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The reliability of a series system of repairable subsystems: A bayesian approach

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  • Frederick L. Hulting
  • Jeffrey A. Robinson

Abstract

Consider the problem of estimating the reliability of a series system of (possibly) repairable subsystems when test data and historical information are available at the component, subsystem, and system levels. Such a problem is well suited to a Bayesian approach. Martz, Waller, and Fickas [Technometrics, 30, 143–154 (1988)] presented a Bayesian procedure that accommodates pass/fail (binomial) data at any level. However, other types of test data are often available, including (a) lifetimes of nonrepayable components, and (b) repair histories for repairable subsystems. In this article we describe a new Bayesian procedure that accommodates pass/fail, life, and repair data at any level. We assume a Weibull model for the life data, a censored Weibull model for the pass/fail data, and a power‐law process model for the repair data. Consequently, the test data at each level can be represented by a two‐parameter likelihood function of a certain form, and historical information can be expressed using a conjugate family of prior distributions. We discuss computational issues, and use the procedure to analyze the reliability of a vehicle system. © 1994 John Wiley & Sons, Inc.

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  • Frederick L. Hulting & Jeffrey A. Robinson, 1994. "The reliability of a series system of repairable subsystems: A bayesian approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(4), pages 483-506, June.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:4:p:483-506
    DOI: 10.1002/1520-6750(199406)41:43.0.CO;2-1
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    Cited by:

    1. Jackson, Chris & Mosleh, Ali, 2012. "Bayesian inference with overlapping data for systems with continuous life metrics," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 217-231.
    2. Jackson, Chris & Mosleh, Ali, 2016. "Bayesian inference with overlapping data: Reliability estimation of multi-state on-demand continuous life metric systems with uncertain evidence," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 124-135.
    3. DeCroix, Gregory A., 1999. "Optimal warranties, reliabilities and prices for durable goods in an oligopoly," European Journal of Operational Research, Elsevier, vol. 112(3), pages 554-569, February.
    4. Jen Tang & Kwei Tang & Herbert Moskowitz, 1997. "Exact bayesian estimation of system reliability from component test data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 127-146, February.

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