Dependability estimation for non-Markov consecutive-k-out-of-n: F repairable systems by fast simulation

A model of consecutive-k-out-of-n: F repairable system with non-exponential repair time distribution and (k-1)-step Markov dependence is introduced in this paper along with algorithms of three Monte Carlo methods, i.e. importance sampling, conditional expectation estimation and combination of the two methods, to estimate dependability of the non-Markov model including reliability, transient unavailability, MTTF, and MTBF. A numerical example is presented to demonstrate the efficiencies of above methods. The results show that combinational method has the highest efficiency for estimation of unreliability and unavailability, while conditional expectation estimation is the most efficient method for estimation of MTTF and MTBF. Conditional expectation estimation seems to have overall higher speedups in estimating dependability of such systems.

[1]  Marnix J. J. Garvels,et al.  The splitting method in rare event simulation , 2000 .

[2]  James C. Fu,et al.  Reliability of Consecutive-k-out-of-n:F Systems with (k-1)-step Markov Dependence , 1986, IEEE Transactions on Reliability.

[3]  Gregory Levitin.  Common supply failures in linear multi-state sliding window systems , 2003, Reliab. Eng. Syst. Saf..

[4]  Yuan Lin Zhang,et al.  Repairable consecutive-2-out-of-n:F system , 1996 .

[5]  Lirong Cui,et al.  Reliabilities of Consecutive-k Systems , 2011, Network Theory and Applications.

[6]  Pierre-Etienne Labeau,et al.  Partially unbiased estimators for reliability and availability calculations , 2000 .

[7]  Xi Zhizhong,et al.  A new method for the fast simulation of models of highly dependable Markov system , 2005 .

[8]  M. Chao,et al.  Survey of reliability studies of consecutive-k-out-of-n:F and related systems , 1995 .

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

[10]  Sandeep Juneja,et al.  Fast Simulation of Markov Chains with Small Transition Probabilities , 2001, Manag. Sci..

[11]  Yeh Lam,et al.  Analysis of repairable consecutive-2-out-of-n : F systems with Markov dependence , 1999, Int. J. Syst. Sci..

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

[13]  Guangping Ge,et al.  Exact reliability formula for consecutive-k-out-of-n:F systems with homogeneous Markov dependence , 1990 .

[14]  Ming Jian Zuo,et al.  A method for evaluation of reliability indices for repairable circular consecutive-k-out-of-n: F systems , 2003, Reliab. Eng. Syst. Saf..

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

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

[17]  Gregory Levitin.  Consecutive k-out-of-r-from-n system with multiple failure criteria , 2004, IEEE Transactions on Reliability.

[18]  Lirong Cui,et al.  On a generalized k-out-of-n system and its reliability , 2005, Int. J. Syst. Sci..

[19]  James C. Fu,et al.  On Reliability of a Large Consecutive-k-out-of-n:F System with (k - 1)-step Markov Dependence , 1987, IEEE Transactions on Reliability.

[20]  Markos V. Koutras,et al.  Consecutive k-out-of-n systems with maintenance , 1992 .

[21]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[22]  Yeh Lam,et al.  Reliability of consecutive-k-out-of-n: G repairable system , 1998, Int. J. Syst. Sci..

[23]  Yeh Lam,et al.  A general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k-1)-step Markov dependence , 2001, Eur. J. Oper. Res..

[24]  Stavros Papastavridis,et al.  Reliability of a Consecutive-k-out-of-n:F System for Markov-Dependent Components , 1987, IEEE Transactions on Reliability.

[25]  J.M. Kontoleon,et al.  Reliability Determination of a r-Successive-out-of-n:F System , 1980, IEEE Transactions on Reliability.

[26]  Yueqin Wu,et al.  Repairable consecutive-k-out-of-n: G systems with r repairmen , 2005, IEEE Trans. Reliab..