Computational method for importance measure of the k-out-of-n system based on stress–strength interference

Importance measures, which are used to evaluate the relative significance of various components to system reliability, have been widely applied in system reliability designs and risk assessments. This article deals with the importance measure for the k-out-of-n system of which components are loaded by common stress. Based on system-level stress–strength interference model, a new computational method for the Birnbaum importance measure is proposed for the k-out-of-n system. Then, two numerical examples are presented to further illustrate the proposed method and some key contents are discussed particularly as follows: (1) the importance measures for the system with s-identical components and nonidentical components are developed, (2) component importance changes as its own strength distribution parameters change and (3) the new method corrects the errors caused by ignoring the failure dependency.