Mixed Weibull distributions for the Bayesian analysis of reliability when failures are progressively censored

Abstract

The progressive type-II censoring has a wide range of applications in reliability studies and survival analysis. The analysis of the mixture models under progressively type-II censored samples has recently been introduced. The reliability estimation from the mixture model under the optimal progressive censoring schemes is still lacking in the current literature. We have discussed the estimation of parameters and reliability characteristics from the Weibull mixture model when failures are progressively censored. The Weibull mixture is proposed for this case as it is S-shaped, which can appropriately handle the mixture data. We have addressed the problem of determination of optimal censoring schemes and estimation of expected test times using the said mixed model. The optimal censoring schemes were found to be less sensitive hence robust. As the corresponding posterior distributions do not provide explicit solutions, we have considered Lindley’s approximation for the approximate numerical solutions.