m -Consecutive- k , l -Out-of- n Systems

Here we present the structure functions for the linear and circularm-consecutive-k,l-out-of-n:F (G) systems, which consists ofnlinearly or circularly ordered components such that the system fails (works) iff there are at leastmtimesl-overlapping runs of consecutivekfailed (working) components. The duality of these F and G systems is obtained, and the proofs are given. The generalized reliability formulae for the systems are obtained by using the finite Markov chain imbedding approach for statistically independent and Markov-dependent cases. Some miscellaneous results on the reliability of these systems and numerical examples are provided to illustrate the results obtained in the paper.