NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore (NUS), Singapore, Singapore.
Anal Bioanal Chem. 2012 Mar;402(7):2463-9. doi: 10.1007/s00216-011-5698-4.
Despite the importance of stating the measurement uncertainty in chemical analysis, concepts are still not widely applied by the broader scientific community. The Guide to the expression of uncertainty in measurement approves the use of both the partial derivative approach and the Monte Carlo approach. There are two limitations to the partial derivative approach. Firstly, it involves the computation of first-order derivatives of each component of the output quantity. This requires some mathematical skills and can be tedious if the mathematical model is complex. Secondly, it is not able to predict the probability distribution of the output quantity accurately if the input quantities are not normally distributed. Knowledge of the probability distribution is essential to determine the coverage interval. The Monte Carlo approach performs random sampling from probability distributions of the input quantities; hence, there is no need to compute first-order derivatives. In addition, it gives the probability density function of the output quantity as the end result, from which the coverage interval can be determined. Here we demonstrate how the Monte Carlo approach can be easily implemented to estimate measurement uncertainty using a standard spreadsheet software program such as Microsoft Excel. It is our aim to provide the analytical community with a tool to estimate measurement uncertainty using software that is already widely available and that is so simple to apply that it can even be used by students with basic computer skills and minimal mathematical knowledge.
尽管在化学分析中陈述测量不确定度非常重要，但这一概念在更广泛的科学界仍未得到广泛应用。《测量不确定度表示指南》批准同时使用偏导数法和蒙特卡罗法。偏导数法有两个局限性。首先，它涉及输出量每个分量的一阶导数的计算。如果数学模型复杂，这需要一些数学技能并且可能很繁琐。其次，如果输入量不是正态分布，则无法准确预测输出量的概率分布。了解概率分布对于确定覆盖区间至关重要。蒙特卡罗法从输入量的概率分布中进行随机抽样；因此，无需计算一阶导数。此外，它将输出量的概率密度函数作为最终结果给出，从中可以确定覆盖区间。在这里，我们展示如何使用 Microsoft Excel 等标准电子表格软件程序轻松实施蒙特卡罗法来估计测量不确定度。我们的目的是为分析界提供一种使用已广泛可用的软件来估计测量不确定度的工具，该工具非常简单易用，甚至可以让具有基本计算机技能和最小数学知识的学生使用。
