On the extensions of Barlow-Proschan importance index and system signature to dependent lifetimes

JOURNAL OF MULTIVARIATE ANALYSIS

卷:115

Article

Marichal, Jean-Luc¹  Mathonet, Pierre² 

[1] Univ Luxembourg, FSTC, Math Res Unit, L-1359 Luxembourg, Luxembourg

[2] Univ Liege, Dept Math, B-4000 Liege, Belgium

关键词: Coherent system;    Component importance;    Barlow Proschan index;    Dependent lifetimes;    System signature;   

DOI  :  10.1016/j.jmva.2012.09.002

来源: Elsevier

【 摘 要 】

For a coherent system the Barlow-Proschan importance index, defined when the component lifetimes are independent, measures the probability that the failure of a given component causes the system to fail. Iyer (1992) [3] extended this concept to the more general case when the component lifetimes are jointly absolutely continuous but not necessarily independent. Assuming only that the joint distribution of component lifetimes has no ties, we give an explicit expression for this extended index in terms of the discrete derivatives of the structure function and provide an interpretation of it as a probabilistic value, a concept introduced in game theory. This enables us to interpret Iyer's formula in this more general setting. We also discuss the analogy between this concept and that of system signature and show how it can be used to define a symmetry index for systems. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free