Comparisons of coherent systems with active redundancy and component lifetimes following the proportional odds model.

The use of redundancies or spares in a system is a widely adopted technique to enhance system reliability and reduce the risk of system failure. Redundancies are typically incorporated into systems at the component or system levels. It is a significant problem to allocate appropriate redundancies into a system from a set of available options for the same. In this paper, we establish sufficient conditions to compare the reliability of coherent systems of dependent components with different sets of active redundancy, whether at the component level or the system level, based on some stochastic orders. We have obtained the results for the component lifetimes following the proportional odds (PO) model (the Marshall–Olkin family of distributions) for any lifetime distribution as a baseline distribution. We have studied the problem in the most general setup, with the consideration of coherent system that includes most of the common system structures, the consideration of non-matching spares, the consideration of dependencies of the components with different associated parameters of the copulas, and the consideration of general distribution as the baseline distribution of the PO model. We provide examples satisfying the sufficient conditions of the theoretical results. Additionally, we illustrate some of the results using real-world data. [ABSTRACT FROM AUTHOR]