The ?signature? of a coherent system and its application to comparisons among systems

TLDR

Various methods and criteria for comparing coherent systems are discussed. All comparisons rely on representing a system’s lifetime distribution via its signature vector p, and the signature is also used to examine a conjecture on componentwise and systemwise redundancy. The authors derive theoretical results for comparing coherent systems with i.i.d. components, provide sufficient conditions for one system’s lifetime to exceed another’s under stochastic, hazard rate, and likelihood ratio orderings, and establish a new preservation theorem for hazard rate ordering.

Abstract

Various methods and criteria for comparing coherent systems are discussed. Theoretical results are derived for comparing systems of a given order when components are assumed to have independent and identically distributed lifetimes. All comparisons rely on the representation of a system's lifetime distribution as a function of the system's "signature," that is, as a function of the vector p= (p1, … , pn), where pi is the probability that the system fails upon the occurrence of the ith component failure. Sufficient conditions are provided for the lifetime of one system to be larger than that of another system in three different senses: stochastic ordering, hazard rate ordering, and likelihood ratio ordering. Further, a new preservation theorem for hazard rate ordering is established. In the final section, the notion of system signature is used to examine a recently published conjecture regarding componentwise and systemwise redundancy. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 507–523, 1999