Methodology to implement adaptive Monte Carlo method in the evaluation of measurement uncertainty, using the Maple symbolic computation. Application to a simple experiment

Abstract

The objective of this study is to apply a rigorous methodology to estimate measurement uncertainty using the adaptive Monte Carlo simulation method (MCM). As an example, the uncertainty in the measurement of the area of a triangle was estimated. The value of the area (y) and its associated uncertainty (uy) were calculated based on an algorithm programmed in Maple 12, generating a total of 10,000 values of the measurand. To calculate the confidence interval (or coverage interval), these values were exported to an MS Excel spreadsheet, where the cumulative percentages of the cumulative probability distribution function (CPDF) were obtained, and the lower and upper limits of the coverage interval (yinf, ysup) at a 95% probability level were evaluated. Based on the results, a histogram was plotted, showing a normal distribution. To verify statistical stability, the adaptive procedure from Supplement 1 of the GUM ISO 2008 guide was applied. The calculations were repeated three times until the desired precision was achieved. The final parameter values of the measurand in cm² were: y = 50.72, uy = 0.13, yinf = 50.48, ysup = 50.96. The classical GUM 1995 method or law of propagation of uncertainty was also applied, yielding the following values: y = 50.72, uy = 0.25, yinf = 50.21, ysup = 51.22. When comparing the two methods, the simulation technique was found to offer greater precision.