Abstract
A problem that frequently occurs in metrology is one of assessing compatibility of data obtained by a user laboratory with the specified values and uncertainty estimates from the certificate of analysis. The user's data are summarized by an estimated measurand value and a confidence interval, which is typically based on a repeatability standard deviation, but may include other variance or bias components. If the lab's interval and the certificate interval do not overlap, or more generally when the ‘no-bias’ hypothesis is rejected, the user may seek guidance on how to confirm this lack of compatibility or how to rectify it. The suggested two-stage statistical approach demonstrates a confidence interval whose width is similar to that of the certificate, and a compatibility test of guaranteed power for the given bias magnitude. Practical computationally simple formulae for each stage sample size are provided.
Highlights
CRM incompatibility problemCertified reference materials (CRMs) incompatibility problemCertified reference materials (CRMs) are well-characterized materials which are certified for one or more physical, chemical or biological properties, and are important to ensure the accuracy and compatibility of measurements
The usual interpretation of nonoverlapping intervals is that the measurements are not CRM compatible
We focus on statistical aspects of a CRM experiment, in particular, how to choose the number of replicates needed to detect a bias of the given magnitude, when testing the hypothesis of no bias
Summary
Certified reference materials (CRMs) are well-characterized materials which are certified for one or more physical, chemical or biological properties, and are important to ensure the accuracy and compatibility of measurements. The usual interpretation of nonoverlapping intervals is that the measurements are not CRM compatible (i.e. the hypothesis discussed in section 3 is convincingly rejected). There is an increasing number of publications on the problem of bias removal and formal assessment of the degree of compatibility between a CRM certified value and user’s best estimates, e.g. To correct for bias, independent estimates of the bias correction uncertainty are required Such estimates are hard or impossible to obtain in the context of just one CRM comparison where a mere replacement of the lab’s mean by the certificate value should raise apprehension. Before the methods can be explored, there are minimal requirements the user’s lab must meet to show its readiness to compare their results with certified values
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