Insufficient method repeatability is a problem characterising the evaluation of certified reference materials (CRMs). In investigating the homogeneity studies of 216 certified parameters from 36 CRMs released by the European Commission’s Joint Research Centre (JRC) over the last four years, it was found that in 1/3 of the cases, the method repeatability (sr) was too high to calculate the standard deviation between units (sbb) by classical analysis of variance (ANOVA). It was also found that the application of the repeatability requirement stated in the ISO Guide 35:2017 is not feasible since it would require unrealistically low repeatability standard deviations or an impossibly high number of replicates per unit. Evaluation of the uncertainty of homogeneity (ubb) as evaluated by ANOVA using both the maximum of sbb and 0, the maximum of sbb and u∗bb, the uncertainty hidden by method repeatability, the maximum of sbb and sbb/√n and Bayesian analysis, using both informative and diffuse priors, as well as the standard deviation of the unit means, were compared using simulated homogeneity studies with repeatabilities of 1–8% and sbb between 0.2 and 2.8%. It was found that using the maximum of sbb and sbb/√n as an estimate of ubb guards against severe underestimation but usually results in a severe overestimation of the between-unit variation. Using the maximum of (sbb, 0) shows the least average bias but results in a severe underestimation of ubb in a high fraction of cases. Using the maximum of (sbb, u∗bb) limits, but does not completely eliminate cases of a severe underestimation. Also, it leads to average results biased towards high values. For the range of sbb and sr investigated, Bayesian analysis performed worse than max (sbb, u∗bb) in limiting severe underestimation of ubb, but limited the average bias towards high results. A risk-based approach to cases of insufficient method repeatability is proposed where, after evaluating the other contributions to the uncertainty of certified values, the effect of severe over- and underestimation of ubb is evaluated, and an appropriate approach is chosen based on this analysis.

中文翻译：

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在方法可重复性不足的情况下评估 CRM 同质性：贝叶斯分析与基于方差分析的估计替代品的比较

方法重复性不足是有证标准物质 (CRM) 评估特征的一个问题。在调查欧盟委员会联合研究中心 (JRC) 过去四年发布的 36 种 CRM 的 216 个认证参数的同质性研究中，发现在 1/3 的案例中，方法重复性 (sr) 过高通过经典方差分析 (ANOVA) 计算单位之间的标准差 (sbb)。还发现应用 ISO 指南 35:2017 中规定的重复性要求是不可行的，因为它需要不切实际的低重复性标准偏差或每单位不可能高的重复次数。使用 sbb 和 0 的最大值通过方差分析评估均匀性 (ubb) 的不确定性，sbb 和 u∗bb 的最大值、方法可重复性隐藏的不确定性、sbb 和 sbb/√n 的最大值和贝叶斯分析，使用信息和扩散先验，以及单位平均值的标准偏差，使用模拟均匀性研究，重复性为 1-8%，sbb 在 0.2 和 2.8% 之间。结果发现，使用 sbb 和 sbb/√n 的最大值作为 ubb 的估计可以防止严重低估，但通常会导致严重高估单位间变异。使用 (sbb, 0) 的最大值显示最小平均偏差，但在大部分情况下会导致对 ubb 的严重低估。使用 (sbb, u∗bb) 限制的最大值，但并不能完全消除严重低估的情况。此外，它导致平均结果偏向高值。对于调查的 sbb 和 sr 范围，贝叶斯分析在限制对 ubb 的严重低估方面比 max (sbb, u∗bb) 表现差，但限制了对高结果的平均偏差。针对方法可重复性不足的情况提出了一种基于风险的方法，在评估了对认证值不确定性的其他贡献后，评估了 ubb 严重高估和低估的影响，并根据此分析选择了适当的方法.