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 T n 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) T n converges to a Weibull distribution, as n →∞