Reliability Inference for Power Rayleigh Distribution Under Block Progressive Censoring: A Pivotal Quantity-Based Approach

In this paper, we study the statistical inference of the unknown parameters and the reliability characteristics (RCs) such as reliability function, hazard function, median time to failure (MdTF) and differences in different test facilities (DDTF) of the power Rayleigh distribution under a block progressive censored scheme. The maximum likelihood and the pivotal inference methods are implemented to estimate the unknown parameters and the RCs of the power Rayleigh distribution. Asymptotic confidence intervals of the unknown parameters and the RCs are derived by applying the asymptotic normality property of maximum likelihood estimator (MLE) and the delta method. In the pivotal inference, generalized confidence intervals are obtained. The performances of these estimation methods are tested and compared with each other with the help of a simulation study. Finally, two real data sets are taken to illustrate the proposed methods.