On interchangeability of two laboratories

This paper proposes a measure for assessing the equivalence between the results of two laboratories. The measure is called asymmetric interchangeability. It is asymmetric since, based on this measure, one laboratory may be considered interchangeable with another laboratory but the converse may not be true. Such a situation can arise when the accuracy and precision of one laboratory are noticeably greater than that of the other. The proposed measure of interchangeability depends on the parameters of the measurement models, which include means, variances and the correlation of the two laboratories being compared. Since the level of correlation is often difficult to assess, it is assumed to be zero in this paper. Fiducial procedures are presented for testing the hypothesis that a laboratory is directionally interchangeable with another. The procedure is based on comparing a probability measure, which is shown to be closely related to asymmetric interchangeability, with an agreed threshold. Computer programs for calculating the p-value of the tests, written by use of open-source software, are listed.