Abstract
The aim of this paper is to investigate the Burr-X competing risks model in the context of adaptive progressively Type-II censored samples. In this scenario, the removal pattern is assumed to be a random variable that follows the binomial distribution, which is a more realistic assumption compared to assuming a fixed removal pattern. In this study, we explore both classical and Bayesian estimation approaches to estimate the parameters of the Burr-X competing risks model, as well as the reliability parameter and the parameter of the binomial distribution. The interval ranges of different parameters are determined by utilizing the asymptotic normality of the maximum likelihood estimators. Furthermore, the Bayes credible intervals are calculated by sampling from the joint posterior distribution using the Markov Chain Monte Carlo procedure. To assess the efficiency of the acquired estimators, a comprehensive simulation study that considered various types of experimental designs is conducted. Finally, two applications are considered by analyzing data sets of electrodes and electronics.
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