EMUE-D6-2-CalibrationUncertaintyGUMvsBayesian

Calibration of a torque measuring system – GUM uncertainty evaluation for least-squares versus Bayesian inference

This example addresses the straight-line calibration of a torque measuring sensor against a reference system using measurements taken at different torque values. For each torque value, a single measurement result of the reference system is available, together with results of repeated measurements of sensor that shall be calibrated. The goal is to determine a linear relationship that relates results of the torque measuring sensor with those of the reference system. The data are analysed by applying (i) ordinary and weighted least-squares estimation in combination with an uncertainty evaluation following the GUM and (ii) Bayesian inference. Analytic expressions are given for the Bayesian uncertainty analysis which simplifies its application. The results obtained by the different approaches are discussed and recommendations given.

Files contained in the dataset are:

• Example_A242.pdf: Report “Calibration of a torque measuring system – GUM uncertainty evaluation for least-squares versus Bayesian inference”;
• Example_A242.tex: LaTeX file to be compiled in order to produce Example_A242.pdf;
• Compendium_A242.bib: bibliography file;
• Fig1.pdf: PDF file needed to compile Example_A242.tex;
• Fig2.pdf: PDF file needed to compile Example_A242.tex;
• data_A242.csv: Date file containing the estimates and standard deviations of the measurements;
• Example_A242.Rmd: R Markdown file for uncertainty evaluation following the GUM and Bayesian inference. As output an HTML file similar to Example_A242.pdf is created with results dynamically produced by underlying R code;
• aps.csl: CSL file needed to cite the reference in Example_A242.Rmd according to the American Physical Society style.