<p>In this paper, we adopt a theoretical framework rooted in information theory, specifically focusing on cumulative residual extropy, to examine and contrast the times of system inactivity across multiple setups. By employing mixture-based models, we characterize the cumulative residual extropy associated with system inactivity time, exploring the variability of this metric in diverse system configurations. The comparative analysis of these systems is performed through the application of stochastic ordering methods, alongside the utilization of stochastically ordered conditional coefficient vectors. Additionally, we derive upper and lower bounds for the cumulative residual extropy in relation to inactivity times. To advance our understanding of system complexity, we introduce a novel metric, the Jensen cumulative residual extropy divergence, designed to quantify the intricacies of system behavior. To showcase the practical utility of our results, we calculate and compare both the cumulative residual extropy and the Jensen cumulative residual extropy divergence for system inactivity times within an exponential distribution framework. Finally, we identify the optimal configuration for system performance by employing the signature criterion, derived from the Jensen cumulative residual extropy, within the exponential model context.</p>