Importance Analysis of k-out-of-n Multi-State Systems based on Direct Partial Logic Derivatives

In this paper, analysis of k-out-of-n Multi-State Systems (MSSs) is considered. This type of systems consists of n components, and it can be in state j if and only if at least k components are in state j or greater. Investigation of such systems has been considered in several works. However, most of them have dealt only with an efficient computation of several global characteristics, such as system state probability or system availability. In this paper, we deal with importance analysis for such systems. Particularly, we focus on two commonly used importance measures – structural importance and Birnbaum’s importance. Using logical differential calculus, we propose an efficient way of how to calculate these measures for a k-out-of-n MSS. The obtained results are then used to analyze an oil supply system.