Bayesian analysis for masked system failure data using non-identical Weibull models

In ideal circumstances, failure time data for a K component series system contain the time to failure along with information on the exact component responsible for the system failure. These data then can be used to estimate system and component reliabilities. In many cases, however, due to cost and time constraints, the exact component causing the system failure is not identified, but the cause of failure is only narrowed down to a subsystem or a smaller set of components. A Bayesian analysis is developed in this article for such masked data from a general K component system. The theoretical failure times for the K components are assumed to have independent Weibull distributions. These K Weibulls can have different scale and shape parameters, thus allowing wide flexibility into the model. Further flexibility is introduced in the choice of the prior. Three different prior models are proposed. They can model different prior beliefs and can further provide a vehicle to check for robustness with respect to the prior. A Gibbs sampling based method is described to perform the relevant Bayesian computations. The proposed model is applied to data on a system unit of a particular type of IBM PS/2 models.