Reliability analysis and optimal replacement for a <i>k</i> -out-of- <i>n</i> system with various components subject to shocks

Consider a k -out-of- n system consisting of L types of components, L=1,2,…,n such that the number of components of the l th type is n l , l=1,2,…,L . Let this system is exposed to external shocks, and each entered shock may fail some components of the system. The system fails when at least n-k+1 components fail. In this paper, we study the reliability of this system under a shock model. In addition to reliability analysis, we investigate a preventive maintenance policy for this system to reduce abrupt failures. Numerical examples are also provided to illustrate theoretical achievements.