On modular decompositions of system signatures
On modular decompositions of system signatures
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DOI：
10.1016/j.jmva.2014.10.002
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发表时间：
2012-08
期刊：
影响因子：
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通讯作者：
J. Marichal;P. Mathonet;F. Spizzichino
中科院分区：
文献类型：
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作者：
J. Marichal;P. Mathonet;F. Spizzichino
Samaniego考虑一个由n个具有连续寿命的部件组成的半相干系统，将其结构特征定义为n元组，其第k个坐标为第k个部件失效导致系统失效的概率。这个n元组只依赖于系统的结构而不依赖于组件寿命的分布，是相干系统理论分析中非常有用的工具。在最近的两篇独立的论文中，给出了如何利用划分为两个不相交模的系统的结构签名来计算这些模的结构签名。本文考虑了系统被划分为任意数目的以任意方式组织的不相交模块的一般情况，并根据模块的签名给出了系统签名的一般公式。签名的概念最近被扩展到半相干系统的一般情况下，其组成部分可能有依赖的生命周期。n元组的相同定义产生了概率签名，这可能取决于系统的结构和组件生命周期的概率分布。在这种一般情况下，我们展示了如何在寿命分布的自然条件下，用模块的概率签名来表示系统的概率签名。最后讨论了该条件在非id和不可交换情况下成立的几种情况，并给出了主要结果的一些应用。
Considering a semicoherent system made up of n components having iid continuous lifetimes, Samaniego defined its structural signature as the n-tuple whose k th coordinate is the probability that the k th component failure causes the system to fail. This n-tuple, which depends only on the structure of the system and not on the distribution of the component lifetimes, is a very useful tool in the theoretical analysis of coherent systems. It was shown in two independent recent papers how the structural signature of a system partitioned into two disjoint modules can be computed from the signatures of these modules. In this work we consider the general case of a system partitioned into an arbitrary number of disjoint modules organized in an arbitrary way and we provide a general formula for the signature of the system in terms of the signatures of the modules. The concept of signature was recently extended to the general case of semicoherent systems whose components may have dependent lifetimes. The same definition for the n-tuple gives rise to the probability signature, which may depend on both the structure of the system and the probability distribution of the component lifetimes. In this general setting, we show how under a natural condition on the distribution of the lifetimes, the probability signature of the system can be expressed in terms of the probability signatures of the modules. We finally discuss a few situations where this condition holds in the non-iid and nonexchangeable cases and provide some applications of the main results.