单点校准线性测量系统不确定度的蒙特卡洛法评定模型构建与应用

线性测量系统是化学分析、物理测试领域最普遍的测量系统,按其线性关系的构建和拟合方式,可分为单点校准、双点校准、多点校准(线性拟合)及标准加入法。其中,单点校准常用于色谱分析、滴定分析等分析方法及气体分析、碳硫分析等测量项目。实验引入2个随机效应修正因子或相对随机误差表征各种条件变异及系统波动对校准用标准物质和实际样品测量重复性的影响,提出了蒙特卡洛法(MCM)评定单点校准线性测量系统不确定度的数学模型与方法,并基于惰性气体熔融-热导法测定TC4钛合金中氢含量的示例,系统阐释了MCM的具体评定流程与应用。在实验测量条件下(标准物质重复4次,实际样品重复7次),平均测量结果为w(H)=(20±3)μg/g,k=2,该扩展不确定度评定结果与采用“不确定度传播律”得到被测量估计值测量不确定度的方法(GUM法)相一致。实验所给出的方法和示例可直接应用于气体分析(惰气熔融-红外吸收法/热导法)、碳硫分析(高频感应燃烧红外吸收法)与色谱分析、滴定分析等单点校准线性测量系统的不确定度的评定,一定程度上解决了MCM应用于化学分析领域的模型构建与仪器校准引入不确定度的量值导入等关键问题,有望推动MCM在单点校准、多点校准、标准曲线法、标准加入法等线性测量系统不确定度的评定中得到实质性的应用,进一步促进测量不确定度的应用研究开创新局面。

Evaluation of the uncertainty for the single-point calibration linear measurement system based on Monte Carlo method

The linear measurement system is the most routine measurement system in the field of chemical analysis and physical testing. According to its linear relationship construction and fitting method, it can be divided into single-point calibration, two-point calibration, multi-point calibration (linear fitting) and standard addition method. Among them, the single point calibration measurement system is often used for analytical methods such as chromatographic analysis, titration analysis, and measurement items such as gas analysis, carbon and sulfur analysis. Two correction factors or relative random errors were introduced to characterize the random effects of conditional variations and system fluctuations on the measurement repeatability of the standard for calibration and the practical sample, and a method and mathematical model for evaluating the uncertainty of single point linear calibration measurement system based on Monte Carlo method (MCM) was proposed. The specific evaluation process and application of MCM was systematically explained based on a case study for determination of hydrogen in TC4 titanium alloy by inert gas fusion-thermal conductivity method. Under the measurement conditions of this paper (the standard repeated 4 times, the practical repeated 7 times), the simulation results was w(H)=(20±3)μg/g, k=2, which was consistent with the result by GUM method. The method and example proposed can be directly applied to the uncertainty evaluation of single-point calibration measurement systems, such as chromatographic analysis and determination of oxygen, hydrogen, nitrogen, carbon and sulfur in solid samples by inert gas fusion-infrared absorption method/thermal conductivity method or high temperature combustion-infrared absorption method. It solved the key issues of MCM applied in the field of chemical analysis to a certain degree, such as the mathematical model construction of measurement system and the introduction of uncertainty from instrument calibration. That is expected that MCM will be applied substantively in the linear measurement system, such as single point calibration, two-point calibration, multi-point calibration (linear fitting) and standard addition method, which will promote the study and application of measurement uncertainty to open up new horizons.