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

A consecutive linear (circular) k-out-of-r-from-n: F system consists of n linear (circular)-ordered components such that the system fails if and only if there exists a set of r consecutive linear (circular) component that contains at least k failed components. Consecutive linear (circular) k-out-of-r-from-n: F systems attract tremendous attention for researchers of reliability analysis. Recent efforts in this area have focused on simple situations or approximation bands for their reliability but closed form and exact amount not gained. In this paper, we designed an innovative algorithm and an innovative program to obtain the exact reliability for an extensive class of consecutive circular k-out-of-r-from-n: F system with particular emphasis for equal and unequal component probabilities. Finally, we reviewed an applied example and applied comparative and numerical results and calculated the exact reliability of this strategic system.