Statistical analysis of adaptive type-II progressively censored competing risks for Weibull models

Abstract In this article, the estimation of the unknown parameters and the survival and hazard functions of Weibull distribution is studied with the adaptive Type-II progressively censored competing risks data, where the lifetime random variables of the individual failure causes are independent and follow Weibull distribution with different scale and shape parameters. For frequentist estimation, the maximum likelihood estimators are obtained utilizing Newton-Raphson method, whose existence and uniqueness are also proved. Making use of the asymptotic normality of maximum likelihood estimators and delta method, we construct the respective confidence intervals of the parameters and the survival and hazard functions. For Bayesian estimation, we take advantage of Monte Carlo Markov Chain technique and importance sampling method to derive the Bayesian estimators and the credible intervals. Extensive Monte Carlo simulation experiments and a real-life mortality dataset analysis are implemented to evaluate the performance of the developed methods. And then, we discuss the issue of expected experimentation time. In the end, the model is extended to the case of dependent failure modes. Marshall-Olkin bivariate Weibull distribution is considered and the theoretical derivations are presented.