Reliability Inference for Gompertz Distribution Using Pivotal Method under Block Progressive Type-II Censored Data

Abstract

In this paper, we primarily focus on making important deductions regarding the estimates of survival characteristics in the context of block progressive censored data. Specifically, we examine the reliability function, hazard rate function, median time to failure, and variations among different test facilities. Our analysis is centered on the lifetime of test units following the Gompertz distribution. We derive maximum likelihood estimators for unknown quantities and investigate their properties regarding existence and uniqueness. Additionally, we construct approximate confidence intervals for all survival characteristics using the delta method and likelihood theory. Moreover, we develop point and generalized confidence interval estimators through a pivotal quantity-based method. To evaluate the performance of our proposed approaches, we conduct a simulation study and find that the pivotal quantity-based approach yields superior estimation results. Finally, we apply the proposed estimates to analyze real-world data, demonstrating their effectiveness.