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System Signatures and their Applications in Engineering Reliability

TL;DR: This paper presents a meta-analysis of the application of Signature-Based Closure, Preservation and Characterization Theorems to Network Reliability and its applications in Reliability Economics and Signature-based Analysis of System Lifetimes.
Abstract: Background on Coherent Systems.- System Signatures.- Signature-Based Closure, Preservation and Characterization Theorems.- Further Signature-Based Analysis of System Lifetimes.- Applications of Signatures to Network Reliability.- Applications of Signatures in Reliability Economics.- Summary and Discussion.
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Journal ArticleDOI
TL;DR: In this paper, it was shown that the distribution of an m-component system's lifetime can be written as a mixture of the distributions of k-out-of-n systems, and that the vector of coefficients in this mixture representation is precisely the signature of the system defined in Samaniego, IEEE Trans Reliabil R-34 (1985) 69−72.
Abstract: Following a review of the basic ideas in structural reliability, including signature-based representation and preservation theorems for systems whose components have independent and identically distributed (i.i.d.) lifetimes, extensions that apply to the comparison of coherent systems of different sizes, and stochastic mixtures of them, are obtained. It is then shown that these results may be extended to vectors of exchangeable random lifetimes. In particular, for arbitrary systems of sizes m < n with exchangeable component lifetimes, it is shown that the distribution of an m-component system's lifetime can be written as a mixture of the distributions of k-out-of-n systems. When the system has n components, the vector of coefficients in this mixture representation is precisely the signature of the system defined in Samaniego, IEEE Trans Reliabil R–34 (1985) 69–72. These mixture representations are then used to obtain new stochastic ordering properties for coherent or mixed systems of different sizes. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

203 citations

Book ChapterDOI
01 Jan 2013
TL;DR: The survival signature is presented, which has similar characteristics and is closely related to the signature, and provides a feasible generalization to systems with multiple types of components.
Abstract: The concept of signature was introduced to simplify quantification of reliability for coherent systems and networks consisting of a single type of components, and for comparison of such systems’ reliabilities. The signature describes the structure of the system and can be combined with order statistics of the component failure times to derive inferences on the reliability of a system and to compare multiple systems. However, the restriction to use for systems with a single type of component prevents its application to most practical systems. We discuss the difficulty of generalization of the signature to systems with multiple types of components. We present an alternative, called the survival signature, which has similar characteristics and is closely related to the signature. The survival signature provides a feasible generalization to systems with multiple types of components.

126 citations

Journal ArticleDOI
TL;DR: In this paper, the reliability functions of residual lifetimes of used coherent systems under two particular conditions on the status of the components or the system in terms of the residual lifetime of order statistics are obtained.
Abstract: The representation of the reliability function of the lifetime of a coherent system as a mixture of the reliability function of order statistics associated with the lifetimes of its components is a very useful tool to study the ordering and the limiting behaviour of coherent systems. In this paper, we obtain several representations of the reliability functions of residual lifetimes of used coherent systems under two particular conditions on the status of the components or the system in terms of the reliability functions of residual lifetimes of order statistics.

106 citations

Journal ArticleDOI
TL;DR: Since the problem under study is combinatorial in nature involving several non-linear decision variables, a simulated annealing algorithm is employed to provide good solutions within reasonable search time.

105 citations

Journal ArticleDOI
01 Sep 2010
TL;DR: In this paper, an overview of the research performed on reliability studies of consecutive k-outof-n and related systems during the last decade is presented, in particular, methods for reliability evaluation, importance and optimal arrangements of components, lifetime distribution, and stochastic orderings of such systems are presented, also research results on related systems are summarized.
Abstract: This paper presents an overview of the research performed on reliability studies of consecutive k-out-of-n and related systems during the last decade. In particular, methods for reliability evaluation, importance and optimal arrangements of components, lifetime distribution, and stochastic orderings of such systems are presented, also research results on related systems are summarized.

97 citations