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The “signature” of a coherent system and its application to comparisons among systems. (English) Zbl 0948.90067
Summary: 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 \({\mathbf p}= (p_1,\dots,p)\), 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.

90B35 Deterministic scheduling theory in operations research
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