Failure extropy properties of mixed system with application

Abstract

Recent research has shown growing interest in quantifying uncertainty in system lifetimes. This paper investigates the failure extropy (FEx) of an n-component mixed system, conditioned on the failure of all components by a given time t. Using the concept of system signature, explicit expressions for the FEx of the system lifetime are derived, along with key properties and informative bounds. To extend this framework, a divergence measure based on FEx is proposed to assess the complexity of system structures. A new discrimination measure is also proposed, serving as a valuable tool to assess how closely a system resembles a parallel system. An application to redundancy allocation has been carried out to demonstrate the practical relevance of the proposed results and provide insights into optimal system design under uncertainty.