On modular decompositions of system signatures

JOURNAL OF MULTIVARIATE ANALYSIS

卷:134

Article

Marichal, Jean-Luc¹  Mathonet, Pierre²  Spizzichino, Fabio³ 

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

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

[3] Univ Roma La Sapienza, Dept Math, I-00185 Rome, Italy

关键词: System signature;    Tail signature;    Semicoherent system;    Modular decomposition;   

DOI  :  10.1016/j.jmva.2014.10.002

来源: Elsevier

【 摘 要 】

Considering a semicoherent system made up of n components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the n-tuple whose kth coordinate is the probability that the kth 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-i.i.d. and nonexchangeable cases and provide some applications of the main results. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free