Eryilmaz, SerkanEryılmaz, SerkanIndustrial Engineering2024-07-052024-07-052012150018-95291558-172110.1109/TR.2011.21824012-s2.0-84858157948https://doi.org/10.1109/TR.2011.2182401https://hdl.handle.net/20.500.14411/1361Eryilmaz, Serkan/0000-0002-2108-1781A combined m-consecutive-k-out-of-n:F & consecutive-k(c)-out-of-n:F system consists of linearly ordered components, and fails iff there exist at least k(c) consecutive failed components, or at least m non-overlapping runs of k consecutive failed components. This structure has applications for modeling systems such as infrared detecting and signal processing, and bank automatic payment systems. In this paper, we derive a combinatorial equation for the number of path sets of this structure including a specified number of working components. This number is used to derive a reliability function, and a signature based survival function formulae, for the system consisting of i.i.d. components. We also obtain a combinatorial equation for the reliability of a system with Markov dependent components.eninfo:eu-repo/semantics/closedAccessConsecutive k(c)-out-of-n:F systemm-consecutive-k-out-of-n:F systemMarkov dependencemean time to failurerunssignaturesurvival functionArticleQ1611215219WOS:000301198500023