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  • Open Access

    ARTICLE

    Confidence Intervals for the Reliability of Dependent Systems: Integrating Frailty Models and Copula-Based Methods

    Osnamir E. Bru-Cordero1, Cecilia Castro2, Víctor Leiva3,*, Mario C. Jaramillo-Elorza4

    CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.2, pp. 1401-1431, 2025, DOI:10.32604/cmes.2025.064487 - 30 May 2025

    Abstract Most reliability studies assume large samples or independence among components, but these assumptions often fail in practice, leading to imprecise inference. We address this issue by constructing confidence intervals (CIs) for the reliability of two-component systems with Weibull distributed failure times under a copula-frailty framework. Our construction integrates gamma-distributed frailties to capture unobserved heterogeneity and a copula-based dependence structure for correlated failures. The main contribution of this work is to derive adjusted CIs that explicitly incorporate the copula parameter in the variance-covariance matrix, achieving near-nominal coverage probabilities even in small samples or highly dependent settings. More >

  • Open Access

    ARTICLE

    Quantile Version of Mathai-Haubold Entropy of Order Statistics

    Ibrahim M. Almanjahie1,2,*, Javid Gani Dar3, Amer Ibrahim Al-Omari4, Aijaz Mir5

    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 907-925, 2021, DOI:10.32604/cmes.2021.014896 - 11 August 2021

    Abstract Many researchers measure the uncertainty of a random variable using quantile-based entropy techniques. These techniques are useful in engineering applications and have some exceptional characteristics than their distribution function method. Considering order statistics, the key focus of this article is to propose new quantile-based Mathai-Haubold entropy and investigate its characteristics. The divergence measure of the Mathai-Haubold is also considered and some of its properties are established. Further, based on order statistics, we propose the residual entropy of the quantile-based Mathai-Haubold and some of its property results are proved. The performance of the proposed quantile-based Mathai-Haubold More >

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