Improved Method of Inclusion-Exclusion Applied to k-out-of-n Systems
- 1 April 1982
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Reliability
- Vol. R-31 (1) , 36-40
- https://doi.org/10.1109/tr.1982.5221218
Abstract
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.Keywords
This publication has 12 references indexed in Scilit:
- Recursive Disjoint Products, Inclusion-Exclusion, and Min-Cut ApproximationsIEEE Transactions on Reliability, 1980
- New Topological Formula and Rapid Algorithm for Reliability Analysis of Complex NetworksIEEE Transactions on Reliability, 1978
- System reliability analysis: A tutorialMicroelectronics Reliability, 1978
- Advanced CombinatoricsPublished by Springer Nature ,1974
- Some Aspects of the Statistical Approach to ReliabilityJournal of the Royal Statistical Society. Series A (General), 1973
- The Maximum Error in System Reliability Calculations by Using a Subset of the Minimal StatesIEEE Transactions on Reliability, 1971
- On the Method of Inclusion and ExclusionJournal of the American Statistical Association, 1967
- On the foundations of combinatorial theory I. Theory of M bius FunctionsProbability Theory and Related Fields, 1964
- Multi-Component Systems and Structures and Their ReliabilityTechnometrics, 1961
- On the Probability of the Occurrence of at Least $m$ Events Among $n$ Arbitrary EventsThe Annals of Mathematical Statistics, 1941