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

Abstract

A consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F system consists of [Formula: see text] linear (circular)-ordered components such that the system fails if and only if there exists a set of [Formula: see text] consecutive linear (circular) component that contains at least [Formula: see text] failed components. Consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: 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 [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: 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.