A Bayes Continuous Reliability Growth Model with Two Categories of Failures

A Bayesian continuous reliability growth model is presented. It is assumed that the development phase of a product consists of m stages. In each stage, the failure mechanism of the product follows a competing risks model with two specific failure modes: inherent and assignable-cause. The hazard rate for each mode is time-invariant within one stage. Under the assumption that modifications of the product improve its reliability, we assign a reasonable joint prior distribution for the hazard rates. Then Bayesian analysis is carried out using this prior distribution. It turns out that the posterior pdf of the hazard rates of interest is just a weighted average of pdf's which have the same form as the prior pdf. A numerical example is given for illustration.