A class of subset selection procedures for Weibull populations

Among distributions that represent component and system life, the Weibull family is presented. Goodness of a Weibull population is defined in terms of the shape parameter. A class of subset selection-procedures based on the U-statistic (derived via the concept of convex ordering) is proposed for two cases: (1) selecting a subset from k Weibull populations which contains the population with the largest shape parameter; and (2) selecting a subset containing all the populations whose shape parameters are at least that of the control population; unknown and known control populations are considered. The approximate implementation of the selection procedures with the help of the existing tables is discussed, and a numerical example is given. Statistical simulation is used to investigate the optimal members of the proposed class in case 1. The simulation shows that a common sample-size of 11 or more can be used to implement the asymptotic results