Brito J A A
Centro de Física Atómica da Universidade de Lisboa, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2 1649-003 Lisbon, Portugal.
Phys Med Biol. 2006 Dec 7;51(23):6125-39. doi: 10.1088/0031-9155/51/23/013. Epub 2006 Nov 8.
The effect of covariance between the K alpha and K beta lead peak concentrations on the uncertainty in the (109)Cd K x-ray fluorescence measurement of lead in bone is addressed here. It is commonly believed that this covariance arises as a result of the mutual dependence of the ratios of x-ray to coherent amplitudes on the same coherent peak amplitude. Previous work assumes statistical independence between spectral quantities of interest, crudely estimates the uncertainties in the lead peak concentrations, and suggests that the effect of covariance on the measurement uncertainty is small and can be ignored. Consequently, the current method followed by most laboratories reports the measurement uncertainty as if the fluctuations in the measured peak concentrations were independent. The robustness of such assumption, however, is undermined by existing epidemiological data. This paper assesses the magnitude of the covariance effect, using a method based on the observed significant correlations between the ratios of x-ray to coherent peak amplitudes in series of repeat phantom measurements. The revised uncertainties following this approach can exceed the uncertainties estimated by the accepted method by as much as 40%, which suggests a much stronger effect of covariance on the measurement uncertainty than previously reported.
本文探讨了Kα和Kβ铅峰浓度之间的协方差对骨中铅的（109）Cd K X射线荧光测量不确定度的影响。通常认为，这种协方差是由于X射线与相干振幅之比对同一相干峰振幅的相互依赖而产生的。先前的工作假设感兴趣的光谱量之间具有统计独立性，粗略估计了铅峰浓度的不确定度，并表明协方差对测量不确定度的影响很小，可以忽略不计。因此，大多数实验室目前采用的方法在报告测量不确定度时，就好像测量峰浓度的波动是独立的一样。然而，现有流行病学数据削弱了这种假设的稳健性。本文使用一种基于在一系列重复体模测量中观察到的X射线与相干峰振幅之比之间的显著相关性的方法，评估了协方差效应的大小。采用这种方法得到的修正不确定度可能比公认方法估计的不确定度高出多达40%，这表明协方差对测量不确定度的影响比先前报道的要大得多。
