Proficiency testing (PT) determines the performance of individual laboratories for specific tests or measurements and it is used to monitor the reliability of laboratories measurements. PT plays a highly valuable role as it provides objective evidence of the competence of the participant laboratories. In this paper, we propose a multivariate calibration model to assess equivalence among laboratories measurements in PT. Our method allows to deal with multivariate data, where the item under test is measured at different levels. Although intuitive, the proposed model is nonergodic, which means that the asymptotic Fisher information matrix is random. As a consequence, a detailed asymptotic analysis was carried out to establish the strategy for comparing the results of the participating laboratories. To illustrate, we apply our method to analyze the data from the Brazilian engine test group, PT program, where the power of an engine was measured by eight laboratories at several levels of rotation.