Comparisons of the Expectations of System and Component Lifetimes in the Failure Dependent Proportional Hazard Model
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In the failure dependent proportional hazard model, it is assumed that identical components work jointly in a system. At the moments of consecutive component failures the hazard rates of still operating components can change abruptly due to a change of the load acting on each component. The modification of the hazard rate consists in multiplying the original rate by a positive constant factor. Under the knowledge of the system structure and parameters of the failure dependent proportional hazard model, we determine tight lower and upper bounds on the expected differences between the system and component lifetimes, measured in various scale units based on the central absolute moments of the component lifetime. The results are specified for the systems with unimodal Samaniego signatures.
KeywordsCoherent system Failure dependent proportional hazard model Generalized order statistics Samaniego signature Sharp bound
Mathematics Subject Classification (2010)Primary: 62N05 Secondary: 60E15 62G30
The authors thank to the anonymous referee for mny valuable comments which helped in preparation of the final version of the paper. The first and third authors were supported by National Science Centre of Poland under grant 2015/19/B/ST1/03100.
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