Statistical Inference of Burr-XII Distribution Under Adaptive Type II Progressive Censored Schemes with Competing Risks

This paper discusses the adaptive type II progressive censored data under the competitive risk model from multiple aspects such as experimental method comparison, data analysis, and optimized censoring scheme. The existence and uniqueness of the maximum likelihood estimation are derived, and the approximate confidence interval is constructed by the Fisher information matrix and delta method. Bayesian estimation under three loss functions and the highest posterior density credible intervals are provided via Markov Chain Monte Carlo simulations. Considering the effect of optimized censoring schemes to improve the efficiency of experiments, three optimization criteria are introduced under the condition of ensuring the amount of data and shortening the test duration. Finally, suggestions for experimental design are presented to better serve the actual production and life.