A methodological proposal to apply the Monte-Carlo method to dimensional metrology in the industrial engineering field

Abstract

 The Monte Carlo method (MCM), applied to uncertainty 
calculation in metrology, is well-suited for nonlinear functions. 
It also provides more accurate solutions in certain complex 
linear models. Although MCM is extensively covered in the 
ISO Guide to the Expression of Uncertainty in Measurement 
(GUM) and in metrological guides from reference institutions in 
various countries, industrial engineering curricula typically only 
introduce concepts related to uncertainty propagation using 
the traditional analytical method. MCM requires programming 
to generate random numbers within the expected range for 
each variable involved in the metrological system, combining 
computing tools with metrology. This methodological proposal 
is based on a basic system for constructing an angle using 
a sine bar and gauge blocks. The problem progressively 
incorporates the temperature variable under different 
behavioural hypotheses and the influence of other factors, 
such as the roundness tolerance of the sine bar supports. The 
results obtained using MCM are compared with those from 
the classical GUM method, and the analysis demonstrates the 
robustness of MCM from a scientific perspective. Based on this 
methodology, further challenges could be explored, such as 
introducing the flatness tolerance of the surface plate used.