Win-probabilities for comparing two Weibull distributions

Abstract

This paper considers the problem of comparing two processes or treatments which are each modelled with a Weibull distribution. Win-probabilities are considered, which compare potential single future observations from each of the two treatments. This information can be useful in helping decide which of the two treatments to adopt, and can be combined with other factors relevant to a practitioner such as the availabilities, costs and side-effects of the two treatments. A methodology employing joint confidence sets is developed which not only allows estimation and confidence interval construction for the win-probabilities, but at the same guaranteed confidence level also tests whether Weibull distributions are appropriate for the data, identifies any common Weibull distributions for the two processes and also provides individual inferences for the two Weibull distributions. Examples are given to illustrate the implementation and application of this methodology, for which R computer code is available from the authors. This methodology can be extended to different models such as other two-parameter and three-parameter Weibull models, and to the comparison of three or more Weibull distributions.