A Statistical Theory of Calibration

The kind of calibration problem considered may be roughly described as follows: There are two related quantities U and V such that U is relatively easy to measure and V relatively difficult, requiring more effort or expense; furthermore the error in a measurement of V is negligible compared with that for U. A distinguishing feature of the problem is, that from a single calibration experiment, where measurements are made on a number of pairs (U, V), we wish subsequently to estimate the unknown values of V corresponding to a very large number of measurements of 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.