Abstract
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.
Highlights
The marginal reliability importance (MRI) of a component measures the change in system reliability with respect to the change in component reliability([5, 6, 24, 35, 36, 37])
Oruc, and Oger [12] obtained general formula for computing the joint reliability importance of two components for a binary coherent system that consists of exchangeable dependent components
One can see that components 1 and 3, and 2 and 4 are reliability complements for p < 0:4; while they are reliability substitutes for p 0:4: The components 2 and 3 are reliability substitutes for p 0:2: In Table 2., we show the sign of joint reliability importance (JRI) between component 1 and others for di¤erent values of m; k; l and n with di¤erent component reliability p when Lin/m/Con/k/l/n : F system contains s-independent and identical components
Summary
The marginal reliability importance (MRI) of a component measures the change in system reliability with respect to the change in component reliability([5, 6, 24, 35, 36, 37]). Oruc, and Oger [12] obtained general formula for computing the joint reliability importance of two components for a binary coherent system that consists of exchangeable dependent components.
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