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Bayesian inference based on partial monitoring of components with applications to preventive system maintenance

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  • Jørund Gåsemyr
  • Bent Natvig

Abstract

Consider a binary, monotone system of n components. The assessment of the parameter vector, θ, of the joint distribution of the lifetimes of the components and hence of the reliability of the system is often difficult due to scarcity of data. It is therefore important to make use of all information in an efficient way. For instance, prior knowledge is often of importance and can indeed conveniently be incorporated by the Bayesian approach. It may also be important to continuously extract information from a system currently in operation. This may be useful both for decisions concerning the system in operation as well as for decisions improving the components or changing the design of similar new systems. As in Meilijson [12], life‐monitoring of some components and conditional life‐monitoring of some others is considered. In addition to data arising from this monitoring scheme, so‐called autopsy data are observed, if not censored. The probabilistic structure underlying this kind of data is described, and basic likelihood formulae are arrived at. A thorough discussion of an important aspect of this probabilistic structure, the inspection strategy, is given. Based on a version of this strategy a procedure for preventive system maintenance is developed and a detailed application to a network system presented. All the way a Bayesian approach to estimation of θ is applied. For the special case where components are conditionally independent given θ with exponentially distributed lifetimes it is shown that the weighted sum of products of generalized gamma distributions, as introduced in Gåsemyr and Natvig [7], is the conjugate prior for θ. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 551–577, 2001.

Suggested Citation

  • Jørund Gåsemyr & Bent Natvig, 2001. "Bayesian inference based on partial monitoring of components with applications to preventive system maintenance," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 551-577, October.
  • Handle: RePEc:wly:navres:v:48:y:2001:i:7:p:551-577
    DOI: 10.1002/nav.1034
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    References listed on IDEAS

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    1. Michael O. Ball & J. Scott Provan, 1988. "Disjoint Products and Efficient Computation of Reliability," Operations Research, INFORMS, vol. 36(5), pages 703-715, October.
    2. Jørund Gåsemyr & Bent Natvig & Erik Sørensen, 2001. "A Comparison of Two Sequential Metropolis-Hastings Algorithms with Standard Simulation Techniques in Bayesian Inference in Reliability Models Involving a Generalized Gamma Distribution," Methodology and Computing in Applied Probability, Springer, vol. 3(1), pages 51-73, March.
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    Citations

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    Cited by:

    1. Skutlaberg, Kristina & Huseby, Arne Bang & Natvig, Bent, 2018. "Partial monitoring of multistate systems," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 434-452.
    2. Jørund Gåsemyr & Bent Natvig, 2005. "Probabilistic Modelling of Monitoring and Maintenance of Multistate Monotone Systems with Dependent Components," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 63-78, March.
    3. David Randell & Michael Goldstein & Philip Jonathan, 2014. "Bayes linear variance structure learning for inspection of large scale physical systems," Journal of Risk and Reliability, , vol. 228(1), pages 3-18, February.
    4. Zu‐Liang Lin & Yeu‐Shiang Huang, 2010. "Nonperiodic preventive maintenance for repairable systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(7), pages 615-625, October.
    5. D Randell & M Goldstein & G Hardman & P Jonathan, 2010. "Bayesian linear inspection planning for large-scale physical systems," Journal of Risk and Reliability, , vol. 224(4), pages 333-345, December.

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