Comparisons of the Expectations of System and Component Lifetimes in the Failure Dependent Proportional Hazard Model

Abstract

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.

Link functions for parameters of sequential order statistics and curved exponential families

“…Sequential order statistics (SOSs) constitute a general model for ordered statistical data and provide a natural modeling framework for multi-unit technical systems, in which the failure of a component may have an impact on the lifetimes of the surviving components; see, e.g., [18], [19], [14], [25], [2], [13], [16], [7], [5], [6], [11]. The modeling is based on the assumption that, upon a failure of some component, the remaining components have a possibly different underlying lifetime distribution.…”