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The “signature” of a coherent system and its application to comparisons among systems
Author(s) -
Kochar Subhash,
Mukerjee Hari,
Samaniego Francisco J.
Publication year - 1999
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/(sici)1520-6750(199908)46:5<507::aid-nav4>3.0.co;2-d
Subject(s) - stochastic ordering , signature (topology) , independent and identically distributed random variables , redundancy (engineering) , conjecture , mathematics , order statistic , representation (politics) , function (biology) , computer science , algorithm , discrete mathematics , random variable , statistics , geometry , evolutionary biology , politics , political science , law , biology , operating system
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 = (p 1 , … , p n ), where p i is the probability that the system fails upon the occurrence of the i th 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