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

摘要

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