Exact Reliability for Consecutive k-out-of-r-from-n: F System with Equal and Unequal Components Probabilities

A consecutive k-out-of-r-from-n: F system consists of n linear ordered components such that the system fails if and only if there exist a set of r consecutive linear component that contains at least k failed components. Consecutive k-out-of-r-from-n: F system has been considered in many fields such as reliability analysis. All recent efforts in this area have been focused on acquiring band or approximation for their reliability such that less attention has been paid to their closed form and exact reliability in the literature. In the present paper, with designing an innovative algorithm the exact reliability for extensive class of consecutive k-out-of-r-from-n: F system is obtained. Specially this task for equal and unequal components probabilities is done. Finally, the numerical results for calculating the exact reliability in extensive class of this strategic systems were applied.