Inferences on the parameters of the Weibull distribution

For the most part, solutions to the problems of making inferences about the parameters in the Weibull distribution have been limited to providing simple estimators of the parameters. Little has been known about the properties of the estimators. In this paper the small and moderate sample size properties of the maximum likelihood estimators are studied and their superiority is established. The problem of making further inferences which are based on the maximum likelihood estimates of the parameters is then considered. The inferences that are presented can be divided into those based on a single sample and those based on two independent samples from Weibull distributions and include solutions to the standard problems of interval estimation and hypothesis testing. In addition tolerance limits and confidence limits on the reliability are given. these procedures are accomplished by the discovery of certain pivotal functions whose distributions can be obtained by Monte Carlo methods. Although the distributions are only tabulated for complete samples the procedures which are presented can be extended to the case of censored sampling since for this type of sampling the basic functions remain pivotal --Abstract, page ii