An algorithmic reliability evaluation approach for a multi-state k-out-of-n:G system with nonidentical and large number of components

This paper deals with the dynamic reliability analysis of two different three-state k-out-of-n:G systems that consist of independent and nonidentical components. Marginal and joint survival functions are represented by using permanents. Due to the permanent-based representations, it is hard to find out the survival probabilities when the number of components in the systems is large. Thus, we propose an effective algorithmic approach to evaluate the survival probabilities for the systems with large number of components. Also, for the dynamic performance evaluation of the three-state systems, non-homogeneous continuous time Markov (NHCTM) degradation process assumption is used. Survival probabilities of each system at different states with different number of components are provided and the results are discussed for both major and minor degradation processes.