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Combinatorial techniques have an important role to compute the joint  reliability importance (JRI) of some coherent systems. We obtain combinatorial formula for calculation of the JRI of two components in a generalized version of consecutive type systems consisting of n linearly ordered components such that system fails if and only if (iff) 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 linear m-consecutive-k-out-of-n:F system (nonoverlapping case when l=0). In addition, some numerical and illustrative examples are presented.

Analysis of joint reliability importance in linear m-consecutive-k,l -out-of-n:F system