An approximation for large consecutive-k-out-of-n:F systems

The authors consider a consecutive-k-out-n:F system consisting of identically distributed and statistically independent components, where the life distribution of an individual component is Weibull distributed with scale parameter 1/λ and shape parameter B. Let T_n be the life length of the consecutive-k-out-of-n:F system. The authors prove that for large values of n, the distribution of the n ¹(ka)/T_n, is satisfactorily approximated by a Weibull distribution with the same scale parameter and shape parameter k times the original shape parameter