Reliability estimation for bathtub-shaped distribution under block progressive censoring

In this article, estimates of reliability performance characteristics are discussed when life test is conducted upon various test facilities under block progressive Type-II censoring. When the differences in different test facilities are taken into account and the lifetime of products follows a bathtub-shaped hazard rate distribution, different estimates are obtained from classical and hierarchical Bayesian frameworks, respectively. Existence and uniqueness of maximum likelihood estimators of model parameters are established, and approximate confidence intervals are obtained as well based on asymptotic theory and delta method. Moreover, associated Bayes estimators are also evaluated using a hybrid Metropolis-Hasting sampling in hierarchical framework. Finally, performances of the proposed approaches are compared via extensive simulation study, and a real data example is also presented for application viewpoint.& COPY; 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.