Optimal Bayesian variable sampling plans for exponential distributions based on modified type-II hybrid censored samples

摘要

For the conventional type-II hybrid censoring scheme (HCS) in Childs etal., a Bayesian variable sampling plan among the class of the maximum likelihood estimators was derived by Lin etal. under the loss function, which does not include the cost of experimental time. Instead of taking the conventional type-II hybrid censoring scheme, a persuasive argument leads to taking the modified type-II hybrid censoring scheme (MHCS) if the cost of experimental time is included in the loss function. In this article, we apply the decision-theoretic approach for the concerned acceptance sampling. With the type-II MHCS, based on a sufficient statistics, the optimal Bayesian sampling plan is derived under a general loss function. Furthermore, for the conjugate prior distribution, the closed-form formula of the Bayes decision rule can be obtained under the quadratic decision loss. Numerical study is given to demonstrate the performance of the proposed Bayesian sampling plan.