Partially Accelerated Dependent Competing Risks Model under Adaptive Type-II Progressive Censoring Based on Copulas

Salah, Rana; Abuelamayem, Ola

doi:10.21608/esju.2025.349560.1061

Partially Accelerated Dependent Competing Risks Model under Adaptive Type-II Progressive Censoring Based on Copulas

Document Type : Original Article

Authors

Rana Salah ¹
Ola Abuelamayem ²

¹ Statistics department, Faculty of economics and political science, Egypt

² Statistics department, Faculty of economics and political science, Cairo University, Egypt

10.21608/esju.2025.349560.1061

Abstract

Most modern products are designed to operate without failures for years, decades or even more. Thus, it becomes very difficult to operate life testing for such products under normal use conditions. One approach that is commonly used to quickly obtain data in a much shorter time is Accelerated Life Testing (ALT) in which test objects are exposed to high levels of stress to shorten their life time. In ALT, the life-stress model should be known, which is not always the case. Consequently, a partially accelerated life test (PALT) could be applied instead. Sometimes, the test units fail because of many different competing risks which are usually dependent. In this paper, the copula approach is applied to model constant-stress partially accelerated life testing with dependent competing risks under the adaptive type II progressive censoring. The lifetime of units under each competing risk is assumed to follow the Inverse Weibull distribution. Two Archimedean copulas are applied; namely, Gumbel-Hougard (GH) and Clayton copula. A comparison between the performances of these copulas is implemented to figure out which one performs best. The maximum likelihood method is utilized to obtain point estimates of the model parameters including the acceleration factor and the dependence parameter. Also, bootstrap confidence intervals are calculated and compared with the approximate confidence intervals. For illustrative purpose a simulation study is developed to investigate the accuracy of the obtained estimates. Finally, a set of real data is analyzed to demonstrate the applicability of the proposed model.

Keywords