Evaluation of Measurement Uncertainty of Oxygen in Titanium Alloys based on Monte Carlo Method

Abstract

Uncertainty is a scientific representation of the quality level and dispersion of measured results. Considering the key issues of the application of Monte Carlo method (MCM) to evaluate the uncertainty of the single-point calibration linear measurement system, such as the MCM evaluation model and the introduction of the uncertainty from the apparatus calibration and repeated measurements, two correction factors were introduced to characterize the random effects of conditional variations and system fluctuations on the measurement repeatability of the certified reference material (CRM) for calibration and the tested sample, and a mathematical model for evaluating the uncertainty of single-point linear calibration measurement system based on MCM was proposed. Then the specific evaluation process and application of MCM was systematically explained based on a case study for determination of oxygen content in Ti-6Al-4V titanium alloy by inert gas fusion - infrared absorption method. Under the measurement condition that the CRM repeated 4 times and the Ti-6Al-4V sample repeated twice, the simulation result was wMCM = 0.178 % ± 0.009 % (k = 2), which was consistent with the result of wGUM = 0.178 % ± 0.009 % (k = 2), based on the traditional GUM method recommended by ISO/IEC Guide 98-3: 2008. The new method solved the application of MCM to evaluate the uncertainty of the single-point calibration linear measurement system. And it can be directly applied to the uncertainty evaluation of a single-point calibration linear measurement system. Further, it is expected that MCM will be developed and applied in other linear measurement system, which will promote the study and application of measurement uncertainty to open up new horizons.