Statistical calibration and exact one-sided simultaneous tolerance intervals for polynomial regression

Abstract

Statistical calibration using linear regression is a useful statistical tool having many applications. Calibration for infinitely many future y-values requires the construction of simultaneous tolerance intervals (STI’s). As calibration often involves only two variables x and y and polynomial regression is probably the most frequently used model for relating y with x, construction of STI’s for polynomial regression plays a key role in statistical calibration for infinitely many future y-values. The only exact STI’s published in the statistical literature are provided by Mee et al. (1991) and Odeh and Mee (1990). But they are for a multiple linear regression model, in which the covariates are assumed to have no functional relationships. When applied to polynomial regression, the resultant STI’s are conservative. In this paper, one-sided exact STI’s have been constructed for a polynomial regression model over any given interval. The available computer program allows the exact methods developed in this paper to be implemented easily. Real examples are given for illustration.