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Exact bayesian estimation of system reliability from component test data

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  • Jen Tang
  • Kwei Tang
  • Herbert Moskowitz

Abstract

System reliability is often estimated by the use of components' reliability test results when system test data are not available, or are very scarce. A method is proposed for computing the exact posterior probability density function, cumulative distribution function, and credible intervals for system reliability in a Bayesian setting, with the use of components' prior probability distributions and current test results. The method can be applied to series, parallel, and many mixed systems. Although in theory the method involves evaluating infinite series, numerical results show that a small number of terms from the infinite series are sufficient in practice to provide accurate estimates of system reliability. Furthermore, because the coefficients in the series follow some recurrence relations, our results allow us to calculate the reliability distribution of a large system from that of its subsystems. Error bounds associated with the proposed method are also given. Numerical comparisons with other existing approaches show that the proposed method is efficient and accurate. © 1997 John Wiley & Sons, Inc.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:44:y:1997:i:1:p:127-146
    DOI: 10.1002/(SICI)1520-6750(199702)44:13.0.CO;2-C
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    References listed on IDEAS

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    1. William E. Thompson & Robert D. Haynes, 1980. "On the reliability, availability and bayes confidence intervals for multicomponent systems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(3), pages 345-358, September.
    2. 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.
    3. Harold Lampkin & Alan Winterbottom, 1983. "Approximate Bayesian intervals for the reliability of series systems from mixed subsystem test data," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(2), pages 313-317, June.
    4. Robert L. Winkler, 1968. "The Consensus of Subjective Probability Distributions," Management Science, INFORMS, vol. 15(2), pages 61-75, October.
    5. Eugene Y. Chang & William E. Thompson, 1976. "Bayes Analysis of Reliability for Complex Systems," Operations Research, INFORMS, vol. 24(1), pages 156-168, February.
    6. Alan Winterbottom, 1984. "The Interval Estimation of System Reliability from Component Test Data," Operations Research, INFORMS, vol. 32(3), pages 628-640, June.
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    Cited by:

    1. Qianru Ge & Willem van Jaarsveld & Zümbül Atan, 2020. "Optimal redesign decisions through failure rate estimates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(4), pages 254-271, June.
    2. Roger Zoh & Alyson Wilson & Scott Vander Wiel & Earl Lawrence, 2018. "The negative log-gamma prior distribution for Bayesian assessment of system reliability," Journal of Risk and Reliability, , vol. 232(3), pages 308-319, June.

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