A Statistical Theory of Calibration

Abstract

The kind of calibration problem considered may be roughly described as follows: There are two related quantities $\mathscr{U}$ and $\mathscr{V}$ such that $\mathscr{U}$ is relatively easy to measure and $\mathscr{V}$ relatively difficult, requiring more effort or expense; furthermore the error in a measurement of $\mathscr{V}$ is negligible compared with that for $\mathscr{U}$. A distinguishing feature of the problem is, that from a single calibration experiment, where measurements are made on a number of pairs $(\mathscr{U}, \mathscr{V})$, we wish subsequently to estimate the unknown values of $\mathscr{V}$ corresponding to a very large number of measurements of $\mathscr{U}$. The problem is solved by a procedure of interval estimation, whose operating characteristic is expressed in terms of a reformulation of the law of large numbers. Some idea of the contents of the article may be obtained from the table of contents.