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<p>In reliability analysis, traditional stress–strength models often assume that the stress and strength variables follow identical distributions. While this assumption simplifies theoretical development, it may not adequately capture real-world complexities-particularly when stress and strength arise from fundamentally different physical processes. This study addresses this gap by proposing a flexible and generalized stress–strength reliability framework that accommodates non-identical distributions and avoids restrictive parameter assumptions. Specifically, we investigate the stress–strength reliability of the Marshall–Olkin (MO) family when the stress and strength components follow either the same or different MO type distributions, such as MO Burr Type XII, MO Chen, and MO Weibull. We develop estimation procedures under both the maximum likelihood and Bayesian paradigms and provide comprehensive inference tools, including asymptotic, bootstrap, and Bayesian interval estimates. Bayesian estimates are obtained via the Markov Chain Monte Carlo method, implemented using the <Emphasis FontCategory="NonProportional">MCMCpack</Emphasis> R package. The performance of the proposed methods is demonstrated through extensive Monte Carlo simulations. Finally, we analyze an original hydrological dataset from Istanbul, Türkiye, to demonstrate the practical application of our methods under a newly introduced drought scenario.</p>

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Statistical inference on stress-strength reliability for the Marshall-Olkin family of distributions

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Gülce Cüran,
  • Fatih Kızılaslan

摘要

In reliability analysis, traditional stress–strength models often assume that the stress and strength variables follow identical distributions. While this assumption simplifies theoretical development, it may not adequately capture real-world complexities-particularly when stress and strength arise from fundamentally different physical processes. This study addresses this gap by proposing a flexible and generalized stress–strength reliability framework that accommodates non-identical distributions and avoids restrictive parameter assumptions. Specifically, we investigate the stress–strength reliability of the Marshall–Olkin (MO) family when the stress and strength components follow either the same or different MO type distributions, such as MO Burr Type XII, MO Chen, and MO Weibull. We develop estimation procedures under both the maximum likelihood and Bayesian paradigms and provide comprehensive inference tools, including asymptotic, bootstrap, and Bayesian interval estimates. Bayesian estimates are obtained via the Markov Chain Monte Carlo method, implemented using the MCMCpack R package. The performance of the proposed methods is demonstrated through extensive Monte Carlo simulations. Finally, we analyze an original hydrological dataset from Istanbul, Türkiye, to demonstrate the practical application of our methods under a newly introduced drought scenario.