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A note on the mixture representation of the conditional residual lifetime of a coherent system. (English) Zbl 1301.62023
Summary: This paper builds a mixture representation of the reliability function of the conditional residual lifetime of a coherent system in terms of the reliability functions of conditional residual lifetimes of order statistics. Some stochastic ordering properties for the conditional residual lifetime of a coherent system with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors.

MSC:
62E15 Exact distribution theory in statistics
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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