Joint Reliability Importance in Linear $m$-Consecutive-$k$-Out-of-$n$: F Systems

We study the joint reliability importance (JRI) of two components in Lin/m/Con/k/n:F systems. A Lin/m/Con/k/n:F system consists of n linearly ordered binary components, and the system fails iff there are at least m nonoverlapping runs of k consecutive failed components (n ≥ mk). In particular, we obtain expressions for the JRI in Lin/m/Con/k/n:F systems when the components are s-independent & identical, when the components are s-independent & nonidentical, and when the components are exchangeable & s-dependent. We present extensive numerical illustrations.