  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 an objective evidence of the competence of the participant
laboratories. In this paper, we propose a multivariate model to assess
equivalence among laboratories measurements in proficiency testing. Our method
allow to include type B source of variation and 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 8 laboratories at several levels of rotation.
