Latest revision as of 13:44, 23 January 2026

Abstract

This work presents a novel and comprehensive inferential framework for analyzing the stress-strength reliability parameter,R= P(Y < X), where X and Y denote independent stress and strength variables, respectively, both modeled as Weibull-distributed with a shared shape parameter but distinct scale parameters. A key innovation of this study lies in its integration of the unified Type-I progressively hybrid censoring scheme, which simultaneously accommodates time constraints and partial failure information, conditions often encountered in real-world reliability testing. To estimate R, we propose and evaluate four distinct inferential strategies: two frequentist (maximum likelihood estimation and maximum spacings estimation) and two Bayesian, each tailored to either the likelihood or spacings-based posterior formulation. The Bayesian methods employ Monte Carlo sampling to compute both Bayes point estimates and credible intervals under informative priors, offering robustness in small-sample or heavily censored contexts. An extensive simulation study is conducted to systematically compare the estimators in terms of bias, efficiency, and interval coverage. To validate the practical applicability of our framework, we further analyze two real-world microdroplet datasets, revealing critical insights into stress-tolerance behavior under experimental constraints. This study not only advances methodological tools for reliability inference under hybrid censoring but also establishes a blueprint for combining classical and Bayesian paradigms in stress-strength modeling.OPEN ACCESS Received: 01/07/2025 Accepted: 02/09/2025 Published: 23/01/2026

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