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<p>This research article estimates the reliability of <i>s</i>-out-of-<i>k</i> multicomponent systems subjected to common stress, where the strength components are non-identical and independently distributed. In practical scenarios, it is often unrealistic to assume that all strength components of a system are identical. To address this problem, we estimate the reliability of multicomponent stress strength (MSS) systems under the assumption of non-identical strength components and a common stress component, following independent generalized inverted exponential distributions. The estimation of MSS reliability is performed using both classical and Bayesian approaches. In the classical framework, the maximum likelihood estimation method is employed for point estimation, while asymptotic confidence intervals are constructed for interval estimation. In the Bayesian framework, point and interval estimates are obtained using Tierney–Kadane’s approximation and Markov chain Monte Carlo techniques under an asymmetric loss function, as the Bayes estimator does not have a closed-form expression. A comprehensive numerical simulation study is conducted to compare the performance of the various estimators developed. Finally, the proposed methodologies are illustrated using a real-life dataset, showcasing their practical applicability and effectiveness. From the numerical studies, it is found that the MSEs for the classical and Bayes estimates are less than 0.010, and the coverage probabilities of the interval estimates attain their nominal level of significance, i.e. <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(95\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>95</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> in most of the cases.</p>

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Reliability estimation of multicomponent stress–strength system with non-identical strength components based on generalized inverted exponential distribution

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • Maya Kumari,
  • Renu Garg,
  • Ranjan Kumar Sahoo,
  • Anita Kumari

摘要

This research article estimates the reliability of s-out-of-k multicomponent systems subjected to common stress, where the strength components are non-identical and independently distributed. In practical scenarios, it is often unrealistic to assume that all strength components of a system are identical. To address this problem, we estimate the reliability of multicomponent stress strength (MSS) systems under the assumption of non-identical strength components and a common stress component, following independent generalized inverted exponential distributions. The estimation of MSS reliability is performed using both classical and Bayesian approaches. In the classical framework, the maximum likelihood estimation method is employed for point estimation, while asymptotic confidence intervals are constructed for interval estimation. In the Bayesian framework, point and interval estimates are obtained using Tierney–Kadane’s approximation and Markov chain Monte Carlo techniques under an asymmetric loss function, as the Bayes estimator does not have a closed-form expression. A comprehensive numerical simulation study is conducted to compare the performance of the various estimators developed. Finally, the proposed methodologies are illustrated using a real-life dataset, showcasing their practical applicability and effectiveness. From the numerical studies, it is found that the MSEs for the classical and Bayes estimates are less than 0.010, and the coverage probabilities of the interval estimates attain their nominal level of significance, i.e. \(95\%\) 95 % in most of the cases.