Inference for the Weibull distribution with progressive hybrid censoring

Recently, progressive hybrid censoring schemes have become quite popular in life-testing and reliability studies. In this paper, we investigate the maximum likelihood estimation and Bayesian estimation for a two-parameter Weibull distribution based on adaptive Type-I progressively hybrid censored data. The Bayes estimates of the unknown parameters are obtained by using the approximation forms of Lindley (1980) and Tierney and Kadane (1986) as well as two Markov Chain Monte Carlo methods under the assumption of gamma priors. Computational formulae for the expected number of failures is provided and it can be used to determine the optimal adaptive Type-I progressive hybrid censoring schemes under a pre-determined budget of experiment.