Nonparametric Bayesian Analysis of Competing Risks Problem with Masked Data

Bayesian analysis of system failure data under a competing-failure framework is considered when the failure causes have not been exactly identified but narrowed down to a subset of all potential failure causes. The usual assumption of independence of failure causes is relaxed. We obtain the posterior distribution of the joint survival function, assuming a Dirichlet process prior, and derive the limiting posterior distribution. We show that the posterior estimate of the reliability of the series system of interest in practice is consistent. A numerical example shows that our approach is feasible.