Reliability estimation for two-parameter Weibull distribution under block censoring

Abstract Weibull distribution and block censoring scheme play an important role in life testing and reliability engineering. The block censoring can improve the efficiency of test by allowing testers to assign a pre-assigned number of units to different test facilities. In this paper, we develop a hierarchical model for estimating reliability performances (reliability, hazard rate and the mean time to failure) as well as the differences in different test facilities under the assumption that the lifetimes of units are block censored Weibull population. We show how proposed estimation methods can be employed to infer these three reliability performances and the differences in different test facilities, and the behavior of Bayes method are compared to maximum likelihood estimates method via extensive simulations. It is found that proposed hierarchical model, together with non-informative priors, utilizing hybrid Metropolis-Hasting sampling, shows better performance than non-hierarchical model using maximum likelihood method by borrowing strength across test units. Finally, one real example from engineering reliability has been analyzed for illustrative purposes.