A Useful Property of ``Graphical´´ Estimators of Location and Scale Parameters

This paper presents a method for constructing exact s-confidence limits for reliability and/or quantiles based on graphical estimators of location and scale parameters. The method arises from the ancillary property of the reliability function estimated by using plotting positions and the least squares method. From the distribution of this estimator alone, one can obtain graphs or tables to calculate directly the s-confidence limits for both reliability and quantiles. These limits are exact even for very small sample-sizes in that they are calculated without using asymptotic approximations. An example of a graph which enables one to calculate these limits for a 2-parameter Weibull distribution, is given. This example uses plotting positions recently proposed by the author.