Improved Method of Inclusion-Exclusion Applied to k-out-of-n Systems

The method of inclusion-exclusion is represented in general form for reliability analysis. Applying it to the reliability of k-out-of-n system causes many cancelling terms. The method is improved to use only noncancelling terms in evaluating bounds on the reliability of k-out-of-n systems. These bounds are appreciably better, and converge to the exact system reliability in at most n - k + 1 steps. In conclusion some numerical considerations suggest the quality of the bounds. Similar results for the reliability analysis of networks were derived by Satyanaraynna & Prabhakar.