An efficient reliability computation of generalized multi-state k-out-of-n systems

Huang et al. (2000) proposed the generalizedmultistate k-out-of-n : G system model, where there can be different k values with respect to different states. The system is in state j or above if there exists an integer value l ( j ≤ l ≤ M ) such that at least kl components are in state l or above. Intuitively, the system is considered to be in state j or above if any of the requirements on the number of components at states j to M are met. The generalized multi-state k-out-of-n system model proposed recently provides more flexibility in describing practical systems. However, the reliability evaluation algorithm proposed in (Huang et al. 2000) is not efficient because it is enumerating in nature. Further, the algorithm is applicable only when the k values follow a monotonic pattern.