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<p>We consider coherent systems with identical components. They have a given structure function and a copula of dependence of component lifetimes which admits the Samaniego representation of the system lifetime distribution. We provide natural necessary and sufficient conditions for preserving distributional properties of the component lifetimes by the system lifetimes which are expressed by the relation of the respective distribution with some fixed life distribution in the star and superadditive orders. This is an extension of the analogous result in Rychlik and Szymkowiak (IEEE Trans Reliab 71:590–602, <CitationRef CitationID="CR34">2022</CitationRef>) and Arnold et al. (Test 31:901–930, <CitationRef CitationID="CR1">2022</CitationRef>) for the convex transform order. In particular, we present necessary and sufficient conditions for preserving the IFRA/DFRA and NBU/NWU properties of component lifetimes by the system lifetimes. Our results are valid for the mixed systems as well. They are illustrated by several examples.</p>

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Preservation of Transform Order Properties of Component Lifetimes by System Lifetimes

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Tomasz Rychlik,
  • Magdalena Szymkowiak

摘要

We consider coherent systems with identical components. They have a given structure function and a copula of dependence of component lifetimes which admits the Samaniego representation of the system lifetime distribution. We provide natural necessary and sufficient conditions for preserving distributional properties of the component lifetimes by the system lifetimes which are expressed by the relation of the respective distribution with some fixed life distribution in the star and superadditive orders. This is an extension of the analogous result in Rychlik and Szymkowiak (IEEE Trans Reliab 71:590–602, 2022) and Arnold et al. (Test 31:901–930, 2022) for the convex transform order. In particular, we present necessary and sufficient conditions for preserving the IFRA/DFRA and NBU/NWU properties of component lifetimes by the system lifetimes. Our results are valid for the mixed systems as well. They are illustrated by several examples.