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<p>In reliability analysis, assessing the stress-strength parameter, or <i>R</i> = Pr(<i>Z</i> &lt; <i>T</i>),&#xa0;is one of the most challenging aspects. The estimation of <i>R</i> is often criticized for being unreliable and unstable when dealing with outliers and high numbers. This study examines the estimation of <i>R</i> when there are outliers and the random variables of stress (<i>Z</i>) and strength (<i>T</i>) have exponentiated Pareto distribution. For the traditional method, the maximum likelihood estimator and asymptotic confidence interval estimator based on the delta method are computed. Furthermore, with independent gamma priors, a Bayesian estimator for <i>R</i> is provided. One could obtain a Bayesian estimator with informative and non-informative priors for the stress-strength parameter using symmetric and asymmetric loss functions. Bayesian credible intervals with the highest posterior densities are established. Advanced computations are performed using Markov chain Monte Carlo techniques. The precision of different <i>R</i> estimates is investigated using simulation research. An analysis revealed that larger sample sizes produced superior estimates for used procedures. Nevertheless, both approaches' accuracy metrics tend to decline as the number of outliers rises. In comparison to the observed estimates under various loss functions, Bayesian estimates consistently perform better under the minimum expected loss function. In the end, a real-world dataset from the insurance studies is used to apply the presented methodology. Analysis of the insurance data shows that both estimating methods are more reliable for smaller outliers and less reliable for larger outliers, supporting the theoretical research.</p>

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Bayesian and frequentist analysis of stress-strength reliability modelling involving outliers with application to insurance data

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Amal S. Hassan,
  • Yostina S. Morgan

摘要

In reliability analysis, assessing the stress-strength parameter, or R = Pr(Z < T), is one of the most challenging aspects. The estimation of R is often criticized for being unreliable and unstable when dealing with outliers and high numbers. This study examines the estimation of R when there are outliers and the random variables of stress (Z) and strength (T) have exponentiated Pareto distribution. For the traditional method, the maximum likelihood estimator and asymptotic confidence interval estimator based on the delta method are computed. Furthermore, with independent gamma priors, a Bayesian estimator for R is provided. One could obtain a Bayesian estimator with informative and non-informative priors for the stress-strength parameter using symmetric and asymmetric loss functions. Bayesian credible intervals with the highest posterior densities are established. Advanced computations are performed using Markov chain Monte Carlo techniques. The precision of different R estimates is investigated using simulation research. An analysis revealed that larger sample sizes produced superior estimates for used procedures. Nevertheless, both approaches' accuracy metrics tend to decline as the number of outliers rises. In comparison to the observed estimates under various loss functions, Bayesian estimates consistently perform better under the minimum expected loss function. In the end, a real-world dataset from the insurance studies is used to apply the presented methodology. Analysis of the insurance data shows that both estimating methods are more reliable for smaller outliers and less reliable for larger outliers, supporting the theoretical research.