Analysis of Joint Reliability Importance in Linear M-Consecutive L-Out System

Abstract

Combinatorial techniques have an important role to compute the joint reliability importance (JRI) of some coherent systems. We obtain combi- natorial formula for calculation of the JRI of two components in a generalised version of consecutive type systems consisting of n linearly ordered components such that system fails if and only if (i§) there are at least m l-overlapping runs of k consecutive failed components (n m(k l) + l; l < k). Overlapping runs mean having common elements which is denoted by l: We concentrate on both s-independent & identical components and exchangeable components. Explicit combinatorial formulae are provided for computing the JRI of the above mentioned cases. For both cases, we also compare the results with lin- ear m-consecutive-k-out-of-n:F system (nonoverlapping case when l = 0). In addition, some numerical and illustrative examples are presented.