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<p>In an <i>r</i>-out-of-<i>n</i> system configuration, the system’s functionality relies on the survival of at least <i>r</i> out of its <i>n</i> components. Many common system structures, such as series, parallel, and fail-safe systems are special cases of this configuration. This paper examines various aging properties of such a system with dependent components, based on the aging properties of the component lifetime distributions. The derived results apply to arbitrary lifetime distributions for the components. By defining dependency structures through arbitrary copulas, we obtain results relevant to diverse scenarios. Special cases, including Archimedean, Farlie-Gumbel-Morgenstern (FGM) and Ali-Mikhail-Haq (AMH) copulas, are examined to demonstrate the versatility of the derived findings.</p>

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Some results on aging properties of r-out-of-n systems having dependent components

  • 期刊论文

  • 发表日期：

    2025年11月19日

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  • Saifur Rahaman,
  • Pradip Kundu,
  • Amarjit Kundu

摘要

In an r-out-of-n system configuration, the system’s functionality relies on the survival of at least r out of its n components. Many common system structures, such as series, parallel, and fail-safe systems are special cases of this configuration. This paper examines various aging properties of such a system with dependent components, based on the aging properties of the component lifetime distributions. The derived results apply to arbitrary lifetime distributions for the components. By defining dependency structures through arbitrary copulas, we obtain results relevant to diverse scenarios. Special cases, including Archimedean, Farlie-Gumbel-Morgenstern (FGM) and Ali-Mikhail-Haq (AMH) copulas, are examined to demonstrate the versatility of the derived findings.