A weibull limit for the reliability of a consecutive k-within-m-out-of-n system

Abstract

A consecutive k-within-m-out-of-n system consists of n identical and stochastically independent components arranged on a line. The system will fail if and only if within m consecutive components, there are at least k failures. Let Tn be the system's lifetime. Then, under quite general conditions we prove that there is a positive constant a such that the random variable n1/kaTn converges to a Weibull distribution as n →∞.