Inference of accelerated dependent competing risks model for Marshall–Olkin bivariate Weibull distribution with nonconstant parameters

Abstract

In this paper, we discuss the statistical inference of constant-stress accelerated dependent competing risks model under Type-II hybrid censoring schemes. The dependency structure is modeled by a Marshall–Olkin bivariate Weibull distribution. Both the shape and the scale parameters in the model are assumed to be dependent on the stress levels through a log-linear relationship. The maximum likelihood estimates (MLEs) of the model parameters are derived. Confidence intervals (CIs) of the model parameters are constructed based on the asymptotic normality of MLEs and the bias-corrected percentile bootstrap method. Bayes estimates with the squared error loss function and the highest posterior density (HPD) credible intervals (CIs) are obtained by using an importance sampling method. In addition, the estimates for the accelerated coefficients and the reliability under normal use stress level at mission time are derived. A Monte Carlo simulation study is used to evaluate the performance of the proposed statistical inference methods. A real data example is used to illustrate the methodologies proposed in this paper and to compare the proposed model with the copula model.