Abstract
The mixture of Type-I and Type-II censoring schemes, called the hybrid censoring scheme (HCS) is quite common in life testing or reliability experiments. Recently Type-II progressive censoring scheme (Type-II PCS) becomes quite popular for analyzing highly reliable data. One drawback of the Type-II PCS is that the length of the experiment can be quite large. In this paper we introduce the estimating problems of the unknown parameters of alpha power exponential distribution (APED) using Type-II progressive hybrid censoring scheme (Type-II PCS) will be considered. The maximum likelihood estimation (MLE) and Bayesian estimations of the unknown parameters based on both squared error loss (SE) and LINEX loss functions are obtained. We propose to apply the Markov Chain Monte Carlo (MCMC) technique to carry out a Bayes estimation procedure. The approximate and credible confidence intervals for the unknown parameters are obtained. Also, we introduced the estimating problems of reliability and hazard rate function of the APED under Type-II PHCS and the corresponding approximate confidence intervals. Finally, all the theoretical results obtained are assessed and compared using two real datasets, coming from engineering and management fields.