Estimation of measurement uncertainties -: an alternative to the ISO Guide

The procedure for uncertainty assessment set out in the Guide to the Expression of Uncertainty in Measurement, published by the International Organization for Standardization (ISO), is compared with an alternative system. The ISO Guide links the overall uncertainty to a so-called k(P) factor, implicitly expressing the degree of confidence that the measured result should cover the true value of the physical quantity in question. Here it is argued that this standard procedure, in which the magnitude of a given k(P) factor is tied to the degree of confidence, presents the experimenter with difficulties. These arise from the need to associate a probability density with so-called unknown systematic errors. Consequently, the recommended procedures may not be taken up by experimenters who carry out laboratory measurements on a daily basis. A simplification of the ISO procedure suggested by the Guide involves the assignment of the values 1 or 2 (or even 3) to k(P). The alternative approach presented here argues that this simplification does not reflect the prevailing physical situation, and that the degree of confidence obtained lacks physical objectivity. Stationary measurement processes, strictly separating random and unknown systematic errors, are considered. Random errors are assumed to be normally distributed, and no probability distribution density is attributed to the unknown systematic errors. As random and systematic errors are kept separate, it is possible to express the influence of random errors by generalized confidence intervals (from Student's t-distribution) and the influence of systematic errors by worst-case estimates. No confidence statement is associated with the overall uncertainties, and the intrinsic problem of the Guide is circumvented. The formalisms are robust, transparent, and locate measured quantities with reasonable reliability.