On a repairable system with detection, imperfect coverage and reboot: Bayesian approach

Abstract System characteristics of a repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the system consists of one active component and one standby component. The detection of standby, the coverage factor and reboot delay of failed components are possibly considered. Time to failure of the components is assumed to follow exponential distribution. Time to repair and time to reboot of the failed components also follow exponential distributions. When time to failure, time to repair and time to reboot have uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper.

[1]  Joong Soon Jang,et al.  Lifetime and reliability estimation of repairable redundant system subject to periodic alternation , 2003, Reliab. Eng. Syst. Saf..

[2]  William J. Kolarik,et al.  A confidence interval for the availability ratio for systems with weibull operating time and lognormal repair time , 1992 .

[3]  Jau-Chuan Ke,et al.  Asymptotic Confidence Limits for Performance Measures of a Repairable System with Imperfect Service Station , 2006 .

[4]  L. R. Goel,et al.  Profit analysis of a two-unit redundant system with provision for rest and correlated failures and repairs , 1991 .

[5]  Jie Mi Interval estimation of availability of a series system , 1991 .

[6]  B. Chandrasekar,et al.  Reliability measures for two-unit systems with a dependent structure for failure and repair times , 1997 .

[7]  Kishor S. Trivedi Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .

[8]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[9]  Andriëtte Bekker,et al.  Bayesian Study of a Two-Component System with Common-Cause shock Failures , 2005, Asia Pac. J. Oper. Res..

[10]  Roy Billinton,et al.  Optimal maintenance scheduling in a two identical component parallel redundant system , 1998 .

[11]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[12]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[13]  A. T. de Almeida,et al.  Decision theory in maintenance strategy for a 2-unit redundant standby system , 1993 .

[14]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[15]  Ashok Kumar,et al.  A Review of Standby Redundant Systems , 1980, IEEE Transactions on Reliability.

[16]  R. Subramanian,et al.  Reliability analysis of a complex standby redundant systems , 1995 .

[17]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Terry Williams,et al.  Probability and Statistics with Reliability, Queueing and Computer Science Applications , 1983 .

[19]  Bala Srinivasan,et al.  A complex two-unit system with random breakdown of repair facility , 1995 .

[20]  R. Natarajan,et al.  A Study on a Two Unit standby System with Erlangian Repair Time , 2004, Asia Pac. J. Oper. Res..

[21]  Toshio Nakagawa,et al.  Bibliography for Reliability and Availability of Stochastic Systems , 1976 .

[22]  Hoang Pham Reliability analysis of a high voltage system with dependent failures and imperfect coverage , 1992 .

[23]  Magdi S. Moustafa Reliability analysis of K-out-of-N: G systems with dependent failures and imperfect coverage , 1997 .

[24]  Marvin Rausand,et al.  System Reliability Theory: Models, Statistical Methods, and Applications , 2003 .

[25]  Prabhaker Reddy,et al.  Standby redundancy in reliability - a review , 1986, IEEE Transactions on Reliability.

[26]  Jeremy E. Oakley,et al.  Uncertain Judgements: Eliciting Experts' Probabilities , 2006 .