Mixture priors for Bayesian performance monitoring 2: variable-constituent model

• Published in: Reliability engineering & system safety Vol. 89; no. 2; pp. 164 - 176
• Main Authors: Atwood, Corwin L., Youngblood, Robert W.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.08.2005; Elsevier
• Subjects: Applied sciences; Binomial distribution; Conjugate prior; Constrained noninformative prior; Discrete mixture; Exact sciences and technology; Operational research and scientific management; Operational research. Management science; Poisson distribution; Reliability theory. Replacement problems; Conjugate prior; Binomial distribution; Discrete mixture; Constrained noninformative prior; Poisson distribution; Bayes estimation; Performance evaluation; Current information; Prior distribution; Failure rate; Failures; Observer; A priori estimation; Reliability; Posterior distribution
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2004.08.016

This paper uses mixture priors for Bayesian assessment of performance. In any Bayesian performance assessment, a prior distribution for performance parameter(s) is updated based on current performance information. The performance assessment is then based on the posterior distribution for the parameter(s). This paper uses a mixture prior, a mixture of conjugate distributions, which is itself conjugate and which is useful when performance may have changed recently. The present paper illustrates the process using simple models for reliability, involving parameters such as failure rates and demand failure probabilities. When few failures are observed the resulting posterior distributions tend to resemble the priors. However, when more failures are observed, the posteriors tend to change character in a rapid nonlinear way. This behavior is arguably appropriate for many applications. Choosing realistic parameters for the mixture prior is not simple, but even the crude methods given here lead to estimators that show qualitatively good behavior in examples.