Reliability of precision data obtained from interlaboratory studies

Precision data, such as laboratory-to-laboratory SD (SL) and repeatability SD, obtained from interlaboratory tests are needed to assess analytical test methods. These precision data describing random error are subject to random variation. In order to avoid distorted assessments of test methods, interlaboratory tests must fulfill minimal requirements for achieving, e.g., a desired reliability in S(L). In 2009, McClure and Lee considered reliability of S(L) as a characteristic of an interlaboratory study. They developed an approach to approximate that reliability to make it possible to adapt the study design of an interlaboratory study to a desired reliability in S(L). The McClure and Lee approach introduces the "margin of relative error" to arrive at the magnitude of the uncertainty in S(L). This article discusses their approach and presents a generalized approach. The limitations of McClure and Lee's approximation are shown to result in underestimation of the actual variability of S(L) due to the disregard of the inherent negative bias of S(L). This bias corresponds to the fact that the expected value of the obtained S(L) lies below the true value sigmaL one would obtain in an interlaboratory study with an infinite number of laboratories and replicates. In order to achieve the reported level of reliability in S(L), the actual number of laboratories required is typically approximately 25% higher than that calculated by McClure and Lee. We present a generalized approach using "margins of relative random error," which takes the impact of the bias of the S(L) into account, resulting in a more realistic estimation of the variability of the precision parameter S(L).