Lifespan extremes as expected minimum and maximum values of a set of Weibull-distributed random values

In the context of reliability theory and the theory of aging of technical andbiological systems, the time of system failure is often modelled with a two-parameter-Weibull-distribution. Of special interest is, beside the mean time tofailure, the time of the first failure as well as the time of the last failure. Theseare expressed as the largest and smallest values of an ensemble of n Weibull dis-tributed random values. In this article, for these extremes approximations arederived for large n.