RELIABILITY OF CONSECUTIVE k-OUT-OF-n SYSTEMS

Abstract

In this thesis, we study the reliability of consecutive-k­ out-of-n systems. Both, the one-dimensional and the two­ dimensional consecutive k out-of-n systems are considered. The study is carried out for F and G systems. A brief survey on the one dimensional consecutive k-out-of-n systems is presented and new results on the two dimensional case are obtained.

For the two dimensional-consecutive-k-out-of-n systems, we are concerned with linear and circular connected {r,s)-out­ of-{n,m) : F(G) lattice systems, as well as linear and circular connected (r,s) or (s,r)-out-of-{n,m):F(G) lattice systems.

We obtain exact reliability formulas for some linear and circular-connected-{r,s)-or-(s,r)-out-of-{n,m): F(G) lattice systems. Generally, the derivation of exact formulas for the reliability of the systems, under consideration, is not an easy task. We obtain approximate formulas and bounds on the reliability of such systems, for any values of r, s, n and m.

Bounds are obtained by different approaches. So a comprehensive comparison between the bounds obtained is performed. Finally, the optimal design of the systems, is discussed.

Key Words : Reliability, minimal cuts, minimal paths, 1-dimensionallinear consecutive k-out-of-n:F & G systems, 1-dimensional circular consecutive k-out-of-n:F & G systems, 2-dimensional consecutive k-out-of-n systems, connected-(r,s) out-of-(n,m): F & G lattice systems, connected-(r,s) or (s,r) out of (n,m): F & G lattice systems.