System Level Extropy of the Past Life of a Coherent System

In this paper, we take a new approach to uncertainty in a coherent system, where components are assumed to be all inactive in a given time. In particular, the signature-based method is used to quantify the extropy of the past lifetime of the system, which serves as a valuable indicator of its predictability. The results provide several key findings, including some bounds and stochastic ordering aspects for this measure. We also introduce a new formula to select the system that is preferable based on its relative extropy in the past. The results of this work can provide insights for designing systems to improve their reliability and resilience.