Exact Inferences for a Weibull Model

This article considers the problem of making exact inferences about a standard two parameter Weibull model. Exact inferences are obtained from the construction of a confidence set for the two parameters that has an exact specified confidence level. This exact confidence set is obtained from Kolmogorov's bounds on the empirical cumulative distribution function of the data set. Simple and compact equations are derived that define the confidence set in terms of a set of linear inequalities. The confidence set can be used, for example, to generate confidence bands for the reliability function, confidence intervals for the moments and quantiles of the distribution, and confidence intervals for the parameters themselves. The methodology can be extended to different models such as other two-parameter and three-parameter Weibull models.