_1_L Scram 1987 0 7 NI 2.71E-04 6.25E-02 2.32E-01 0.5 — —

CNID 6.52E-05 6.25E-02 2.54E-01 0.393 — —

PORV fail to open (liquid) (init) PORV_O_1_L Scram 1987 0 7 NI 2.71E-04 6.25E-02 2.32E-01 0.5 — —

CNID 6.52E-05 6.25E-02 2.54E-01 0.393 — —

PORV fail to close/reseat (liquid) 

(after)

PORV_C_2_L Scram 1987 0 698 NI 2.82E-06 7.15E-04 2.75E-03 0.5 — —

CNID 2.78E-06 7.15E-04 2.75E-03 0.498 — —

PORV fail to open (liquid) (after) PORV_O_2_L Scram 1987 0 698 NI 2.82E-06 7.15E-04 2.75E-03 0.5 — —

CNID 2.78E-06 7.15E-04 2.75E-03 0.498 — —

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood estimate 

found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.
B-15

Table B-6. Failure probabilities for PWR code safety valves. 

Failure Mode Abbreviation Discovery

Baseline

Period

Start

Year Failure Demand

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

SVV fail to open (event) SVV_O_N Scram 1987 0 139 NI 1.41E−05 3.57E−03 1.37E−02 0.5 — —

CNID 1.33E−05 3.57E−03 1.38E−02 0.495 — —

SVV fail to open (event) (not 

recovered)

SVV_O_N_NR Scram 1987 0 139 NI 1.41E−05 3.57E−03 1.37E−02 0.5 — —

CNID 1.33E−05 3.57E−03 1.38E−02 0.495 — —

SVV fail to open SVV_O Scram & 

Tests

1999 0 9980.6 NI 1.97E−07 5.01E−05 1.92E−04 0.5 — —

CNID 1.97E−07 5.01E−05 1.92E−04 0.500 — —

SVV fail to open (not recovered) SVV_O_NR Scram 1987 0 773 NI 2.54E−06 6.46E−04 2.48E−03 0.5 — —

CNID 2.52E−06 6.46E−04 2.48E−03 0.499 — —

SVV fail to open (init) SVV_O_1 Scram 1987 0 773 NI 2.54E−06 6.46E−04 2.48E−03 0.5 — —

CNID 2.52E−06 6.46E−04 2.48E−03 0.499 — —

SVV fail to open (after) SVV_O_2 Scram 1987 0 196 NI 1.00E−05 2.54E−03 9.74E−03 0.5 — —

CNID 9.62E−06 2.54E−03 9.77E−03 0.496 — —

SVV fail to close/reseat (event) SVV_C_N Scram 2000 2 16 NI 3.69E−02 1.47E−01 3.05E−01 2.5 — —

CNID 4.11E−05 1.47E−01 5.99E−01 0.322 — —

NA — — — — Year 0.3851

NA — — — — Plant 0.3729

SVV fail to close/reseat (event) 

(not recovered)

SVV_C_N_NR Scram 1990 3 104 NI 1.05E−02 3.33E−02 6.62E−02 3.5 — —

CNID 7.42E−05 3.33E−02 1.31E−01 0.447 — —

NA — — — — Year 0.8353

NA — — — — Plant 0.6651

EB 5.43E−04 1.97E−01 6.78E−01 0.440 System 

(MSS/ 

RCS)

0.0033

P[Recov. SVV fail to close/reseat 

(event)]

SVV_C_N_PR Failures 1987 8 15 NI 3.29E−01 5.31E−01 7.29E−01 8.5 — —

CNID 9.53E−03 5.31E−01 9.96E−01 0.533 — —

NA — — — — Year 0.6175

EB 9.22E−04 4.76E−01 9.98E−01 0.358 Plant 0.0995

NA — — — — System 

(MSS/ 

RCS)

0.1982
Table B-6. (continued). 

B-16

Failure Mode Abbreviation Discovery

Baseline

Period

Start

Year Failure Demand

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

SVV fail to close/reseat SVV_C Scram & 

Tests

2000 3 8835.9 NI 1.23E−04 3.96E−04 7.96E−04 3.5 — —

CNID 1.55E−06 3.96E−04 1.52E−03 0.499 — —

EB 2.57E−12 1.25E−02 7.25E−02 0.125 Scr/ test <1.E−05

EB 7.27E−06 3.39E−04 1.13E−03 0.743 Year 0.1725

EB 1.04E−72 7.06E−04 1.44E−03 0.018 Plant <1.E−05

NA — — — — BWR/PW

R 

0.7617

NA — — — — System 

(MSS/ 

RCS)

0.7168

SVV fail to close/reseat (not 

recovered)

SVV_C_NR Scram 1995 1 368 NI 4.78E−04 4.07E−03 1.06E−02 1.5 — —

CNID 1.51E−05 4.07E−03 1.57E−02 0.494 — —

P[Recov. SVV fail to close/reseat] SVV_C_PR Failures 1987 10 17 NI 3.92E−01 5.83E−01 7.64E−01 10.5 — —

CNID 1.93E−02 5.83E−01 9.98E−01 0.600 — —

NA — — — — Year 0.2175

EB 5.11E−05 4.78E−01 1.00E+00 0.245 Plant 0.0302

NA — — — — System 

(MSS/ 

RCS)

0.1547

SVV fail to close/reseat (init) SVV_C_1 Scram 2001 3 77 NI 1.42E−02 4.49E−02 8.87E−02 3.5 — —

CNID 7.65E−05 4.49E−02 1.79E−01 0.427 — —

NA — — — — Year 0.4109

EB 4.85E−05 4.63E−02 1.89E−01 0.396 Plant 0.1038

SVV fail to close/reseat (after) SVV_C_2 Scram 1987 0 196 NI 1.00E−05 2.54E−03 9.74E−03 0.5 — —

CNID 9.62E−06 2.54E−03 9.77E−03 0.496 — —

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood estimate 

found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.
B-17

Table B-7. Failure probabilities for BWR safety-relief valves. 

Failure Mode Abbreviation Discovery

Baseline

Period

Start

Year Failure Demand

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.

SRV fail to open (event) SRV_O_N Scram 2000 1 55 NI 3.21E−03 2.68E−02 6.89E−02 1.5 — —

CNID 6.79E−05 2.68E−02 1.05E−01 0.458 — —

SRV fail to open (event) (not 

recovered) SRV_O_N_NR Scram 1989 3 186 NI 5.85E−03 1.87E−02 3.74E−02 3.5 — —

CNID 5.49E−05 1.87E−02 7.28E−02 0.471 — —

NA — — — — Year 0.9495

EB 4.39E−09 2.14E−02 1.15E−01 0.179 Plant 0.0148

P[Recov. SRV fail to open (event)] SRV_O_N_PR Failures 1987 2 6 NI 1.04E−01 3.57E−01 6.59E−01 2.5 — —

CNID 7.36E−04 3.57E−01 9.59E−01 0.389 — —

NA — — — — Year 1.0000

NA — — — — Plant 0.4647

SRV fail to auto open SRV_O_A

Scram & 

Tests 1991 0 7495.1 NI 2.62E−07 6.67E−05 2.56E−04 0.5 — —

CNID 2.62E−07 6.67E−05 2.56E−04 0.500 — —

SRV fail to open SRV_O

Scram & 

Tests 1989 11 9054.1 NI 7.23E−04 1.27E−03 1.94E−03 11.5 — —

CNID 4.90E−06 1.27E−03 4.88E−03 0.498 — —

NA — — — —

Scram/ 

test 0.6417

EB 1.68E−04 1.27E−03 3.22E−03 1.616 Year 0.1481

EB 5.14E−11 2.30E−03 1.26E−02 0.158 Plant <1.E−5

SRV fail to open (not recovered) SRV_O_NR Scram 2001 1 1122 NI 1.57E−04 1.34E−03 3.48E−03 1.5 — —

CNID 5.15E−06 1.34E−03 5.14E−03 0.498 — —

P[Recov. SRV fail to open] SRV_O_PR Failures 1987 0 5 NI 3.74E−04 8.33E−02 3.06E−01 0.5 — —

CNID 4.88E−05 8.33E−02 3.45E−01 0.361 — —

SRV fail to open (pres.) SRV_O_P Scram 1987 0 35 NI 5.58E−05 1.39E−02 5.30E−02 0.5 — —

4.41E−05 1.39E−02 5.39E−02 0.479 — —

SRV fail to auto. open (init) SRV_O_1_A Scram 1987 2 705 NI 8.13E−04 3.54E−03 7.83E−03 2.5 — —

CNID 1.32E−05 3.54E−03 1.36E−02 0.495 — —

NA — — — — Year 0.7241

NA — — — — Plant 0.0335
Table B-7. (continued). 

B-18

Failure Mode Abbreviation Discovery

Baseline

Period

Start

Year Failure Demand

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.

SRV fail to open(init) SRV_O_1 Scram 1988 3 855 NI 1.27E−03 4.09E−03 8.20E−03 3.5 — —

CNID 1.52E−05 4.09E−03 1.57E−02 0.494 — —

EB 3.64E−09 3.50E−03 1.81E−02 0.200 Year 0.1030

EB 8.78E−42 8.62E−03 4.03E−02 0.032 Plant 0.0018

SRV fail to auto. open (after) SRV_O_2_A Scram 1987 0 689 NI 2.85E−06 7.25E−04 2.78E−03 0.5 — —

CNID 2.82E−06 7.25E−04 2.78E−03 0.499 — —

SRV fail to open (after) SRV_O_2 Scram 2001 1 841 NI 2.09E−04 1.78E−03 4.64E−03 1.5 — —

CNID 6.83E−06 1.78E−03 6.85E−03 0.497 — —

SRV fail to close/reseat (event) SRV_C_N Scram 2000 1 55 NI 3.21E−03 2.68E−02 6.89E−02 1.5 — —

CNID 6.79E−05 2.68E−02 1.05E−01 0.458 — —

SRV fail to close (event) (not 

recovered) SRV_C_N_NR Scram 2000 1 55 NI 3.21E−03 2.68E−02 6.89E−02 1.5 — —

CNID 6.79E−05 2.68E−02 1.05E−01 0.458 — —

P[Recov. SRV fail to close (event)] SRV_C_N_PR Failures 1987 0 1 NI 1.54E−03 2.50E−01 7.71E−01 0.5 — —

CNID 1.40E−04 2.50E−01 8.54E−01 0.338 — —

SRV fail to auto. close SRV_C_A

Scram & 

Tests 1987 0 7737.1 NI 2.54E−07 6.46E−05 2.48E−04 0.5 — —

CNID 2.54E−07 6.46E−05 2.48E−04 0.500 — —

SRV fail to close/reseat SRV_C

Scram & 

Tests 2003 2 3536.6 NI 1.62E−04 7.07E−04 1.56E−03 2.5 — —

CNID 2.75E−06 7.07E−04 2.72E−03 0.499 — —

NA — — — —

Scram/ 

test 0.1979

NA — — — — Year 0.5765

NA — — — — Plant 0.0742

SRV fail to close (not recovered) SRV_C_NR Scram 2001 1 1122 NI 1.57E−04 1.34E−03 3.48E−03 1.5 — —

CNID 5.15E−06 1.34E−03 5.14E−03 0.498 — —

P[Recov. SRV fail to close] SRV_C_PR Failures 1987 0 1 NI 1.54E−03 2.50E−01 7.71E−01 0.5 — —

CNID 1.40E−04 2.50E−01 8.54E−01 0.338 — —

SRV fail to close/reseat (pres.) SRV_C_P Scram 1987 0 35 NI 5.58E−05 1.39E−02 5.30E−02 0.5 — —

CNID 4.41E−05 1.39E−02 5.39E−02 0.479 — —

SRV fail to auto. close (init) SRV_C_1_A Scram 1987 0 705 NI 2.79E−06 7.08E−04 2.72E−03 0.5 — —

CNID 2.76E−06 7.08E−04 2.72E−03 0.499 — —
Table B-7. (continued). 

B-19

Failure Mode Abbreviation Discovery

Baseline

Period

Start

Year Failure Demand

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value 

for Diff.

SRV fail to close/reseat (init) SRV_C_1 Scram 2000 1 311 NI 5.66E−04 4.81E−03 1.25E−02 1.5 — —

CNID 1.76E−05 4.81E−03 1.85E−02 0.493 — —

SRV fail to auto. close (after) SRV_C_2_A Scram 1987 0 689 NI 2.85E−06 7.25E−04 2.78E−03 0.5 — —

CNID 2.82E−06 7.25E−04 2.78E−03 0.499 — —

SRV fail to close/reseat (after) SRV_C_2 Scram 1987 0 928 NI 2.12E−06 5.38E−04 2.07E−03 0.5 — —

CNID 2.10E−06 5.38E−04 2.07E−03 0.499 — —

SRV fail to open (liquid) (init) SRV_O_1_L Scram 1987 0 56 NI 3.50E-05 8.77E-03 3.36E-02 0.5 — —

CNID 3.02E-05 8.77E-03 3.39E-02 0.486 — —

SRV fail to close (liquid) (init) SRV_C_1_L Scram 1987 0 56 NI 3.50E-05 8.77E-03 3.36E-02 0.5 — —

CNID 3.02E-05 8.77E-03 3.39E-02 0.486 — —

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood estimate 

found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.
B-20

Table B-8. Failure rates, per valve per reactor critical year. 

Failure Mode Abbreviati Discovery

Baseline

Period

Start

Year Failure

Valve

Standby

Years

Gamma Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

PWR power-operated relief valves

PORV spurious operation PORV_S All methods 2003 8 1928.8 NI 2.25E−03 4.41E−03 7.15E−03 8.5 — —

CNID 1.73E−05 4.41E−03 1.69E−02 0.5 — —

NA — — — — Year 0.8707

EB 1.32E−06 4.60E−03 2.03E−02 0.336 Plant 0.3431

NA — — — — System 

(MSS/ 

RCS)

0.0714

PORV spurious operation 

(not recovered) 

PORV_S_NR All methods 1998 12 3788.1 NI 1.93E−03 3.30E−03 4.97E−03 12.5 — —

CNID 1.30E−05 3.30E−03 1.27E−02 0.5 — —

EB 7.92E−04 3.16E−03 6.81E−03 2.739 Year 0.0666

EB 1.23E−04 3.43E−03 1.08E−02 0.875 Plant 0.6390

NA — — — — System 

(MSS/ 

RCS)

0.1469

P[Recov. PORV spurious 

operation] 

PORV_S_PR Failures 2001 5 15 NI 1.66E−01 3.44E−01 5.45E−01 5.5 — —

CNID 5.97E−04 3.44E−01 9.51E−01 0.382 — —

NA — — — — Year 0.2420

NA — — — — Plant 0.7784

NA — — — — System 

(MSS/ 

RCS)

1.0000

PORV setpoint out of 

specification

PORV_D All methods 1999 2 3445.2 NI 1.66E−04 7.26E−04 1.61E−03 2.5 — —

CNID 2.85E−06 7.26E−04 2.79E−03 0.5 — —

NA — — — — Year 1.0000

NA — — — — Plant 1.0000

NA — — — — System 

(MSS/ 

RCS)

0.4986
Table B-8. (continued). 

B-21

Failure Mode Abbreviati Discovery

Baseline

Period

Start

Year Failure

Valve

Standby

Years

Gamma Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

Code safety valves

SVV spurious operation SVV_S All methods 2003 2 6483.4 NI 8.83E−05 3.86E−04 8.54E−04 2.5 — —

CNID 1.52E−06 3.86E−04 1.48E−03 0.5 — —

NA — — — — Year 1.0000

NA — — — — Plant 1.0000

NA — — — — BWR/

PWR 

0.5011

NA — — — — System 

(MSS/ 

RCS)

0.3299

SVV spurious operation (not 

recovered)

SVV_S_NR All methods 2003 2 6483.4 NI 8.83E−05 3.86E−04 8.54E−04 2.5 — —

CNID 1.52E−06 3.86E−04 1.48E−03 0.5 — —

NA — — — — Year 1.0000

NA — — — — Plant 1.0000

NA — — — — BWR/

PWR 

0.5015

NA — — — — System 

(MSS/ 

RCS)

0.3331

P[Recov. SVV spurious 

operation]

SVV_S_PR Failures 1987 0 2 NI 8.68E−04 1.67E−01 5.69E−01 0.5 — —

CNID 4.78E−05 1.67E−01 6.63E−01 0.321 — —

SVV setpoint out of 

specification 

SVV_D All methods 2001 23 9061.8 NI 1.78E−03 2.59E−03 3.53E−03 23.5 — —

CNID 1.02E−05 2.59E−03 9.96E−03 0.5 — —

EB 4.59E−04 2.54E−03 6.00E−03 2.027 Year 0.0199

EB 5.10E−08 2.45E−03 1.18E−02 0.255 Plant <1.E−05

NA — — — — BWR/

PWR 

<1.E−05

NA — — — — System 

(MSS/ 

RCS)

<1.E−05
Table B-8. (continued). 

B-22

Failure Mode Abbreviati Discovery

Baseline

Period

Start

Year Failure

Valve

Standby

Years

Gamma Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

BWR safety relief valves

SRV spurious operation SRV_S All methods 1998 10 3673.5 NI 1.58E−03 2.86E−03 4.45E−03 10.5 — —

CNID 1.12E−05 2.86E−03 1.10E−02 0.5 — —

EB 3.64E−04 2.71E−03 6.85E−03 1.637 Year 0.1562

EB 2.47E−05 3.07E−03 1.12E−02 0.579 Plant 0.3394

SRV spurious operation (not 

recovered)

SRV_S_NR All methods 2003 2 1888.4 NI 3.03E−04 1.32E−03 2.93E−03 2.5 — —

CNID 5.21E−06 1.32E−03 5.09E−03 0.5 — —

NA — — — — Year 1.0000

NA — — — — Plant 1.0000

P[Recov. SRV spurious 

operation]

SRV_S_PR Failures 1987 4 10 NI 1.85E−01 4.09E−01 6.53E−01 4.5 — —

CNID 1.63E−03 4.09E−01 9.79E−01 0.423 — —

NA — — — — Year 0.3558

NA — — — — Plant 0.2189

SRV setpoint out of 

specification 

SRV_D All methods 1999 115 3365.6 NI 2.92E−02 3.43E−02 3.97E−02 115.5 — —

CNID 1.35E−04 3.43E−02 1.32E−01 0.5 — —

EB 2.31E−03 3.45E−02 9.94E−02 1.119 Year <1.E−05

EB 3.88E−11 3.32E−02 1.86E−01 0.136 Plant <1.E−05

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood estimate 

found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.

b. Probabilities of recovery, based on the failure data, are all beta distributions rather than gamma distributions.
B-23

Table B-9. RVLC failure probabilities (5-year testing) for both PWRs and BWRs. 

Failure Mode Abbreviation Discovery

Baseline

Period

Start Year Failure Demand

Beta Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

RVLC fail to open RVLC_O Testing 2000 5 21460.5 NI 1.07E−04 2.56E−04 4.58E−04 5.5 — —

CNID 1.00E−06 2.56E−04 9.85E−04 0.500 — —

EB 2.46E−05 2.35E−04 6.26E−04 1.403 Year 0.1903

EB 1.42E−24 2.05E−04 1.16E−03 0.062 Plant 0.0030

NA — — — — Medium 0.8118

RVLC fail to open (not 

recovered) 

RVLC_O_NR Testing 2000 5 21460.5 NI 1.07E−04 2.56E−04 4.58E−04 5.5 — —

CNID 1.00E−06 2.56E−04 9.85E−04 0.500 — —

EB 2.46E−05 2.35E−04 6.26E−04 1.403 Year 0.1903

EB 1.42E−24 2.05E−04 1.16E−03 0.062 Plant 0.0030

NA — — — — Medium 0.8118

P[Recov. RVLC fail to 

open] 

RVLC_O_PR Failures 1987 0 10 NI 1.92E−04 4.55E−02 1.71E−01 0.5 — —

CNID 7.63E−05 4.55E−02 1.81E−01 0.426 — —

RVLC fail to close/reseat RVLC_C Testing 2002 1 15791.2 NI 1.11E−05 9.50E−05 2.47E−04 1.5 — —

CNID 3.73E−07 9.50E−05 3.65E−04 0.500 — —

NA — — — — Year 0.3876

EB 3.94E−15 6.73E−05 3.85E−04 0.119 Plant 0.0023

NA — — — — Medium 0.9156

RVLC fail to close/reseat 

(not recovered) 

RVLC_C_NR Testing 2002 1 15791.2 NI 1.11E−05 9.50E−05 2.47E−04 1.5 — —

CNID 3.73E−07 9.50E−05 3.65E−04 0.500 — —

NA — — — — Year 0.3876

EB 3.94E−15 6.73E−05 3.85E−04 0.119 Plant 0.0023

NA — — — — Medium 0.9156

P[Recov. RVLC fail to 

close/reseat] 

RVLC_C_PR Failures 1987 1 8 NI 2.25E−02 1.67E−01 3.97E−01 1.5 — —

CNID 4.78E−05 1.67E−01 6.63E−01 0.321 — —

RVLC fail to open (RHR) RVLC_O_RHR Testing 1987 0 2378.1 NI 8.27E−07 2.10E−04 8.07E−04 0.5 — —

CNID 8.24E−07 2.10E−04 8.07E−04 0.500 — —

RVLC fail to close/reseat 

(RHR)

RVLC_C_RHR Testing 1987 2 2378.1 NI 2.41E−04 1.05E−03 2.33E−03 2.5 — —

CNID 4.07E−06 1.05E−03 4.04E−03 0.498 — —

EB 1.09E−16 8.07E−04 4.70E−03 0.095 Year 0.0459

NA — — — — Plant 0.0139

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood 

estimate found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.
B-24

Table B-10. RVLC failure rates, per valve per calendar year. 

Failure Mode Abbreviation Discovery

Baseline

Period

Start

Year Failure

Valve

Standby

Years

Gamma Distribution Variation

Typea5

th Mean 95th Alpha Source

P-value

for Diff.

RVLC spurious operation RVLC_S All methods 2002 4 61416.0 NI 2.71E−05 7.33E−05 1.38E−04 4.5 — —

CN 2.88E−07 7.33E−05 2.81E−04 0.5 — —

NA — — — Year 0 7227

NA — — — — Plant 1.0000

NA — — — — Medium 0.0159

RVLC spurious operation 

(not recovered) 

RVLC_S_NR All methods 2002 4 61416.0 NI 2.71E−05 7.33E−05 1.38E−04 4.5 — —

CNID 2.88E−07 7.33E−05 2.81E−04 0.5 — —

NA — — — — Year 0.7229

NA — — — — Plant 1.0000

NA — — — — Medium 0.0150

P[Recov. RVLC spurious 

operation] 

RVLC_S_PR Failuresb1987 1 13 NI 1.37E−02 1.07E−01 2.64E−01 1.5 — —

CNID 3.95E−05 1.07E−01 4.47E−01 0.337 — —

RVLC setpoint out of 

specification

RVLC_D All methods 2002 3 61416.0 NI 1.76E−05 5.70E−05 1.15E−04 3.5 — —

CNID 2.24E−07 5.70E−05 2.19E−04 0.5 — —

NA — — — — Year 0.4447

NA — — — — Plant 1.0000

NA — — — — Medium 0.0615

RVLC leakage RVLC_LK All methods 1988 22 110037.0 NI 1.39E−04 2.04E−04 2.80E−04 22.5 — —

CNID 8.04E−07 2.04E−04 7.85E−04 0.5 — —

EB 2.34E−05 1.99E−04 5.18E−04 1.502 Year 0.0071

EB 1.18E−07 2.20E−04 9.44E−04 0.364 Plant 0.0016

NA — — — — Medium <1.E−05

RVLC spurious operation 

(RHR)

RVLC_S_RHR All methods 2001 2 5887.0 NI 9.73E−05 4.25E−04 9.40E−04 2.5 — —

CNID 1.67E−06 4.25E−04 1.63E−03 0.5 — —

NA — — — — Year 1.0000

NA — — — — Plant 1.0000

RVLC setpoint out of 

specification (RHR)

RVLC_D_RHR All methods 1987 4 9040.7 NI 1.84E−04 4.98E−04 9.36E−04 4.5 — —

CNID 1.96E−06 4.98E−04 1.91E−03 0.5 — —

EB 4.49E−05 4.47E−04 1.20E−03 1.371 Year 0.4559

NA — — — — Plant 1.0000

a. CNID = constrained noninformative distribution, EB = maximum likelihood distribution (prior for empirical Bayes updates), NA = not applicable (no maximum likelihood estimate 

found for distribution parameters that would account for the specified variation), NI = update of Jeffreys noninformative prior.

b. Probabilities of recovery, based on the failure data, are all beta distributions rather than gamma distributions.
B-25

B-1. REFERENCES 

Atwood, C.L., et al., 2003,, Handbook of Parameter Estimation for Probabilistic Risk Assessment, 

Nuclear Regulatory Commission, NUREG/CR-6823, September. 

Eide, S., et al., 2007a, Industry-Average Performance for Components and Initiating Events at U.S. 

Commercial Nuclear Power Plants, NUREG/CR-6928 (INL/EXT-06-11119), February. 
Appendix C 

Relief Valve Response Modeling 

C-1 

Appendix C 

Relief Valve Response Modeling 

Section 6 of this report presents results from the analysis of the relief valve experience. This study 

identified several pieces of previously unknown information (e.g., the fraction of initiating events where 

the relief valves are demanded, expected number of total demands, and the separation of the failure to 

open on the initial and subsequent demands). This appendix provides guidance and a demonstration of 

the use of the results in generic relief valve response models. 

The models presented herein use these data in an idealized event tree/fault tree relief valve response 

model for boiling water reactor (BWR) and pressurized water reactor (PWR) plants for a loss of 

condenser heat sink (LOCHS). The possible end states are (1) overpressure of the primary coolant 

system, (2) steam leak from the secondary system, and (3) a stuck open relief valve (SORV). 

Table C-1 shows the basic event probability and uncertainty data used in the BWR and PWR relief 

valve response models. The source column refers to the table in this report where the value was located 

and the abbreviation is the column that identifies the row from that table that was used. Section C-1 

discusses relief valve response at a BWR; Section C-2 discusses relief valve response at a PWR. 
C-2

Table C-1. Basic event data used in the demonstration models. 

Basic Event Type Mean Alpha Beta Sourcea Abbreviation Notes

MSS-SRV-DEM-PROB 3.86E−01 - - Table 11 LOCHS BWR LOCHS % Scrams with Demands

MSS-SRV-DEM-AFTER 4.78E+00 - - Table 11 LOCHS BWR LOCHS Avg Pulses per Event minus 

the initial demand equals 3.78

SRV VALVES PERPULSE 3.20E−01 - - Table 11 LOCHS BWR LOCHS % Valves Demanded per 

Pulse (modeled as 5 of 6 to fail)

MSS-SRV-FTO-ACT-1 to 6 3.54E−03 0.495 139.336 Table 31 SRV_O_1_A Fail to open initial actuation demand

MSS-SRV-FTO-ACT-AFTER-1 to 6 7.25E−04 0.499 687.777 Table 31 SRV_O_2_A Fail to open subsequent actuation demand

MSS-SRV-FTO-PRES-1 to 6 1.39E−02 0.479 33.981 Table 31 SRV_O_P Fail to open initial pressure demand

MSS-SRV-FTO-PRES-AFTER-1 to 6 1.39E−02 0.479 33.981 Table 31 SRV_O_P Fail to open subsequent pressure demand 

(no data; use initial pressure demand)

MSS-SRV-RESEAT-INIT-1 to 2 7.08E−04 0.499 704.303 Table 31 SRV_C_1_A Fail to reseat from actuation initial demand

MSS-SRV-RESEAT-AFTER-1 to 2 7.25E−04 0.499 687.777 Table 31 SRV_C_2_A Fail to reseat from actuation subsequent 

demand

MSS-SRV-RESEAT-PRES-INIT-1 to 2 1.39E−02 0.479 33.981 Table 31 SRV_C_P Fail to reseat from pressure initial demand

MSS-SRV-RESEAT-PRES-AFTER-1 to 2 1.39E−02 0.479 33.981 Table 31 SRV_C_P Fail to reseat from pressure initial demand 

(no data; use initial pressure demand)

MSS-SRV-ACT-RESEAT-REC 2.50E−01 0.338 1.014 Table 31 SRV_C_N_PR Probability of recovery from fail to reseat

MSS-SRV-PRES-RESEAT-REC 2.50E−01 0.338 1.014 Table 31 SRV_C_N_PR Probability of recovery from fail to reseat

SG-IE-PORV-DEM-PROB 2.58E+01 - - Table 11 LOCHS PWR LOCHS % Scrams with Demands

SG-PORV-AFTER-DEMANDS 2.61E+00 - - Table 11 LOCHS PWR LOCHS Avg Pulses per Event Minus 

the initial demand equals 1.61

SG PORV VALVES PER PULSE 8.87E−01 - - Table 11 LOCHS PWR LOCHS % Valves Demanded per 

Pulse (modeled as 2 of 2 to fail)

SG-IE-SVV-DEM-PROB 1.64E−01 - - Table 11 LOCHS PWR LOCHS % Scrams with Demands

SG-SVV-AFTER-DEMANDS 1.33E+00 - - Table 11 LOCHS PWR LOCHS Avg Pulses per Event Minus 

the initial demand equals 0.33

SG SVV VALVES PER PULSE 2.49E−01 - - Table 11 LOCHS PWR LOCHS % Valves Demanded per 

Pulse (modeled as 5 of 6 to fail)

RCS-IE-PORV-DEM-PROB 7.80E−02 - - Table 11 LOCHS PWR LOCHS % Scrams with Demands

RCS-PORV-AFTER-DEMANDS 8.90E+00 - - Table 11 LOCHS PWR LOCHS Avg Pulses per Event Minus 

the initial demand equals 7.9

RCS PORV VALVES PER PULSE 7.14E−01 - - Table 11 LOCHS PWR LOCHS % Valves Demanded per 

Pulse (modeled as 2 of 2 to fail)

RCS-IE-SVV-DEM-PROB 8.00E−03 - - Table 11 LOCHS PWR LOCHS % Scrams with Demands

RCS-SVV-AFTER-DEMANDS 1.00E+00 - - Table 11 LOCHS PWR LOCHS Avg Pulses per Event Minus 
Table C-1. (continued). 

C-3

Basic Event Type Mean Alpha Beta Sourcea Abbreviation Notes

the initial demand equals 0.00

RCS SVV VALVES PERPULSE 5.00E−01 - - Table 11 LOCHS PWR LOCHS % Valves Demanded per 

Pulse (modeled as 2 of 2 to fail)

SG-PORV-FTO-1 to 2-INIT 1.12E−02 0.483 42.642 Table 30 PORV_O_1 Fail to open initial demand

SG-PORV-FTO-1 to 2-OTHER 6.00E−04 0.499 831.168 Table 30 PORV_O_2 Fail to open subsequent demand

SG-SVV-FTO-1 to 6-INIT 6.46E−04 0.499 771.947 Table 31 SVV_O_1 Fail to open initial demand

SG-SVV-FTO-1 to 6-OTHER 2.54E−03 0.500 196.350 Table 31 SVV_O_2 Fail to open subsequent demand

RCS-PORV-FTO-1 to 2-INIT 1.12E−02 0.483 42.642 Table 30 PORV_O_1 Fail to open initial demand

RCS-PORV-FTO-1 to 2-OTHER 6.00E−04 0.499 831.168 Table 30 PORV_O_2 Fail to open subsequent demand

RCS-SVV-FTO-1 to 2-INIT 6.46E−04 0.499 771.947 Table 31 SVV_O_1 Fail to open initial demand

RCS-SVV-FTO-1 to 2-OTHER 2.54E−03 0.500 196.350 Table 31 SVV_O_2 Fail to open subsequent demand

SG-PORV-1 to 2-RESEAT 1.19E−02 6.500 539.718 Table 30 PORV_C_1 Fail to reseat from initial demand

SG-PORV-1 to 2-RESEAT-AFTER 6.00E−04 0.499 831.168 Table 30 PORV_C_2 Fail to reseat from subsequent demand

SG-SVV-1 to 2-RESEAT 4.63E−02 0.396 8.157 Table 31 SVV_C_1 Fail to reseat from initial demand

SG-SVV-1 to 2-RESEAT-AFTER 2.54E−03 0.496 194.780 Table 31 SVV_C_2 Fail to reseat from subsequent demand

SG-PORV-RESEAT-REC 5.42E−01 6.500 5.493 Table 30 PORV_C_PR PORV probability of recovery from fail to 

reseat

SG-SVV-RESEAT-REC 5.83E−01 10.500 7.510 Table 31 SVV_C_PR SVV probability of recovery from fail to 

reseat

RCS-PORV-1 to 2-RESEAT 1.19E−02 6.500 539.718 Table 30 PORV_C_1 Fail to reseat from initial demand

RCS-PORV-1 to 2-RESEAT-AFTER 6.00E−04 0.499 831.168 Table 30 PORV_C_2 Fail to reseat from subsequent demand

RCS-SVV-1 to 2-RESEAT 4.63E−02 0.396 8.157 Table 31 SVV_C_1 Fail to reseat from initial demand

RCS-SVV-1 to 2-RESEAT-AFTER 2.54E−03 0.496 194.780 Table 31 SVV_C_2 Fail to reseat from subsequent demand

RCS-PORV-RESEAT-REC 5.42E−01 6.500 5.493 Table 30 PORV_C_PR PORV probability of recovery from fail to 

reseat

RCS-SVV-RESEAT-REC 5.83E−01 10.500 7.510 Table 31 SVV_C_PR SVV probability of recovery from fail to 

reseat

a. The source refers to the table in the main body of this report.
C-4 

C-1. BWR Relief Valve Response to an Initiating Event 

The modeled BWR plant consists of six dual action SRVs on the main steam line. Table C-2 

summarizes the BWR relief valve responses. Figure C-1shows an event tree to model the response of the 

BWR SRVs to a LOCHS initiating event (IE). 

The model displays the required SRV demands, with the success of the opening requiring a successful 

closure. Actuation is either a manual or automatic signal to the SRVs to open. Success of the actuation 

mode is assumed to preclude the need to open the SRVs in pressure mode. An actuation mode failure is 

recovered by opening the SRVs in the pressure mode and subsequently reseating. 

Both of the opening top events model the initial lift and the estimated additional lifts identified in this 

study. The model assumes that the SRVs are in a group of six; for success, two valves must open in both 

the actuation and pressure cases. A failure to reseat is any one of the demanded SRVs failing to reseat. 

The common cause failure (CCF) of the SRVs is included where applicable. Figures C-3 through C-7 

show the fault trees that support Figure C-1

Table C-2. Sequence result summary for BWR relief valve responses. 

Name

Point 

Estimate Cut Set Count Description

BWR-LOCHS-OVERPRESSURE 1.46E−07 196 Overpressure event in the primary 

coolant

BWR-LOCHS-SORV 6.66E−04 60 Stuck open primary coolant relief valve; 

failed to reseat
C-5

INIT-EV-BWR

LOCHS at a BWR Plant

SRVDEMLOCHS

Demand of MSS SRVs 

During a LOCHS

MSSSRVFTOACT

SRVs Fail to Open in 

Actuation Mode

MSSSRVRESEAT

MSS SRVS Fail to 

Reseat Actuation Mode

MSSSRVRESEATREC

Recovery of MSS SRV Fail 

to Close Actuation Mode

MSSSRVFTOPRESSURE

SRVs Fail to Open in 

Pressure Mode

MSSSRVRESEATPRESSURE

MSS SRVs Fail to

Reseat Pressure Mode

MSSSRVRESEATREC2

Recovery of MSS SRV Fail 

to Close Pressure Mode

# End State

(Phase - PH1)

SRVs Not Demanded 

1 OK

2 OK

3 OK

4

BWR-LOCHS-SORV

5 OK

6 OK

7 BWR-LOCHS-SORV

8

BWR-LOCHS-OVERPRESSURE

Figure C-1. BWR LOCHS relief valve response event tree. 

Figure C-2. SRV demand fraction for LOCHS. 

SRVDEMLOCHS

Demand of MSS SRVs During a 

LOCHS

MSS-SRV-DEM-PROB 3.86E-01

Probability of an SRV Demand, 

Given an LOCHS
C-6

Figure C-3. BWR SRVs fail to open in actuation mode. 

MSSSRVFTOACT

SRVs Fail to Open in Actuation 

Mode

MSS-SRV-FTO-AUTO9

SRVs Fail to Open in Actuation 

Mode Initial Demand

SRV-FTO-ACT-INIT-IE

5 6

SRVs Fail to Open in Actuation 

Mode Initial Demand

MSS-SRV-FTO-ACT-1 3.54E-03

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-2 3.54E-03

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-3 3.54E-03

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-4 3.54E-03

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-5 3.54E-03

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-6 3.54E-03

SRVs Fail to Open in Actuation 

Mode Initial Demand

MSS-SRV-FTO-CCF 1.22E-04

SRV FTO CCF 5 of 6

MSS-SRV-FTO-ACT-AFTER-IE

SRVs Fail to Open in Actuation 

Mode Subsequent Demands

MSS-SRV-FTO-AUTO02

SRVs Fail to Open in Actuation 

Mode Subsequent Demand

MSS-SRV-FTO-ACT-AFTER-IE-O

5 6

SRVs Fail to Open in Actuation 

Mode Subsequent Demand

MSS-SRV-FTO-ACT-AFTER-1 7.25E-04

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-AFTER-2 7.25E-04

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-AFTER-3 7.25E-04

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-AFTER-47.25E-04

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-AFTER-5 7.25E-04

SRVs Fail to Open in Actuation 

MSS-SRV-FTO-ACT-AFTER-6 7.25E-04

SRVs Fail to Open in Actuation 

Mode Subsequent Demands

MSS-SRV-FTO-CCF-AFTER 2.50E-05

SRV FTO CCF 5 of 6 Subsequent 

Demands

MSS-SRV-DEM-AFTER 3.78E+00

Number of SRV Pulses after the 

Initial Demand LOCHS
C-7 

Figure C-4. SRVs fail to reseat on initial or subsequent demands after opening in actuation mode. 

Figure C-5. SRV recovery from failure to reseat; actuation mode. 

MSSSRVRESEATREC

Recovery of MSS SRV Fail to 

Close Actuation Mode

MSS-SRV-ACT-RESEAT-REC 2.50E-01

Recovery of MSS SRV Fail to 

Close Actuation Mode

MSSSRVRESEAT

MSS SRVS Fail to Reseat 

Actuation Mode

MSS-SRV-RESEAT-AFTER

SRVs Fail to Reseat on 

Subsequent Lifts

MSS-SRV-RESEAT-AFTER

SRVs Fail to Reseat on 

Subsequent Lift

MSS-SRV-RESEAT-AFTER-17.25E-04

MSS SRV Fail to Reseat From

MSS-SRV-DEM-AFTER 3.78E+00

Number of SRV Pulses after the 

Initial Demand LOCHS

MSS-SRV-RESEAT-INIT

SRVs Fail to Reseat on Initial Lift

MSS-SRV-RESEAT-INIT-1 7.08E-04

SRV Fail to Reseat from Actuation 

MSS-SRV-RESEAT-INIT-2 7.08E-04

SRV Fail to Reseat from Actuation 

After Initial Demand

After Initial Demand 

Actuation on Subsequent Lifts

MSS-SRV-RESEAT-AFTER-27.25E-04

MSS SRV Fail to Reseat From 

Actuation on Subsequent Lifts
C-8

Figure C-6. BWR SRVs fail to open in pressure mode. 

MSSSRVFTOPRESSURE

SRVs Fail to Open in Pressure 

Mode

MSS-SRV-FTO-PRESSURE2

SRVs Fail to Open in Pressure 

Mode Initial Demand

MSS-SRV-FTO-PRESS-INIT-IE

5 6

SRVs Fail to Open in Pressure 

Mode Initial Demand

MSS-SRV-FTO-PRES-1 1.39E-02

SRVs Fail to Open in Pressure

Mode Initial Demand

MSS-SRV-FTO-PRES-2 1.39E-02

MSS-SRV-FTO-PRES-3 1.39E-02

MSS-SRV-FTO-PRES-4 1.39E-02

MSS-SRV-FTO-PRES-5 1.39E-02

MSS-SRV-FTO-PRES-6 1.39E-02

SRVs Fail to Open in Pressure 

Mode Initial Demand

MSS-SRV-FTO-CCF-PRESS4.89E-04

SRV FTO CCF 5 of 6 Pressure 

Mode

MSS-SRV-FTO-PRESS-AFTER-IE

SRVs Fail to Open in Pressure 

Mode Subsequent Demands

MSS-SRV-FTO-PRESSURE12

SRVs Fail to Open in Pressure 

Mode Subsequent Demand

MSS-SRV-FTO-PRESS-AFTER-IE-O

5 6

SRVs Fail to Open in Pressure 

Mode Subsequent Demand

MSS-SRV-FTO-PRES-AFTER-11.39E-02

SRVs Fail to Open in Pressure 

MSS-SRV-FTO-PRES-AFTER-21.39E-02

SRVs Fail to Open in Pressure 

MSS-SRV-FTO-PRES-AFTER-31.39E-02

SRVs Fail to Open in Pressure 

MSS-SRV-FTO-PRES-AFTER-41.39E-02

SRVs Fail to Open in Pressure 

SRVs Fail to Open in Pressure 

MSS-SRV-FTO-CCF-PRESS-A 4.89E-04

SRV FTO CCF 5 of 6 Pressure 

Mode Subsequent Demands

MSS-SRV-DEM-AFTER 3.78E+00

Number of SRV Pulses after the 

Initial Demand LOCHS

SRVs Fail to Open in Pressure

Mode Initial Demand

SRVs Fail to Open in Pressure

Mode Initial Demand

SRVs Fail to Open in Pressure

Mode Initial Demand

SRVs Fail to Open in Pressure

Mode Initial Demand

MSS-SRV-FTO-PRES-AFTER-51.39E-02

MSS-SRV-FTO-PRES-AFTER-61.39E-02

SRVs Fail to Open in Pressure 

Mode Subsequent Demands

Mode Subsequent Demands

Mode Subsequent Demands

Mode Subsequent Demands

Mode Subsequent Demands

Mode Subsequent Demands
C-9 

Figure C-7. SRVs fail to reseat on initial or subsequent demands after opening in pressure mode. 

Figure C-8. SRV recovery from fail to reseat in pressure mode. 

MSSSRVRESEATREC2

Recovery of MSS SRV Fail to 

Close Pressure Mode

MSS-SRV-PRES-RESEAT-REC 2.50E-01

Recovery of MSS SRV Fail to 

Close Pressure Mode

MSSSRVRESEATPRESSURE

MSS SRV Fail to Reseat 

Pressure Mode

MSS-SRV-RESEAT-PRES-AFTER

SRVs Fail to Reseat in Pressure 

Mode on Subsequent Lifts

MSS-SRV-RESEAT-AFTER-PRESS

SRVs Fail to Reseat on 

Subsequent Lift

MSS-SRV-RESEAT-AFTER-17.25E-04

MSS SRV Fail to Reseat From

Actuation on Subsequent Lifts 

MSS-SRV-RESEAT-AFTER-27.25E-04

MSS SRV Fail to Reseat From 

Actuation on Subsequent Lifts

MSS-SRV-DEM-AFTER 3.78E+00

Number of SRV Pulses after the 

Initial Demand LOCHS

MSS-SRV-RESEAT-PRES-INIT

SRVs Fail to Reseat Pressure 

Mode on Initial Lift

MSS-SRV-RESEAT-INIT-1

SRV Fail to Reseat from Actuation 

After Initial Demand

MSS-SRV-RESEAT-INIT-2

SRV Fail to Reseat from Actuation 

After Initial Demand

7.08E-04

7.08E-04
C-10 

C-2. PWR Relief Valve Response to Initiating Event 

The PWR-modeled plant consists of two steam generators (SGs) in the secondary system. 

Each SG has one power-operated relief valve (PORV) (atmospheric dump) and three code safety 

valves (SVVs). The reactor coolant system (RCS) has two PORVS and two SVVs on the steam 

generator. Table C-3 summarizes the PWR responses. Figures C-9 and C-10 show an event tree 

that models the response of the PWR relief valves to a LOCHS initiating event (IE). 

The assumed initial plant response is the demand of the SG relief valves. First the SG 

PORVs are demanded, then the SG SVVs. As with the BWR valves, the success of the opening 

requires a successful closure. The demand of the SG SVVs occurs on either failure of the SG 

PORVs or as a fraction of the successful SG PORV openings. 

If the SG relief valves fail, the RCS relief valves are demanded: PORVs first and then the 

SVVs. A successful opening requires a successful closure of each opened relief valve. The 

demand of the RCS PORVs and SVVs occurs on either failure of the SG relief valves or as a 

fraction of the successful SG relief valve openings. 

All of the relief valves opening top events model the initial lift and the estimated additional 

lifts identified in this study. The model assumes that the SG SVVs are in a group of six, and that 

two of the six openings are necessary for success. The CCF of the PORVs and SVVs are 

included where applicable. Figures C-11 to C-25 show the fault trees that support Figure C-9. 

Table C-3. Sequence result summary for PWR relief valve responses. 

Name

Point 

Estimate

Cut 

Set 

Count Description

PWR-LOCHS-OVERPRESSURE 3.78E−15 206 Overpressure event in the primary coolant

PWR-LOCHS-SORV 1.43E−03 3096 Stuck open primary coolant relief valve; 

failed to reseat

PWR-LOCHS-STEAMLEAK 3.60E−03 40 Steam release through secondary reliefs; 

failed to close
C-11

Figure C-9. PWR LOCHS relief valve response event tree (part 1 of 2). 

INIT-EV-PWR

LOCHS at a PWR Plant

SGPORVDEM

Demand of SG PORVs 

During a LOCHS

SGDEMPORVOPEN

SG PORVs Open on 

Demand

SGPORVRESEAT

SG PORV Reseat

SGPORVRESEATREC

Recovery of SG PORVs 

Fail to Reseat

SGSVVDEM

Demand of SG SVVs 

During LOCHS

SGDEMSVVOPEN

SG Safety Relief Valves 

Open on Demand

SGSVVRESEAT

SG SVVs Reseat

SGSVVRESEATRECOVERY

Recovery of SG SVVs Fail 

to Reseat

RCSPORVDEM

Demand of RCS PORVs 

During LOCHS

# End State

(Phase - PH1)

SG PORVs not demanded 1 OK

SG SVVs not demanded 2 OK

3 OK

4

LOCHSRESPONSE-PWR-RCS

5 OK

6

LOCHSRESPONSE-PWR-RCS

7 PWR-LOCHS-STEAMLEAK

8

LOCHSRESPONSE-PWR-RCS

9 OK

10 OK

11 LOCHSRESPONSE-PWR-RCS

12 OK

13 LOCHSRESPONSE-PWR-RCS

14 PWR-LOCHS-STEAMLEAK

15 LOCHSRESPONSE-PWR-RCS

16 PWR-LOCHS-STEAMLEAK

17 OK

18 LOCHSRESPONSE-PWR-RCS

19 OK

20 LOCHSRESPONSE-PWR-RCS

21 PWR-LOCHS-STEAMLEAK

22 LOCHSRESPONSE-PWR-RCS
C-12

Figure C-9. PWR LOCHS relief valve response event tree (part 2 of 2). 

RCSPORVDEM

Demand of RCS PORVs 

During LOCHS

RCSDEMPORVOPEN

RCS PORVs Open on 

Demand

RCSPORVRESEAT

RCS PORVs Reseat

RCSPORVRESEATREC

Recovery of RCS PORVs 

Fail to Reseat

RCSSVVDEM

Demand of RCS SVVs 

During LOCHS

RCSDEMSVVOPEN

RCS SVVs Open on 

Demand

RCSSVVRESEAT

RCS SVVs Reseat

RCSSVVRESEATRECOVERY

Recovery of RCS SVVs 

Fail to Reseat

# End State

(Phase - PH1)

1 OK

2 OK

3 OK

4 PWR-LOCHS-SORV

5 PWR-LOCHS-OVERPRESSURE

6 OK

7 OK

8 OK

9 PWR-LOCHS-SORV

10 PWR-LOCHS-OVERPRESSURE

11 OK

12 OK

13 PWR-LOCHS-SORV

14 PWR-LOCHS-OVERPRESSURE
C-13 

Figure C-10. SG PORV demand fraction for LOCHS. 

Figure C-11. SG PORVs fail to open on demand. 

SGDEMPORVOPEN

SG PORVs Open on Demand

SG-DEM-PORV2

SG PORVs FTO Initial Demand

SG-PORV-FTO-INIT

SG PORVs FTO Initial Demand

SG-PORV-FTO-1-INIT 1.12E-02

MSS PORV FTO Initial Demand

SG-PORV-FTO-2-INIT 1.12E-02

MSS PORV FTO Initial Demand

SG-PORV-FTO-CCF 5.80E-04

SG PORVs FTO CCF

SG-DEM-PORV3

SG PORVs FTO Subsequent 

Demands

SG-PORV-FTO-AFTER

SG PORVs FTO Subsequent 

Demands

SG-PORV-AFTER-DEMANDS 1.61E+00

SG PORV Subsequent Demands

SG-PORV-FTO-1-OTHER 6.00E-04

MSS PORV FTO Subsequent 

SG-PORV-FTO-2-OTHER 6.00E-04

MSS PORV FTO Subsequent 

Demands

SG-PORV-FTO-CCF-AFTER3.11E-05

SG PORVs FTO CCF Subsequent 

Demands

SGPORVDEM

Demand of SG PORVs During a 

LOCHS

SG-IE-PORV-DEM-PROB 2.58E-01

Probability of a Demand of the SG 

PORVs, Given a LOCHS
C-14 

SGPORVRESEAT

SG PORV Reseat

SG-PORV-RESEAT2

SG PORVs Fail to Reseat on Initial 

Lift

SG-PORV-1-RESEAT 1.19E-02

SG PORV Fail to Reseat Initial 

SG-PORV-2-RESEAT 1.19E-02

SG PORV Fail to Reseat Initial 

Demand

SG-PORV-RESEAT3

SG PORVs Fail to Reseat on 

Subsequent Lift

SG-PORV-RESEAT32

SG PORVs Fail to Reseat on 

Subsequent Lift

SG-PORV-1-RESEAT-AFTER6.00E-04

SG PORVs Fail to Reseat

Subsequent Demand

SG-PORV-AFTER-DEMANDS1.61E+00

SG PORV Subsequent Demands

SG PORVs Fail to Reseat 

Subsequent Demand

SG-PORV-2-RESEAT-AFTER6.00E-04

Figure C-12. SG PORVs fail to reseat on initial or subsequent demands after opening. 
C-15 

Figure C-13. Recovery of the SG PORVs failure to reseat. 

Figure C-14. SG SVV demand fraction for LOCHS. 

SGSVVDEM

Demand of SG SVVs During 

LOCHS

SG-IE-SVV-DEM-PROB 1.64E-01

Probability of SG SVV Demand 

During LOCHS

SGPORVRESEATREC

Recovery of SG PORVs Fail to 

Reseat

SG-PORV-RESEAT-REC 5.42E-01

Recovery of SG PORVs Fail to 

Reseat
C-16

Figure C-15. SG SVVs fail to open on demand.

SGDEMSVVOPEN

SG Safety Relief Valves Open on 

Demand

SG-DEM-SVV2

SG SVVs Fail to Open on 

Subsequent Demands

SG-DEM-SVV20

SG SVVs Fail to Open on 

Subsequent Demands

SG-SVV-FTO-OTHER

5 6

SG SVVs Fail to Open on 

Subsequent Demands

SG-SVV-FTO-1-OTHER 2.54E-03

MSS SVV Fail to Open 

SG-SVV-FTO-2-OTHER 2.54E-03

MSS SVV Fail to Open 

SG-SVV-FTO-3-OTHER 2.54E-03

MSS SVV Fail to Open 

SG-SVV-FTO-4-OTHER 2.54E-03

MSS SVV Fail to Open 

SG-SVV-FTO-5-OTHER 2.54E-03

MSS SVV Fail to Open 

SG-SVV-FTO-6-OTHER 2.54E-03

MSS SVV Fail to Open 

Subsequent Demands

SG-SVV-AFTER-DEMANDS 3.30E-01

SG SVV Subsequent Demands

SG-SVV-FTO-CCF-AFTER 8.80E-05

SG SVVs FTO 5 of 6 CCF 

Subsequent Demands

SG-DEM-SVV3

SG Code Safeties Fail to Open 

Initial Demand

SG-SVV-FTO-INIT

5 6

SG Code Safeties Fail to Open 

Initial Demand

SG-SVV-FTO-1-INT 6.46E-04

SG SVV Fail to Open Initial Demand

SG-SVV-FTO-2-INT 6.46E-04

SG SVV Fail to Open Initial Demand

SG-SVV-FTO-3-INT 6.46E-04

SG SVV Fail to Open Initial Demand

SG-SVV-FTO-4-INT 6.46E-04

SG SVV Fail to Open Initial Demand

SG-SVV-FTO-5-INT 6.46E-04

SG SVV Fail to Open Initial Demand

SG-SVV-FTO-6-INT 6.46E-04

SG SVV Fail to Open Initial Demand 

SG-SVV-FTO-CCF 2.22E-05

SG SVVs FTO 5 of 6 CCF

Subsequent Demands

Subsequent Demands

Subsequent Demands

Subsequent Demands

Subsequent Demands
C-17 

Figure C-16. SG SVVs on initial or subsequent demands after opening. 

Figure C-17. Recovery of SG SVVs fail to reseat. 

SGSVVRESEATRECOVERY

Recovery of SG SVVs Fail to 

Reseat

SG-SVV-RESEAT-REC 5.83E-01

Recovery of SG SVVs Fail to 

Reseat

SGSVVRESEAT

SG SVVs Reseat

SG-SVV-RESEAT6

Reseat After Initial Demand

SG-SVV-1-RESEAT 4.63E-02

SG SVV Fail to Reseat After Initial

Demand

SG-SVV-2-RESEAT 4.63E-02

SG SVV Fail to Reseat After Initial 

Demand

SG-SVV-RESEAT7

Reseat on Subsequent Demands

SG-SVV-RESEAT70

Reseat on Subsequent Demands

SG-SVV-1-RESEAT-AFTER2.54E-03

SG SVV Fail to Reseat in

Subsequent Demands

SG-SVV-2-RESEAT-AFTER 2.54E-03

SG SVV Fail to Reseat in 

Subsequent Demands

SG-SVV-AFTER-DEMANDS3.30E-01

SG SVV Subsequent Demands
C-18 

Figure C-18. RCS PORV demand fraction for LOCHS 

Figure C-19. RCS PORVs fail to open on demand. 

RCSDEMPORVOPEN

RCS PORVs Open on Demand

RCS-DEM-PORV3

RCS PORVs Fail to Open Initial 

Demand

RCS-PORV-FTO-INIT

RCS PORVs Fail to Open Initial 

Demand

RCS-PORV-FTO-1-INIT 1.12E-02

RCS PORV FTO Initial Demand

RCS-PORV-FTO-2-INIT 1.12E-02

RCS PORV FTO Initial Demand

RCS-PORV-FTO-CCF 5.80E-04

RCS PORVs FTO CCF

RCS-DEM-PORV4

RCS PORVs Fail to Open 

Subsequent Demand

RCS-DEM-PORV40

RCS PORVs Fail to Open 

Subsequent Demand

RCS-PORV-FTO-1-OTHER 6.00E-04

RCS PORV FTO Subsequent Demands

RCS-PORV-FTO-2-OTHER 6.00E-04

RCS PORV FTO Subsequent Demands

RCS-PORV-AFTER-DEMANDS7.90E+00

RCS PORV Subsequent Demands

RCS-PORV-FTO-CCF-AFTER 3.11E-05

RCS PORVs FTO CCF 

Subsequent Demands

RCSPORVDEM

Demand of RCS PORVs During 

LOCHS

RCS-IE-PORV-DEM-PROB 7.80E-02

Probability of a demand of the 

RCS PORVs, given a LOCHS
C-19 

Figure C-20. RCS PORVs on initial or subsequent demands after opening. 

RCSPORVRESEAT

RCS PORVs Reseat

RCS-PORV-RESEAT2

Reseat After Initial Demand

RCS-PORV-1-RESEAT 1.19E-02

RCS PORV Fail to Reseat After

Initial Demand

RCS-PORV-2-RESEAT 1.19E-02

RCS PORV Fail to Reseat After 

Initial Demand

RCS-PORV-RESEAT3

Reseat on Subsequent Demands

RCS-PORV-RESEAT31

Reseat on Subsequent Demands

RCS-PORV-1-RESEAT-AFTER6.00E-04

RCS PORV Fail to Reseat

Subsequent Demand

RCS-PORV-2-RESEAT-AFTER6.00E-04

RCS PORV Fail to Reseat 

Subsequent Demand

RCS-PORV-AFTER-DEMANDS7.90E+00

RCS PORV Subsequent 

Demands
C-20 

Figure C-21. Recovery of the RCS PORVs failure to reseat. 

Figure C-22. RCS SVV demand fraction for LOCHS 

RCSSVVDEM

Demand of RCS SVVs During 

LOCHS

RCS-IE-SVV-DEM-PROB 8.00E-03

Probability of a Demand of the 

RCS SVVs, Given a LOCHS

RCSPORVRESEATREC

Recovery of RCS PORVs Fail to 

Reseat

RCS-PORV-RESEAT-REC 5.42E-01

Recovery of RCS PORVs Fail to 

Reseat
C-21 

Figure C-23. RCS SVVs fail to open on demand. 

RCSDEMSVVOPEN

RCS SVVs Open on Demand

RCS-DEM-SVV0

RCS Code Safeties Fail to Open 

Initial Demand

RCS-DEM-SVV00

RCS Code Safeties Fail to Open 

Initial Demand

RCS-SVV-FTO-1-INIT 6.46E-04

RCS SVV Fail to Open Initial

Demand

RCS-SVV-FTO-2-INIT 6.46E-04

RCS SVV Fail to Open Initial 

Demand

RCS-SVV-FTO-CCF 5.60E-05

RCS SVVs FTO CCF

RCS-DEM-SVV1

RCS SVVs Fail to Open on 

Subsequent Demands

RCS-DEM-SVV10

RCS SVVs Fail to Open on 

Subsequent Demands

RCS-SVV-FTO-1-OTHER 2.54E-03

RCS SVV Fail to Open

Subsequent Demands

RCS-SVV-FTO-2-OTHER 2.54E-03

RCS SVV Fail to Open 

Subsequent Demands

RCS-SVV-FTO-CCF-AFTER2.20E-04

RCS SVVs FTO CCF Subsequent 

Demands
C-22 

Figure C-24. RCS SVVs fail to reseat on initial or subsequent demands after opening. 

Figure C-25. Recovery of the RCS SVVs failure to reseat. 

RCSSVVRESEATRECOVERY

Recovery of RCS SVVs Fail to 

Reseat

RCS-SVV-RESEAT-REC 5.83E-01

Recovery of RCS SVVs Fail to 

Reseat

RCSSVVRESEAT

RCS SVVs Reseat

RCS-SVV-RESEAT2

Reseat After Initial Demand

RCS-SVV-1-RESEAT 4.63E-02

RCS SVV Fail to Reseat After

Initial Demand

RCS-SVV-2-RESEAT 4.63E-02

RCS SVV Fail to Reseat After 

Initial Demand

RCS-SVV-RESEAT3

Reseat on Subsequent Demands

RCS-SVV-RESEAT31

RCS SVV Fail to Reseat In 

Subsequent Demands

RCS-SVV-1-RESEAT-AFTER2.54E-03

RCS SVV Fail to Reseat in

Subsequent Demands

RCS-SVV-2-RESEAT-AFTER2.54E-03

RCS SVV Fail to Reseat in 

Subsequent Demands

RCS-SVV-AFTER-DEMANDS0.00E+00

RCS SVV Subsequent Demands