A study on reliability and component importance of linear overlapping m-consecutive-k-out-of-n: F system

A linear overlapping m-consecutive-k-out-of-n: F system can be applied to pattern recognition, communication and bio-information etc. The system consists of n components arranged orderly in a line and has failure rule that m overlapping failed sections exist in the system, and there are consecutive-k failed components in each section. In order to obtain the reliability indexes of linear overlapping m-consecutive-k-out-of-n: F system, formulas of the system reliability and the importance of every component were deduced by Markov chain method, which provide basis for optimal design of the system.