CORRIGENDA ON “NEW COMPARISONS IN BIRNBAUM IMPORTANCE FOR THE CONSECUTIVE-k-OUT-OF-n SYSTEM”
Probability in the Engineering and Informational Sciences
NEW COMPARISONS IN BIRNBAUM IMPORTANCE FOR THE CONSECUTIVE-k-OUT-OF-n SYSTEM
Probability in the Engineering and Informational Sciences
Joint importance of multistate systems
Computers and Industrial Engineering
Structure importance of consecutive-k-out-of-n systems
Operations Research Letters
Network reliability importance measures: combinatorics and Monte Carlo based computations
WSEAS Transactions on Computers
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The joint structural importance (JSI) is an important measure of how two components interact in contributing to the system reliability. The value of JSI is positive (negative) if and only if one component becomes more important (less important) when the other works. A consecutive-k-out-of-n system is a linear arrangement of n components such that the system is failed if and only if some consecutive k components are all failed. In this paper, we study joint structural importance JSI (i, j) in the consecutive-k-out-of-n system. We completely solve JSI(i, j) for k = 1 (the series system), k = n (the parallel system), k=n-1, and k=n-2, respectively. For the other k, we prove that JSI(1, j′) = JSI(1,k) n) = JSI(1,k+2) j) k+1), for 2 ≤ j′ ≤ k-1 and k+3≤j≤n-1. For a fixed i, we prove that the graph of JSI (i, j) has a W-shape property for max{1, i-k-1}≤ j ≤ min{n,i+k+1} with JSI (i,i)=0. We also present exact formula for JSI(i,j) and obtain many relations among them.