Cumulative Entropy of Past Lifetime for Coherent Systems at the System Level

Abstract

This paper explores the cumulative entropy of the lifetime of an n-component coherent system, given the precondition that all system components have experienced failure at time t. This investigation utilizes the system signature to compute the cumulative entropy of the system’s lifetime, shedding light on a crucial facet of a system’s predictability. In the course of this research, we unearth a series of noteworthy discoveries. These include formulating expressions, defining bounds, and identifying orderings related to this measure. Further, we propose a technique to identify a preferred system on the basis of cumulative Kullback–Leibler discriminating information, which exhibits a strong relation with the parallel system. These findings contribute significantly to our understanding of the predictability of a coherent system’s lifetime, underscoring the importance of this field of study. The outcomes offer potential benefits for a wide range of applications where system predictability is paramount, and where the comparative evaluation of different systems on the basis of discriminating information is needed.