SIMPLE METHOD TO ACCOUNT FOR THE STATE OF KNOWLEDGE CORRELATION

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1 SIMPLE METHOD TO ACCOUNT FOR THE STATE OF KNOWLEDGE CORRELATION PSA 017, Pittsburgh, PA September 017 Michael Lloyd Risk Informed Solutions Consulting Services, Inc. Jason Hall Entergy Corporation/Arkansas Nuclear One Ross C. Anderson ENERCON Corporation David S. Teolis Westinghouse Electric Corporation LLC 1

2 Incentive for Paper PRA Standard SR QU-A3 requires accounting of SOKC, when significant, i.e., ISLOCA scenarios, which tend to include terms that use the same failure rates. Statistical sampling processes (e.g., Monte Carlo using UNCERT) automatically account for the SOKC effect; but, do not provide cutset-level results. Cutset quantifiers (e.g., CAFTA) DO NOT account for SOKC. But, cutset results are typically used in many plant applications, e.g., Maintenance Rule (a)(4). Therefore, we need a method to account for SOKC in cutset results.

3 Objectives of Paper DESCRIBE State-of-Knowledge Correlation (SOKC) And its IMPACT on Risk Results DEVELOP SOKC MULTIPLIERS to account for SOKC in cutset results DEMONSTRATE a Simple and Practical METHOD to INCORPORATE the SOKC into Cutset Results (WITHOUT Performing an Uncertainty Analysis) 3

State of Knowledge Correlation - Definition PRA Standard (ASME Standard RA-Sb-013) defines the state-of-knowledge correlation: the correlation that arises between sample values when performing

4 State of Knowledge Correlation - Definition PRA Standard (ASME Standard RA-Sb-013) defines the state-of-knowledge correlation: the correlation that arises between sample values when performing uncertainty analysis for cutsets consisting of basic events using a sampling approach (such as the Monte Carlo method); when taken into account, this results, for each sample, in the same value being used for all basic event probabilities to which the same data applies. 4

State of Knowledge Correlation - Impact From a practical perspective, SOKC impact whenever a cutset contains multiple terms that use the same failure rate data, the mean frequency of

5 State of Knowledge Correlation - Impact From a practical perspective, SOKC impact whenever a cutset contains multiple terms that use the same failure rate data, the mean frequency of the cutset will be greater than the product of the mean probabilities of its terms. The SOKC effect is due to the fact that the terms in a cutset are distributions, not point values. 5

6 Development of SOKC Multiplier Consider an ISLOCA pathway containing two normally-closed motor-operated valves (e.g., MOV1 and MOV). Figure 1 depicts this pathway. Consider one of the cutsets contributing to the ISLOCA initiating event for this pathway: the internal leakage failure of both MOV1 and MOV. 6

7 Development of SOKC Multiplier (cont d) Point Estimate-generated (e.g., CAFTA) Internal Leakage Cutset Probability, P MMMM, III. LLLL = Probability MIII Probability MII = λ MMMT λ MMMT = λ MMM T where, T = Exposure interval λ MMM = Mean failure rate based on MOV Internal Leakage (MIL) probability density function (pdf) 7

8 Development of SOKC Multiplier (cont d) Reminder: Several failure rate pdfs are being used in the industry: Gamma distribution, recommended by NUREG/CR-698 for failures with units of failures/time: f G λ; α, β = βα Γ α λα 1 e λλ, where λ, α, β > 0. Beta distribution, recommended by NUREG/CR-698 for failures with units of failures/demand: f B λ; α, β = Γ α+β Γ α Γ β λα 1 (1 λ) β 1, where λ, α, β > 0. Lognormal distribution has also been used: f LL λ; μ, σ = 1 σ π e λ μ σ, where λ, μ, σ > 0. 8

9 Development of SOKC Multiplier (cont d) Point Estimate-generated (e.g., CAFTA) Internal Leakage Cutset Probability, P MMMM, III. LLLL = Probability MIII Probability MII = λ MMMT λ MMMT = λ MMM T = λf G λ; α MMM, β MMM dd 0 = E λ MMM T where, T = Exposure interval T E λ MMM = Mean value (first moment) of MOV Internal Leakage (MIL) failure rate gamma pdf 9

10 Development of SOKC Multiplier (cont d) Monte Carlo calculated Internal Leakage Cutset Probability, samples where, P MMMM, III. LLLL = 1 N N i=1 P MMMM, III. LLLL = 1 N λ N i=1 MMM,iT λ MMM,i T N = 1 λ N i=1 MMM,i * T N λ f G λ; α MMM, β MMM dd 0, where N= no. of, where λ MMM,i is sampled * T E λ MMM * T (EUREKA MOMENT!) E λ MMM Second Moment of λ MMM 10

11 Development of SOKC Multiplier (cont d) For ISLOCA pathway containing normally-closed motoroperated valves (e.g., MOV1 and MOV) in series, all using the same leakage failure rate (λ MMM ). To account for SOKC impact, multiply the CAFTA-calculated cutset probability by the Ratio of the second moment divided by the square of the first moment: P E λ P = MMM E λ MMM This factor is greater than one. SOKC Multiplier for cutset w/ BEs using MOV ILS failure rate 11

12 Development of SOKC Multiplier (cont d) For ISLOCA pathway containing 3 normally-closed motoroperated valves (e.g., MOV1, MOV, MOVn) in series, all using the same leakage failure rate (λ MIL ). To account for SOKC impact, multiply the CAFTA-calculated cutset probability by the Ratio of the third moment divided by the cube of the first moment: P E λ 3 P = MMM E λ MMM This factor is greater than one. 3 SOKC Multiplier for cutset w/3 BEs using MOV ILS failure rate 1

13 Development of SOKC Multiplier (cont d) IN GENERAL, for ISLOCA pathway containing n normallyclosed motor-operated valves (e.g., MOV1, MOV, MOVn) in series, all using the same leakage failure rate (λ MIL ). To account for SOKC impact, multiply the CAFTA-calculated cutset probability by the Ratio of the nth moment divided by the nth power of the first moment: P P = E λ n MMM E λ MMM This factor is greater than one. n SOKC Multiplier for cutset w/ n BEs using MOV ILS failure rate 13

14 Development of SOKC Multiplier (cont d) EVEN MORE GENERAL, in order to correct for SOKC, SSSS MMMMMMMMMM λ, n E λn E λ should be applied to any cutset containing n BEs that use the same failure rate (λ). where, E λ n = n th moment of the component failure rate probability density function, f λ SOKC Multipliers applied to cutsets are always 1. n 14

15 Calculating SOKC Multiplier Values Gamma Distribution Moments Mom. Moment Equation E λ α β E λ α α + 1 E λ 3 E λ 4 Gamma Distribution SOKC Multipliers β α β 3 + 3α α α β α + 6α 7α 3 Mult.. SOKC Multiplier Equation SSSSS 1 SSSSS α + 1 α SSSSS 1 α + 3α α SSSSS 1 α α + 6α 7α 3 SOKCMIL = 4.33 SOKCMIL3 = 31. SOKCMIL4 = per Table 5-1, MIL NUREG/CR-698 (Feb. 007, 010) 15

16 QRECOVER Rule to Apply SOKC Multiplier SOKC Multipliers can be applied to cutset results using the EPRI QRECOVER MISSION TIME EVENT (MTE) rules. QRECOVER MTE Recovery Rule That Applies SOKC Multipliers in the Example ISLOCA Model. **RECOVERY RULES** ; This QRECOVER rule file uses the MTE ; command to apply SOKC Multipliers **MISSION TIME EVENTS** 1 MOV-ILL-* list of MIL BEs ; The following rule corrects for SOKC in cutsets ; with MOV large Internal Leakage (MIL) failure BEs SOKC **RECOVERY** SOKCMIL 4.33 Multiplier MTE1= for MIL Rules can be extended to apply to all applicable SOKC 16

17 QRECOVER Rule for SOKC Multipliers (cont d) Paper demonstrates its application in a relatively complex ISLOCA example and demonstrates that results are the same as generated by uncertainty analysis. 17

18 Limitations of SOKC Multipliers 1) SOKC Multipliers should NOT be applied to cutsets to be used in Monte Carlo (or similar) uncertainty analyses, because the presence of these multipliers would doublecount SOKC effect. ) SOKC-adjusted cutset results may be slightly incomplete due to the fact that the SOKC multipliers are applied after cutset quantification and are greater than one. This issue can be avoided by applying a factor equal to the largest SOKC Multiplier to the top gate(s) of ISLOCA logic in the model prior to quantification. ) SOKC Multipliers may cause a slight overestimation of calculated risk importance values for basic events impacted by the SOKC. 18

19 Conclusions SOKC Multipliers can be developed and applied to ISLOCA cutsets using QRECOVER rule files in order to address the SOKC as required by SR QU-A3 of the PRA Standard to Meet Category II. Although application of the SOKC Multipliers does not dispense with the need to perform uncertainty analysis, their application of SOKC Multipliers does provide a simple alternative method to the use of uncertainty analysis to assure that the SOKC is reflected in the nominal cutset results. It is recommended for general use in the industry Its use will allow the PRA analyst to WORK SMARTER, NOT HARDER! 19

20 CONTACT FOR ADDITIONAL INFORMATION: Mike Lloyd 0

21 QUESTIONS? 1

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