On Uncertainty Analysis in the Calibration of Gauge Block: Another Look at Example S4 from EA-4/02

We present application of three alternative approaches for solving the Example S4 from EA-4/02 (Calibration of a gauge block of nominal length 50 mm); see [4]. As a result, application of the alternative approaches validates usage of the standard GUM uncertainty framework; see [1]. In particular, we consider the following alternative approaches to obtain the expanded uncertainty of measurement and/or the proper coverage interval for the measurand, namely (i) GUF (GUM uncertainty framework) based on using the Guide to the expression of uncertainty in measurement [1], (ii) MCM (Monte Carlo method) based on using Supplement 1 to the Guide to the Expression of Uncertainty in Measurement – propagation of distributions using a Monte Carlo (MC) method [2], and (iii) CFA (characteristic function approach) based on using the inverted characteristic function of the optimal linear estimator of the measurand [5]. Application of the methods (i), (ii), and (iii) is illustrated by uncertainty analysis of a well-known dataset, and the results are compared. Some useful mathematical results concerning probability density functions (pdf) and characteristic functions (cf) are given in the Appendix.