Use of prediction methods to assess laboratory bias and mean values associated with an interlaboratory study for...

Two methods of prediction of random variables, best predictor (BP) and best linear unbiased predictor (BLUP), are discussed as potential statistical methods to predict laboratory true mean and bias values using the sample laboratory mean (y(i)) from interlaboratory studies. The predictions developed here require that the interlaboratory and/or proficiency study be designed and conducted in a manner consistent with the assumptions of a one-way completely randomized model (CRM). Under the CRM the individual laboratory true mean and bias are not parameters but are defined to be random variables that are unobservable and considered as realized values that cannot be estimated but can be predicted using methods of "prediction." The BP method is applicable when all salient parameters are known, e.g., the consensus true overall mean (mu) and repeatability and reproducibility components (sigma2(r) and sigma2(R)), while the BLUP method is useful when sigma2(r) and sigma2(R) are known, but mu is estimated by the generalized least square estimator. Although the derivations of predictors are obtained by minimizing the mean-square error under the CRM assumptions, the predictors are the expected laboratory true mean and bias given the sample laboratory mean, i.e., conditional expectation.