How is the performance of a laboratory assessed

The assessment of laboratory performance is different for quantitative and qualitative PT schemes.

For quantitative PT schemes, the provider compares the result reported by the participating laboratory with the assigned value, i.e. the provider's best estimate of the value of the measurand. The difference between both is then weighted against an assessment criterion, the standard deviation for proficiency assessment, and thus converted into a performance score. A performance score widely used in the field of testing is the z-score:

where x_lab is the value reported by the laboratory, X_ass the assigned value, and the standard deviation for proficiency assessment. The z-scores between -2.0 and +2.0 are commonly considered satisfactory, between -2.0 to -3.0 and 2.0 to 3.0 questionable, and outside the range from –3.0 to 3.0 unsatisfactory and indicating that the measurement process should be investigated by the laboratory and any necessary corrective action taken.

There are a number of other performance scores used in proficiency testing. The En number and the zeta score may be used when the PT provider and the participants provide traceable measurement values together with their associated uncertainties. Both scores indicate whether the participant's estimate of uncertainty is consistent with the observed deviation from the assigned value. The En number is defined as:

where x_lab and U_lab are the reported value and its expanded uncertainty, and X_ass and U_ass the assigned value and its expanded uncertainty. En numbers between -1 and +1 are considered satisfactory, and En numbers outside this range unsatisfactory. An unsatisfactory result might be due to an underestimation of U_lab, but might also be due to a large deviation x_lab-X_ass.

The En number and the zeta score are very similar, the difference being that the former is calculated from expanded (k=2), the latter from standard (k=1) uncertainties. As a consequence, the zeta score is double the En number, and its classification into satisfactory, questionable and unsatisfactory results is thus comparable with the z-score.

Scoring is only sensible if the purpose of the PT is in agreement with the aims of the laboratory. The purpose of the PT may be to test a laboratory for its compliance with regulations, agreement with its peers, ability to work according to a certain method etc. This purpose is reflected in the standard deviation for proficiency assessment, the denominator of the z-score. Thus, laboratories should be aware that schemes with a different purpose may calculate different scores for the same measurement result.

For qualitative PT schemes, a comparison of the participant's result and the assigned value is normally made. If they are identical, then performance is acceptable. If they are not identical, expert judgement is needed to determine if the result is fit for its intended use. In some qualitative PT schemes this expert judgement is provided by the scheme's advisory group.