(untitled) (Austrian Journal of Statistics, 2014)
Statistical tolerance intervals are another tool for making statistical inference on an unknown population. The tolerance interval is an interval estimator based on the results of a calibration experiment, which can be asserted with stated confidence level 1 ? , for example 0.95, to contain at least a specified proportion 1 ? , for example 0.99, of the items in the population under consideration. Typically, the limits of the tolerance intervals functionally depend on the tolerance factors. In contrast to other statistical intervals commonly used for statistical inference, the tolerance intervals are used relatively rarely. One reason is that the theoretical concept and computational complexity of the tolerance intervals is significantly more difficult than that of the standard confidence and prediction intervals. In this paper we present a brief overview of the theoretical background and approaches for computing the tolerance factors based on samples from one or several univariate normal (Gaussian) populations, as well as the tolerance factors for the non-simultaneous and simultaneous two-sided tolerance intervals for univariate linear regression. Such tolerance intervals are well motivated by their applicability in the multiple-use calibration problem and in construction of the calibration confidence intervals. For illustration, we present examples of computing selected tolerance factors by the implemented algorithm in MATLAB.