@article{article_635829, title={Analysis of joint reliability importance in linear m-consecutive-k,l -out-of-n:F system}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={69}, pages={699–716}, year={2020}, DOI={10.31801/cfsuasmas.635829}, author={Kan, Cihangir and Ozkut, Murat}, keywords={m-consecutive-k-l-out-of-n:F systems,Joint Reliability Importance,Exchangeability,System Reliability,Combinatorial Method}, abstract={<div> <span style="font-size:12.6px;">Combinatorial techniques have an important role to compute the joint  </span>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.  <span style="font-size:.9em;">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. </span> </div>}, number={1}, publisher={Ankara University}