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A “Deterministic” Approach to Reliability of Repairable Systems

A “Deterministic” Approach to Reliability of Repairable Systems. Paul Nelson (TAMU) & Shuwen “Eric” Wang (ABS Consulting). Background. DeVooght presentation in Atlant a

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A “Deterministic” Approach to Reliability of Repairable Systems

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  1. A “Deterministic” Approach to Reliability of Repairable Systems Paul Nelson (TAMU) & Shuwen “Eric” Wang (ABS Consulting)

  2. Background • DeVooght presentation in Atlanta • “… first reviewed … a unified summary of results on dynamic reliability that follow from the integral form of the Chapman–Kolmogorov (C–K) equation… he … closed with a very provocative comparison between dynamic reliability and neutron transport theory, suggesting that perhaps this could be a new area in which transport theorists might be able to make important contributions.” • but D solves the C-K equations by MC • can also do deterministically? • Mid 2000s interest in Risk-Informed Asset Management at NPPs

  3. Entry-time Process (Motivation) • Uses discrete algorithm to solve the Chapman-Kolmogorov (C-K) equations • Allows time-dependent transition rates • Can be used as a substitution where simulation is used • Definition of states is flexible, depending on need of particular applications

  4. Entry-time Process (Formal) • A marked point process {N(t),Zn}, where {N(t)}is a point process with no simultaneous arrivals • Mark Zn associated to arrival time Tn(more completely, to sojourn period [Tn, Tn +Sn+1]) • Rates of transition λij(τ,t) from state j to state i are specified as a function of calendar time t and entry time t

  5. How Does Entry-time Process Work? • Determine the time-dependant state probabilities • The generalized state-transition equations:

  6. A Pictorial Representation

  7. Finite-difference Methodology Any P(m,n) not along diagonal : Any P(n,n) along diagonal :

  8. Comparison to Simulation for a 3-state example State 1: In service; State 2: Out of service for PM; State 3: Out for corrective maintenance. Tr=3 years; Tpm=0.2 years; Tcm=0.4 years 10

  9. Comparison of Results 11

  10. Published Details • Nelson & Wang, Reliability Engineering and System Safety (2007), for details and further verification against simple models • Same authors, various conference papers, and Wang PhDdissertation (TAMU, Nucl. Engnrg., 2008) for verification against increasingly more realistic models. • Following application not (yet) published

  11. Toward a NPP Application A PM-Based scenario, for a NPP SSC for which time-dependent transition rate is important Failure rate (aging or infant mortality) Transition rates due to different PM Policies Failure data for the SSC must be available for a direct application of entry-time process An extraction methodology must exist that will permit the time-dependent transition rates to be obtained from the failure data no BNL or ENDF to the rescue 13

  12. Data—the Challenge • Time-dependent failure data are not easy to acquire from any single NPP • Need to find the “best fit” for the data to get time-dependent failure rates • INPO-EPIX database currently is the best database available for such applications

  13. Data Selection for Main Generators Option 1: Query failure records for all main generators manufactured by Westinghouse Option 2: Query all the failure records for main generators manufactured by Westinghouse that have model numbers similar to those of the STP generators Option 3: Query the failure records for main generator with STP model number only 16

  14. Data Interpretation Option 1: Interval Censored: Discovery by inspection procedure Option 2: No Censored Data (Exact failure): Discovery by alarm procedure 17

  15. States and Transitions(Main Generators) • Four States: • State 1 :In-Service • State 2: Out-of-Service for PM • State 3: Out-of-Service for Non-catastrophic failure • State 4: Out-of-Service for Catastrophic failure • Transition Relations:

  16. Annual Cost/Loss for each state

  17. NPV Cost and Survival Function for Different PM Policies

  18. Analysis of Results • The reliability performance of the main generator system tends to be better with a shorter maintenance period • The financial performance (NPV) tends to be better when the replacement period is close to 9 years • The $200M difference is about 10% of the net value of a typical existing NPP • Considering the requirement to minimize the NPV cost and still get a better reliability performance, replacement period of 9 years is preferred • There are no significant effects in decision making process when using Weibull distribution or lognormal distribution

  19. Thanks to Everybody!

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