Comparison of GUM and Monte Carlo methods for the uncertainty estimation in hardness measurements

Gouda M Mahmoud,Riham S Hegazy

doi:10.1051/ijmqe/2017014

Abstract

Monte Carlo Simulation (MCS) and Expression of Uncertainty in Measurement (GUM) are the most common approaches for uncertainty estimation. In this work MCS and GUM were used to estimate the uncertainty of hardness measurements. It was observed that the resultant uncertainties obtained with the GUM and MCS without correlated inputs for Brinell hardness (HB) were ±0.69 HB, ±0.67 HB and for Vickers hardness (HV) were ±6.7 HV, ±6.5 HV, respectively. The estimated uncertainties with correlated inputs by GUM and MCS were ±0.6 HB, ±0.59 HB and ±6 HV, ±5.8 HV, respectively. GUM overestimate a little bit the MCS estimated uncertainty. This difference is due to the approximation used by the GUM in estimating the uncertainty of the calibration curve obtained by least squares regression. Also the correlations between inputs have significant effects on the estimated uncertainties. Thus the correlation between inputs decreases the contribution of these inputs in the budget uncertainty and hence decreases the resultant uncertainty by about 10%. It was observed that MCS has features to avoid the limitations of GUM. The result analysis showed that MCS has advantages over the traditional method (GUM) in the uncertainty estimation, especially that of complex systems of measurement. MCS is relatively simple to be implemented.

Highlights

The guide to the expression of measurement uncertainty (GUM, JCGM 100) and the propagation of distributions by a Monte Carlo method (GUMS1, JCGM 101) are two of the most widely used documents concerning measurement uncertainty evaluation in metrology
Monte Carlo Simulation (MCS) is relatively simple to implement; there is no need for complex mathematics related to calculating sensitivity coefficient by partial differentiation and it was demonstrated that the MCS is relatively compatible with the conventional uncertainty estimation methods of linear systems and systems that have small uncertainties
From this research article it was concluded that: – the expanded uncertainty results estimated with the GUM Framework and the MCS showed no significant differences

Summary

Introduction

The guide to the expression of measurement uncertainty (GUM, JCGM 100) and the propagation of distributions by a Monte Carlo method (GUMS1, JCGM 101) are two of the most widely used documents concerning measurement uncertainty evaluation in metrology. Both documents describe three phases: (a) the construction of a measurement model, (b) the assignment of probability distributions to quantities, and (c) a computational phase that specifies the distribution for the quantity of interest. GUM provides a framework and procedure for evaluating and expressing measurement uncertainty.

Methods

Findings

Discussion

Conclusion