On two exponential populations under a joint adaptive type-II progressive censoring

In this paper, we introduce a new joint adaptive Type-II progressive censoring (JAPC) scheme for independent samples from two different populations. We place two independent samples simultaneously on a life testing experiment. It is assumed that the lifetime of the experimental units of the populations follow exponential distribution with mean theta(1) and theta(2), respectively. The maximum likelihood estimators of the unknown parameters and their exact distributions are derived. Based on the exact distributions of the maximum likelihood estimators, approximate confidence intervals are constructed. Further, the Bayesian inference of the model parameters is considered under a very flexible Beta-Gamma prior. We obtain Bayes estimators and associated credible intervals of the unknown parameters under squared error loss function. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. A real dataset is considered for implementing the proposed model on it. Also we use the variable neighbourhood search (VNS) method to derive the optimal censoring scheme of the model in the Bayesian framework.