Reliability and Reliability Importance of Weighted-r-Within-Consecutive-k-out-of-n : F System

In this paper, we consider a weighted-r-withinconsecutive- k-out-of-n : F system. The weighted system has in general n components, each one having a positive integer weight wi, i = 1, 2,..., n. The weighted-r-within-consecutive-k-out-of- n : F system fails if and only if the total weight of failed components among k consecutive components is at least r. We introduce a binomial-type weighted scan statistic and study the reliability, the Birnbaum, improvement potential importance and Bayesian reliability importance of the system taken into consideration. We develop an explicit closed-form formula for the evaluation of reliability and reliability importance measures of a weightedr- within-consecutive-k-out-of-n : F system and demonstrate the results numerically. We present a study showing the effectiveness of the method in terms of CPU time.