Bayesian analysis of masked system lifetime data

In the masked system lifetime data, the exact failure causes are 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 introduce auxiliary variables to simplify likelihood function. In addition to exponential distributions for the component lifetimes, we also consider Weibull distributions. A Bayesian approach that uses Gibbs sampling will be developed for each of the models.