Practical Correlation in Repetitive Measurements

Abstract

Anyone who is conversant with the standard G.U.M. method for calculating uncertainties using the so-called “Law for the Propagation of Uncertainties” knows that it is important to include any correlations among the components in the calculation. We have all seen simple examples of correlation, such as the comparison of height and weight in a sample of people. But in calculating an uncertainty budget with correlated uncertainties, it is not possible to measure the correlation coefficients. They have to be estimated. It is a fact that any two instruments which are not perfect, will have errors which will be correlated. Unless one has a perfect calibration standard, the correlation coefficient cannot be measured. This paper deals with a practical example calibrating thread wires in which 18 short term measurements are recorded using the same micrometer. During the short time of the calibration, many of the Type B uncertainties will be constant, although they will most likely vary tomorrow, next week and next year. This paper will show a method for estimating the correlation coefficient for uncertainties for calculated parameters such as roundness, taper and the master average.