On Stress–Strength Reliability Estimation for the Generalized Inverted Exponential Distribution Under Unified Hybrid Censoring

ABSTRACT Stress–strength reliability (SSR) analysis plays a fundamental role in reliability engineering, particularly when lifetime data are subject to censoring due to cost or time limitations. In this article, we study the estimation of the reliability parameter when the strength and stress follow the two‐parameter generalized inverted exponential distribution (GIED) under a unified hybrid censoring (UHC) scheme, which ensures both a prespecified number of failures and a bounded test duration. Classical inference is developed via maximum likelihood estimation using the EM algorithm, and the corresponding asymptotic confidence intervals are obtained. Bayesian estimation is carried out using MCMC methods under a generalized entropy loss function, along with HPD credible intervals. The UMVUE of is also derived for comparison. A Monte Carlo simulation study is conducted to evaluate the performance of the proposed estimators under different censoring scenarios. The results indicate that Bayesian methods, particularly under informative priors, often provide improved estimation accuracy in heavily censored cases. Two real data sets are analyzed to demonstrate the practical applicability of the proposed methodology.