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The negative log-gamma prior distribution for Bayesian assessment of system reliability

Author

Listed:
  • Roger Zoh
  • Alyson Wilson
  • Scott Vander Wiel
  • Earl Lawrence

Abstract

This paper presents the negative log-gamma distribution as a prior distribution useful for Bayesian assessment of system reliability. When the scale parameter is held fixed, the negative log-gamma distribution is closed under products, making it convenient for specifying priors for series systems. In particular, for series systems, negative log-gamma component priors can be specified to give an exact desired system prior and vice versa. We consider pass/fail data at the system and component levels for both static and time-varying data collection schemes and propose two new prior distributions for analyzing time-varying reliability. Finally, we consider an application of the negative log-gamma to a missile reliability problem and illustrate diagnostics useful for developing the priors.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:risrel:v:232:y:2018:i:3:p:308-319
    DOI: 10.1177/1748006X17692154
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    References listed on IDEAS

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    1. Guikema, Seth D., 2007. "Formulating informative, data-based priors for failure probability estimation in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 490-502.
    2. David V. Mastran & Nozer D. Singpurwalla, 1978. "A Bayesian Estimation of the Reliability of Coherent Structures," Operations Research, INFORMS, vol. 26(4), pages 663-672, August.
    3. David V. Mastran, 1976. "Incorporating Component and System Test Data into the Same Assessment: A Bayesian Approach," Operations Research, INFORMS, vol. 24(3), pages 491-499, June.
    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.
    Full references (including those not matched with items on IDEAS)

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