Reliability of linear consecutively-connected systems with multistate components

A linear consecutively-connected system with multistate components (LCCSMC) consists of n+2 linear ordered statistically independent multistate components C/sub i/, i/spl isin/[0,n], and the sink C/sub n+1/ (which is absolutely reliable in a certain sense). System failure is caused by the C/sub i/. If C/sub i/ is in state 0 then it is failed, if it is in the state j (1/spl les/j/spl les/k/sub j/ for a given k/sub j/) then there are paths from C/sub i/ to the next min(j,n-i+1) components. The system fails if there is no path from C/sub 0/ to C/sub n+1/. This system generalizes the linear consecutive-k-out-of-n:F system and the consecutively-connected system of Shanthikumar (1987). The paper gives recursive algorithms for determining the LCCSMC reliability.<
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