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A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components. (English) Zbl 1218.90068

Summary: We give necessary and sufficient conditions based on signatures to obtain distribution-free stochastic ordering properties for coherent systems with exchangeable components. Specifically, we consider the stochastic, the hazard (failure) rate, the reversed hazard rate, and the likelihood ratio orders. We apply these results to obtain stochastic ordering properties for all the coherent systems with five or less exchangeable components. Our results extend some preceding results.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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