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Bayes Analysis of Reliability for Complex Systems

Author

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  • Eugene Y. Chang

    (ESL Inc., Vienna, Virginia)

  • William E. Thompson

    (ARINC Research Corporation, Annapolis, Maryland)

Abstract

We present a method for computing Bayes confidence limits for the reliability of an arbitrary series-parallel system consisting of failure independent modules. Each module has an internal structure of one or more failure independent devices in series, and each device consists of one operating component with identical nonoperating standby components. Each component is assumed to have exponential distribution of life with unknown failure rates that must be estimated from test data. We outline a systematic procedure to compute the posterior distribution of system reliability, from which exact confidence limits can be obtained. The posterior distribution function is developed in terms of an expansion in shifted Chebyshev polynomials of the second kind whose convergence properties and numerical evaluation are well suited for practical applications.

Suggested Citation

  • Eugene Y. Chang & William E. Thompson, 1976. "Bayes Analysis of Reliability for Complex Systems," Operations Research, INFORMS, vol. 24(1), pages 156-168, February.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:1:p:156-168
    DOI: 10.1287/opre.24.1.156
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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. 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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