<p>This study presents a comprehensive examination of the extropy associated with the inactivity times of failed components in coherent systems. In contrast to conventional reliability measures that emphasize system inactivity or residual lifetime analysis, the proposed framework captures the underlying informational characteristics embedded in the inactivity times of failed components while the overall system remains operational. By employing system signatures, we derive closed-form representations for the extropy of these inactivity times and establish a series of stochastic bounds and comparative results that elucidate the influence of system structure and configuration. Furthermore, we assess the sensitivity of extropy through numerical experiments based on Weibull-distributed lifetimes. On the applied side, we develop two non-parametric estimators for the extropy of inactivity times of failed components in coherent systems. The proposed estimators’ efficiency are demonstrated via simulated datasets and further illustrated through an image processing application, highlighting the practical relevance of the extropy-based approach in reliability and information-theoretic analysis.</p>