Statistical Inference for Heterogeneous Competing Risks Model Under Improved Adaptive Type-II Progressive Censoring

This study investigates statistical inference for a heterogeneous competing risks model under an improved adaptive Type-II progressive censoring scheme, which effectively controls testing time while ensuring sufficient failure data. Assuming the latent lifetimes of distinct failure causes are independent and follow Chen and Weibull distributions, we develop both frequentist and Bayesian approaches to derive point and interval estimates for the unknown parameters. Interval estimators include approximate confidence intervals, bootstrap confidence intervals, and highest posterior density credible intervals. Under the Bayesian framework, Markov Chain Monte Carlo techniques are utilized to obtain numerical solutions under the squared error loss function, assuming independent gamma priors. Extensive Monte Carlo simulations and a real-world data application are presented to demonstrate the efficacy and practical utility of the proposed methodologies.