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

  • G. WimmerEmail author
  • V. Witkovský

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.



The research was supported by the Slovak Research and Development Agency, project APVV-15-0295, and by the Scientific Grant Agency VEGA of the Ministry of Education of the Slovak Republic and the Slovak Academy of Sciences, by the projects VEGA 2/0054/18 and VEGA 2/0011/16.


  1. 1.
    JCGM 100:2008, Guide to the Expression of Uncertainty in Measurement (GUM). Google Scholar
  2. 2.
    JCGM 101:2008, Evaluation of Measurement Data – Suplement 1 to the Guide to the Expression of Uncertainty in Measurement – Propagation of Probability Distributions Using a Monte Carlo Method. Google Scholar
  3. 3.
    JCGM 200:2008, International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM). Google Scholar
  4. 4.
    EA-4/02 M:2013, Evaluation of the Measurement in Calibration. Google Scholar
  5. 5.
    A. Rényi, Probability Theory, Akadémiai Kiadó, Budapest (1970).zbMATHGoogle Scholar
  6. 6.
    V. Witkovský, G. Wimmer, Z. Ďurišová, et al., “Brief overview of methods for measurement uncertainty analysis: GUM uncertainty framework, Monte Carlo method, characteristic function approach,” in Measurement 2017: 11th Int. Conf. on Measurement, IEEE (2017), pp. 35–38.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia
  2. 2.Faculty of ScienceMatej Bel UniversityBanská BystricaSlovakia
  3. 3.Institute of Measurement ScienceSlovak Academy of SciencesBratislavaSlovakia

Personalised recommendations