An algorithm for computing the reliability of weighted-k-out-of-n systems

This paper constructs a new k-out-of-n model, viz, a weighted-k-out-of-n system, which has n components, each with its own positive integer weight (total system weight=w), such that the system is good (failed) if the total weight of good (failed) components is at least k. The reliability of the weighted-k-out-of-n:G system is the complement of the unreliability of a weighted-(w-k+1)-out-of-n:F system. Without loss of generality, the authors discuss the weighted-k-out-of-n:G system only. The k-out-of-n:G system is a special case of the weighted-k-out-of-n:G system wherein the weight of each component is 1. An efficient algorithm is given to evaluate the reliability of the weighted-k-out-of-n:G system. The time complexity of this algorithm is O(n.k)