Reliability evaluation of combined k-out-of-n: F, consecutive-k-out-of-n: F and linear connected-(r, s)-out-of-(m, n): F system structures

Based on a real industrial application, three new system reliability models are proposed: combined k-out-of-n:F and consecutive-k/sub c/-out-of-n:F system; combined k-out-of-m/spl middot/n:F and linear connected-(r,s)-out-of-(m,n):F system; and combined k-out-of-m/spl middot/n:F consecutive-k/sub c/-out-of-n:F and linear connected-(r,s)-out-of-(m,n):F system. Reliability evaluation algorithms are provided for these models. The computation times of the algorithms for these models are, respectively: O(n/spl middot/k), O(k/spl middot/n/spl middot/2/sup m//spl middot/s/sup m-r+2/), O(k/spl middot/n/spl middot/(2k/sub c/)/sup m/spl middot//s/sup m-r+1/). The algorithms are used for system reliability evaluation of furnace systems. The concept of the combined k-out-of-n:F and 1-dimensional and 2-dimensional consecutive-k-out-of-n:F systems can be extended to other variations of the consecutive-k-out-of-n:F systems, e.g., the consecutive-k-out-of-n:G system and 1-dimensional and 2-dimensional r-within-k-out-of-n:F systems. The concept of Markov chain imbeddable (MIS) systems is another excellent tool that can be used for analysis of such combined system structures.