Abstract
The estimation of reliability using mixture models has been frequently studied in last two decades. The main reason for the use of mixture models in estimation of reliability has been the presence of more than one failure modes in the data. In case of multimodal failure data, the reliability estimation has mostly been carried out via conventional type-II censoring. The conventional type-II censoring allows the analyst to remove all the surviving items from the test at the time of last desired failure. However, in many practical situations, the analysts need the freedom to remove the desired number of live items from the test at different times. This situation can be handled while using progressive type-II censoring. In addition, the optimal progressive type-II censoring plans can provide significant gain in efficiencies, as compared to conventional type-II censoring, for the estimation of reliability. In this article, we have considered the Bayesian reliability estimation from the progressively censored multimodal data using mixture of generalized exponential distributions (GEMD). The optimal censoring schemes have been explored for this case. The estimates corresponding to these optimal schemes provided significant gain in efficiencies as compared to the competing censoring schemes. As the Bayes estimates from the GEMD do not exist in the explicit form, we have used the Lindley's approximation and MCMC method for the numerical solutions of these estimates.