The influence of homogeneity on the stability assessment of reference materials

Accurate estimation of the uncertainty of stability is crucial for certified reference materials (CRMs), as it forms a component of the overall uncertainty budget. In case of between-unit heterogeneity, results obtained on the same unit of a CRM are not independent which leads to a bias in the estimated uncertainty of stability when used ordinary least squares. This bias depends on the ratio of between-unit heterogeneity to method repeatability and the number of replicate analyses performed per unit and can reach nearly 50 % for as few as three replicates per unit. A study on actual certified values shows that this bias can influence the certified values. The study shows that employing linear mixed-effects models (LME) with restricted maximum likelihood (REML) for parameter estimation provides consistent estimate of uncertainty of stability, even in the presence of significant between-unit heterogeneity. Simpler, alternative approaches for specific scenarios, such as well-balanced datasets are also provided.