Inference for Constant-Stress Accelerated Life Tests With Dependent Competing Risks From Bivariate Birnbaum–Saunders Distribution Based on Adaptive Progressively Hybrid Censoring

Abstract

In life testing, the competing risks model is usually discussed under the assumption of independence. In this paper, we consider a dependent competing risks model using bivariate Birnbaum–Saunders distribution in constant-stress accelerated life testing. To observe expected failure times and terminate the life tests around a predetermined time, the adaptive progressively hybrid censoring scheme is adopted. Based on the accelerated competing risks model with the adaptive progressively hybrid censoring scheme, we obtain the maximum-likelihood estimators, approximate confidence intervals, and bootstrap confidence intervals of unknown parameters. To test the independence between the bivariate competing risks and find the relationship of shape and scale parameters, we discuss the likelihood ratio tests for hypotheses of interest. In addition, we compute the maximum-likelihood predictors of unobserved competing risks times in the constant-stress accelerated life tests. Finally, a simulation study and an illustrative example are provided to support the proposed model and methods, and to examine the performance of estimators and testing.