Technical publications concerning ILC

Beta risk in proficiency testing in relation with the number of participants


The Monte Carlo method was applied to PT schemes to investigate their efficiency. Probabilities that the computed z values are over 3 while the true value is less than 2 and that the computed z values are less than 2 while the true values are over 3 are computed for a series of situations: number of participants from 5 to 30, various ratios of repeatability over reproducibility and number of test results per participant, introduction or not of outliers with z from 3,5 to 10. For each situation, the probabilities of not detecting true outliers and to trigger false alerts are discussed. Guidance and keys are proposed to check and improve the efficiency of real PT programs.

Abstract of conclusions:

This study demonstrates that:

  1. The ratio λ=σr/(σL×Nr) is of main importance to control the efficiency of a PT scheme, even more than the number of participants. The PT providers should then care Nr, number of test results per participant that they request;
  2. Even in adverse conditions, the α-risk is always very low (less than 0,7%);
  3. Robust algorithms improve the efficiency of the PT program (i.e. β-risk) at a slight expense on α-risk (which always remain very low). This comes from a significantly better estimation of the standard deviation of reference when an outlier is present among the participants when these algorithms are used;
  4. A number of 6 participants is large enough to detect a strongly outlying participant provided that good PT conditions (i.e. low value of λ) are present;
  5. PT with a low number of participants is (almost) always better than no PT at all.

ISO 5725-1 and ISO 13528 recommend not to organise an ILC with less than 12 participants. This makes sense for ISO 5725-1, which goal is to determine the performance of a test method. It makes less sense for ISO 13528, which goal is to check the performance of a lab. Obviously, when no PT is organised, β-risk is 100%: any lab having a problem can never at all realise it! Consequently, for test methods that are performed by a little number of labs, it is obviously better to organise PT with 6 participants than nothing. In those cases, the PT provider should specially care the Nr it requests, to ensure a proper λ value and consequently assure an efficiency as good as possible.

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Beta risks in proficiency testing EN