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

• This paper provides, for the first time, exact one-sided STI’s for a polynomial regression model of any order over any given interval.

Statistical calibration using linear regression is a useful statistical tool having many applications. Calibration for infinitely many future yy-values requires the construction of simultaneous tolerance intervals (STI’s). As calibration often involves only two variables xx and yy and polynomial regression is probably the most frequently used model for relating yy with xx, construction of STI’s for polynomial regression plays a key role in statistical calibration for infinitely many future yy-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.