Unavailability estimation of shutdown system of a fast reactor by Monte Carlo simulation

Abstract The safety systems of fast breeder reactors are designed to be highly reliable and have small failure probabilities. Traditionally fault tree technique is employed to analyse such systems. However fault tree approach has limitations in analyzing dependence between components and phased mission objectives. In this paper the application of Monte Carlo simulation technique to estimate the unavailability and Mean Time To Failure of shutdown system of a fast reactor is studied. Different biasing schemes are also compared for performance. Balanced failure biasing scheme gives better variance reduction as compared to simple failure biasing and direct Monte Carlo simulation. The balanced failure biasing scheme for system hardware evolution is integrated with physical process for a simple example system. The probability of crossing the safety limits on temperature is estimated.

[1]  Peter W. Glynn,et al.  A Markov chain perspective on adaptive Monte Carlo algorithms , 2001, Proceeding of the 2001 Winter Simulation Conference (Cat. No.01CH37304).

[2]  Vivek S. Borkar,et al.  Adaptive Importance Sampling Technique for Markov Chains Using Stochastic Approximation , 2006, Oper. Res..

[3]  Marvin K. Nakayama A characterization of the simple failure-biasing method for simulations of highly reliable Markovian Systems , 1994, TOMC.

[4]  C. Papadopoulos A New Technique for MTTF Estimation in Highly Reliable Markovian Systems , 1998, Monte Carlo Methods Appl..

[5]  Elmer E Lewis,et al.  Introduction To Reliability Engineering , 1987 .

[6]  Perwez Shahabuddin,et al.  Importance sampling for the simulation of highly reliable Markovian systems , 1994 .

[7]  Enrico Zio,et al.  Procedures of Monte Carlo transport simulation for applications in system engineering , 2002, Reliab. Eng. Syst. Saf..

[8]  Ad Ridder,et al.  Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy , 2005, Ann. Oper. Res..

[9]  Philip Heidelberger,et al.  A Unified Framework for Simulating Markovian Models of Highly Dependable Systems , 1992, IEEE Trans. Computers.

[10]  Mohammad Modarres,et al.  Reliability engineering and risk analysis : a practical guide , 2016 .

[11]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[12]  Marvin K. Nakayama,et al.  Techniques for fast simulation of models of highly dependable systems , 2001, IEEE Trans. Reliab..

[13]  Bruno Tuffin,et al.  Approximating zero-variance importance sampling in a reliability setting , 2011, Ann. Oper. Res..

[14]  Gerardo Rubino,et al.  Rare Event Simulation using Monte Carlo Methods , 2009 .

[15]  B. Tuffin Bounded normal approximation in simulations of highly reliable Markovian systems , 1999 .

[16]  Enrico Zio,et al.  Monte Carlo approach to PSA for dynamic process systems , 1996 .

[17]  Elmer E Lewis,et al.  Monte Carlo simulation of Markov unreliability models , 1984 .

[18]  Enrico Zio,et al.  The Monte Carlo Simulation Method for System Reliability and Risk Analysis , 2012 .

[19]  Tunc Aldemir,et al.  A survey of dynamic methodologies for probabilistic safety assessment of nuclear power plants , 2013 .

[20]  Gerardo Rubino,et al.  MTTF Estimation using importance sampling on Markov models , 2002, Monte Carlo Methods Appl..

[21]  Vinh N. Dang,et al.  A dynamic event tree informed approach to probabilistic accident sequence modeling: Dynamics and variabilities in medium LOCA , 2015, Reliab. Eng. Syst. Saf..

[22]  Enrico Zio,et al.  Nonlinear Monte Carlo reliability analysis with biasing towards top event , 1993 .

[23]  Christos Alexopoulos,et al.  Estimating reliability measures for highly-dependable Markov systems, using balanced likelihood ratios , 2001, IEEE Trans. Reliab..