The reliability of a series system of repairable subsystems: A Bayesian approach

Consider the problem of estimating the reliability of a series system of (possibly) repairable subsystems when test data and historical information are available at the component, subsystem, and system levels. Such a problem is well suited to a Bayesian approach. Martz, Waller, and Fickas presented a Bayesian procedure that accommodates pass/fail (binomial) data at any level. However, other types of test data are often available, including (a) lifetimes of nonrepairable components, and (b) repair histories for repairable subsystems. In this article the authors describe a new Bayesian procedure that accommodates pass/fail, life, and repair data at any level. They assume a Weibull model for the life data, a censored Weibull model for the pass/fail data, and a power-law process model for the repair data. Consequently, the test data at each level can be represented by a two-parameter likelihood function of a certain form, and historical information can be expressed using a conjugate family of prior distributions. The authors discuss computational issues, and use the procedure to analyze the reliability of a vehicle system.