Statistical Inference of a Chen Lifetime Competing Risks Model Based on Improved Adaptive Type‐II Progressive Censored Data

ABSTRACT In this paper, a competing risks model is studied under an improved adaptive type‐II progressive censoring scheme (IAT‐II PCS). Two independent competing causes of failure are considered, where lifetime of these failures are assumed to follow the Chen distribution with unknown scale and shape parameters. Maximum likelihood estimators (MLEs) of the unknown parameters are derived. Existence and uniqueness properties of the MLEs have been studied. Asymptotic confidence intervals (ACIs) are constructed using the asymptotic normality property of the MLE. Bayes estimates are obtained with respect to both non‐informative priors (NIP) and informative priors (IP). Three different loss functions, say squared error loss, linex loss, and generalized entropy loss, are considered for the purpose of Bayesian estimation. The Bayes estimates are difficult to compute analytically, and thus, the M‐H algorithm is used. The Highest posterior density (HPD) credible intervals are calculated. A Monte Carlo simulation study using software is conducted to compare the performance of the proposed estimates. Three optimality criteria are studied to obtain the optimal censoring scheme. Finally, two real‐life datasets (related to the voltage endurance life test and the lifetime of electrical appliances) have been analyzed for further validation of the proposed methods.