Recursive Formulas for the Reliability of Multi-State Consecutive- k -out-of- n :G Systems

In this paper, we provide an algorithm for evaluating the system state distribution for any multi-state consecutive-k-out-of-n:G system including the decreasing multi-state G system, the increasing multi-state G system, and other G systems. We evaluated our proposed algorithms in terms of the orders of computation time, and memory requirement. Furthermore, we conducted a numerical experiment to determine the actual computation time. Our proposed algorithm is more effective for systems with a large n.