Classical and Bayesian Stress-Strength Reliability Estimation for Weibull Data under Unified Hybrid Censoring Scheme with LED Application

Abstract

The stress-strength reliability parameter is a key metric used in various fields, including engineering, medicine, and business. In engineering, it quantifies the probability that a system’s strength X exceeds the applied stress Y . In this study, we examine for the first time four estimation approaches for evaluating the stress-strength reliability parameter R= P(Y < X ), where X and Y are independent Weibull random variables with different scale parameters but a common shape parameter. The analysis is conducted under a unified hybrid censoring scheme. From the classical perspective, we employ the maximum likelihood and maximum product of spacings methods to obtain both point and interval estimates. From the Bayesian perspective, two forms of the posterior distribution, based on the likelihood and spacings functions, are derived and analyzed using Markov Chain Monte Carlo sampling techniques. The Bayes estimates of R are obtained under the symmetric squared error loss, and the corresponding Bayesian credible intervals are also computed. To compare the four point estimators and the four interval estimators, an extensive simulation study is performed using various experimental scenarios. Finally, comprehensive analyses for organic white light-emitting diode datasets mixed with three colors, namely red, green, and blue, are provided.OPEN ACCESS Received: 29/06/2025 Accepted: 16/09/2025 Published: 23/01/2026

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