Inference and Model Discrimination for the Power Muth Distribution Under Type II Censoring in Reliability Engineering

The power Muth distribution (PMD) is a flexible two‐parameter lifetime model for data whose failure behavior may depart from standard monotone patterns. This paper develops inference and model discrimination procedures for the PMD under exact Type‐II censoring. We first revisit the hazard‐rate behavior of the PMD and show that its bathtub‐shaped form occurs for , whereas the hazard rate is increasing for . We then derive maximum likelihood, least‐squares, and maximum product spacing estimators, together with asymptotic confidence intervals based on the observed information matrix. A Bayesian estimation framework is also developed under squared‐error and LINEX loss functions using Markov chain Monte Carlo methods, and highest posterior density credible intervals are obtained. A Monte Carlo study compares the finite‐sample behavior of the proposed estimators under different sample sizes, censoring proportions, and hazard‐rate regimes. Three engineering datasets involving submarine engine maintenance, air‐conditioning failures, and software reliability are analyzed to assess model fit and likelihood‐based discrimination against Weibull, gamma, and log‐normal competitors. The results show that the PMD is particularly useful when censoring changes the apparent tail behavior of the data and when conventional lifetime models lose adequacy under information loss.