A limit theorem for the reliability of a consecutive-k-out-of-n system

A consecutive-k-out-of-n system consists of n identical and linearly ordered components. The system will fail if and only if at least k consecutive components fail. Let Tn be the system&s lifetime. Then, under very general conditions we prove that there is a positive constant a, so that the distribution of the random variable n (1/ka) Tn converges to a Weibull distribution, as n→∞