Sample Size for Selecting the Better of Two Weibull Populations

Suppose an experimenter wishes to select the better of two Weibull populations. In a life testing situation he may have some time t* for which the device must perform properly and he would consider the better population to be the one with the larger reliability at time t*. It is reasonable for the experimenter to test n items from each of the two populations until there are r(r < n) failures from each and then select as better the population for which the maximum likelihood estimate of the reliability at time t* is the larger. This paper presents the sample sizes needed to achieve a desired level for the probability of correct selection with such a decision rule.