A Bayesian Model for Integrating Multiple Sources of Lifetime Information in System-Reliability Assessments

We present a Bayesian model for assessing the reliability of multicomponent systems. Novel features of this model are the natural manner in which lifetime data collected at either the component, subsystem, or system level are integrated with prior information at any level. The model allows pooling of information between similar components, the incorporation of expert opinion, and straightforward handling of censored data. The methodology is illustrated with two examples.

[1]  M. S. Hamada,et al.  Using simultaneous higher-level and partial lower-level data in reliability assessments , 2008, Reliab. Eng. Syst. Saf..

[2]  A. Raftery,et al.  Inference for Deterministic Simulation Models: The Bayesian Melding Approach , 2000 .

[3]  Alyson G. Wilson,et al.  Information integration for complex systems , 2007, Reliab. Eng. Syst. Saf..

[4]  Harry F. Martz,et al.  Bayesian Reliability Analysis of High-Reliability Systems of Binomial and Poisson Subsystems , 1997 .

[5]  Jeffrey A. Robinson,et al.  The reliability of a series system of repairable subsystems: A bayesian approach , 1994 .

[6]  David V. Mastran Incorporating Component and System Test Data into the Same Assessment: A Bayesian Approach , 1976, Oper. Res..

[7]  Nozer D. Singpurwalla,et al.  A Bayesian Estimation of the Reliability of Coherent Structures , 1978, Oper. Res..

[8]  Christine M. Anderson-Cook Evaluating the Series or Parallel Structure Assumption for System Reliability , 2008 .

[9]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[10]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[11]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[12]  Bo Bergman,et al.  System reliability prediction using data from non-identical environments , 1997 .

[13]  So Young Sohn Growth curve analysis applied to ammunition deterioration , 1996 .

[14]  K. B. Misra,et al.  On Bayesian estimation of system reliability , 1993 .

[15]  Vicki M. Bier,et al.  On the concept of perfect aggregation in Bayesian estimation , 1994 .

[16]  D. L. Dietrich,et al.  Attribute data reliability decay models , 1994 .

[17]  Irwin Guttman,et al.  A Bayesian approach to system reliability when two components are dependent , 1988 .

[18]  Alan Winterbottom,et al.  Approximate Bayesian intervals for the reliability of series systems from mixed subsystem test data , 1983 .

[19]  K. D. Russell,et al.  Systems analysis programs for hands-on integrated reliability evaluations (SAPHIRE), Version 5.0 , 1995 .

[20]  Herbert Moskowitz,et al.  Exact Bayesian estimation of system reliability from component test data , 1997 .

[21]  Eugene Y. Chang,et al.  Bayes Confidence Limits for Reliability of Redundant Systems , 1975 .

[22]  Valen E. Johnson A Bayesian x2 test for goodness-of-fit , 2004 .

[23]  Alan Winterbottom,et al.  The Interval Estimation of System Reliability from Component Test Data , 1984, Oper. Res..

[24]  V. E. Johnson,et al.  A hierarchical model for estimating the early reliability of complex systems , 2005, IEEE Transactions on Reliability.

[25]  D. Robinson,et al.  A system-level reliability-growth model , 1988, 1988. Proceedings., Annual Reliability and Maintainability Symposium,.

[26]  Brian Gough,et al.  GNU Scientific Library Reference Manual - Third Edition , 2003 .

[27]  Herbert Moskowitz,et al.  Bayes credibility intervals for reliability of series systems with very reliable components , 1994 .

[28]  R. E. Barlow Combining Component and System Information in System Reliability Calculation , 1985 .

[29]  Steven E. Rigdon,et al.  Bayes Inference for General Repairable Systems , 2009 .

[30]  Henry W. Block,et al.  A Continuous, Bivariate Exponential Extension , 1974 .

[31]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

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

[33]  Christine M. Anderson-Cook,et al.  Reliability Models for Almost-Series and Almost-Parallel Systems , 2010, Technometrics.

[34]  Peter V.Z. Cole A Bayesian Reliability Assessment of Complex Systems for Binomial Sampling , 1975, IEEE Transactions on Reliability.

[35]  Eugene Y. Chang,et al.  Bayes Analysis of Reliability for Complex Systems , 1976, Oper. Res..

[36]  Harry F. Martz,et al.  Bayesian reliability analysis of series systems of binomial subsystems and components , 1988 .

[37]  Alyson G. Wilson,et al.  A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation , 2004, Reliab. Eng. Syst. Saf..

[38]  Debasis Bhattacharya,et al.  Estimating component characteristics from system failure‐time data , 2010 .

[39]  Alyson G. Wilson,et al.  Advances in Data Combination, Analysis and Collection for System Reliability Assessment. , 2006, 0708.0355.

[40]  K. K. Sharma,et al.  Bayesian reliability analysis of a parallel system , 1992 .

[41]  R. A. Waller,et al.  Bayesian reliability analysis of complex series/parallel systems of binomial subsystems and components , 1990 .

[42]  Bo Bergman,et al.  Bayesian System Reliability Prediction , 1997 .

[43]  Eric R. Ziegel,et al.  System Reliability Theory: Models, Statistical Methods, and Applications , 2004, Technometrics.

[44]  K. K. Sharma,et al.  Bayesian reliability analysis of a series system , 1994 .

[45]  Ananda Sen,et al.  A survey of discrete reliability-growth models , 1996, IEEE Trans. Reliab..

[46]  Harry F. Martz,et al.  A fully Bayesian approach for combining multi-level information in multi-state fault tree quantification , 2007, Reliab. Eng. Syst. Saf..

[47]  M. Springer,et al.  Bayesian confidence limits for the product of N binomial parameters , 1966 .

[48]  Nozer D. Singpurwalla,et al.  On the reliability function of a system of components sharing a common environment , 1988 .