Equipment failure rate updating—Bayesian estimation

• Published in: Journal of hazardous materials Vol. 159; no. 1; pp. 87 - 91
• Main Author: Shafaghi, Ahmad
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 15.11.2008; Elsevier
• Subjects: Applied sciences; Bayes Theorem; Conjugate gamma distribution; Equipment Failure - statistics & numerical data; Exact sciences and technology; Failure rate; Gamma distribution; Likelihood Functions; Poisson distribution; Pollution; Posterior distribution; Prior distribution; Proportional Hazards Models; Gamma distribution; Conjugate gamma distribution; Prior distribution; Bayes’ theorem; Failure rate; Poisson distribution; Posterior distribution; Uncertainty; Beta distribution; Bayes' theorem; Updating
• ISSN: 0304-3894; 1873-3336
• DOI: 10.1016/j.jhazmat.2008.01.042

The paper presents a Bayes’ method for augmenting generic equipment failure data with a prior distribution – predicated on the evidence, e.g., plant data – resulting in a posterior distribution. The depth of the evidence is significant in shaping the characteristics of the posterior distribution. In conditions of insufficient data about the prior distribution or great uncertainty in the generic data sources, we may use “constrained non-informative priors”. This representation of the prior preserves the mean value of the failure rate estimate and maintains a broad uncertainty range to accommodate the site-specific event data. Although the methodology and the case study presented in this paper focus on the calculation of a time-based (i.e., failures per unit time) failure rate, based on a Poisson likelihood function and the conjugate gamma distribution, a similar method applies to the calculation of demand failure rates utilizing the binomial likelihood function and its conjugate beta distribution.