Farrance Ian, Frenkel Robert
School of Medical Sciences, RMIT University, Bundoora, Victoria 3083;
National Measurement Institute Australia, Bradfield Road, West Lindfield, NSW 2070, Australia.
Clin Biochem Rev. 2014 Feb;35(1):37-61.
The Guide to the Expression of Uncertainty in Measurement (usually referred to as the GUM) provides the basic framework for evaluating uncertainty in measurement. The GUM however does not always provide clearly identifiable procedures suitable for medical laboratory applications, particularly when internal quality control (IQC) is used to derive most of the uncertainty estimates. The GUM modelling approach requires advanced mathematical skills for many of its procedures, but Monte Carlo simulation (MCS) can be used as an alternative for many medical laboratory applications. In particular, calculations for determining how uncertainties in the input quantities to a functional relationship propagate through to the output can be accomplished using a readily available spreadsheet such as Microsoft Excel. The MCS procedure uses algorithmically generated pseudo-random numbers which are then forced to follow a prescribed probability distribution. When IQC data provide the uncertainty estimates the normal (Gaussian) distribution is generally considered appropriate, but MCS is by no means restricted to this particular case. With input variations simulated by random numbers, the functional relationship then provides the corresponding variations in the output in a manner which also provides its probability distribution. The MCS procedure thus provides output uncertainty estimates without the need for the differential equations associated with GUM modelling. The aim of this article is to demonstrate the ease with which Microsoft Excel (or a similar spreadsheet) can be used to provide an uncertainty estimate for measurands derived through a functional relationship. In addition, we also consider the relatively common situation where an empirically derived formula includes one or more 'constants', each of which has an empirically derived numerical value. Such empirically derived 'constants' must also have associated uncertainties which propagate through the functional relationship and contribute to the combined standard uncertainty of the measurand.
《测量不确定度表示指南》（通常简称为GUM）为评估测量不确定度提供了基本框架。然而，GUM并不总是能提供适用于医学实验室应用的清晰可辨的程序，特别是在使用内部质量控制（IQC）来得出大部分不确定度估计值的情况下。GUM建模方法的许多程序都需要先进的数学技能，但蒙特卡罗模拟（MCS）可作为许多医学实验室应用的替代方法。特别是，对于确定函数关系中输入量的不确定度如何传播到输出的计算，可以使用诸如Microsoft Excel之类的现成电子表格来完成。MCS程序使用算法生成的伪随机数，然后强制其遵循规定的概率分布。当IQC数据提供不确定度估计值时，通常认为正态（高斯）分布是合适的，但MCS绝不仅限于这种特殊情况。通过随机数模拟输入变化，函数关系随后以也提供其概率分布的方式给出输出中的相应变化。因此，MCS程序无需与GUM建模相关的微分方程即可提供输出不确定度估计值。本文的目的是证明使用Microsoft Excel（或类似的电子表格）可以轻松地为通过函数关系得出的被测量提供不确定度估计值。此外，我们还考虑了一种相对常见的情况，即凭经验得出的公式包含一个或多个“常数”，每个常数都有凭经验得出的数值。这些凭经验得出的“常数”也必须具有相关的不确定度，这些不确定度会通过函数关系传播并对被测量的合成标准不确定度产生影响。
