Bayesian Reliability Modeling for Masked System Lifetime Data

In the masked system lifetime data, the exact component that causes the system's failure is often unknown. For each series system at test, we observe its system's failure time and a set of components that includes the component actually causing the system to fail. The objective is to make inferences for the reliability of the components. In this paper we consider various probability models for the conditional masking probabilities that identify the set of possible failed components given the true cause of failure and the system's failure time. In addition to exponential distributions for the component lifetimes, we consider Weibull distributions. A Bayesian approach that uses Gibbs sampling will be developed for each of the models. Model selection by a predictive approach will also be developed. We show that improved inference can be obtained by modeling the masking probabilities.