Domination of k-out-of-n systems

The main objective of this paper is to derive a formula for the signed domination of k-out-of-n systems. The behavior of such systems is investigated when pivotal decomposition is applied to them. The nature of the two resulting subsystems has been examined; the signed domination theorem has been extended to those systems and used as a proving tool for the main objective. A closed formula is presented for computing exactly the reliability of k-out-of-systems with the same component reliabilities by means of paths or cut sets. Most of the theoretical results based on domination theory are still restricted to linear networks (without duplicated edges). They should be extended to the realistic cases, such as fault trees and block diagrams. This paper is such an effort and is a beginning in this direction. A major area for further investigation is to attend to exploit the extraction of these results to broader and more general classes of nonlinear systems.