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Rules for Stating When a Limiting Value is Exceeded
This is a brief summary of an IUPAC activity carried out under the Chemistry and Human Health Division. The former Commission of Toxicology (COMTOX) has established a set of rules for stating whether or not a measurement result is in conformity with given specifications.
Conformity testing is a systematic examination of the extent to which a measurement result indicates that the value of the measurand (e.g., the concentration of a substance in a matrix) conforms or not with a given limiting value. This procedure has some very well-known and practical applications, such as detecting doping in sports, alcohol levels in drivers’ blood, levels of toxic metals in workers’ blood, the proportion of gold in alloys, and the amount of pesticides in drinking water. The objective of the rules for stating when a limiting value is exceeded is to provide assurance of conformity, either in the form of a supplier’s declaration, or of a third-party certification. A specification is usually formulated as a single limiting value or upper and lower limiting values. The assurance may be in the form of a supplier’s declaration or of a third-party certification.
When conformity testing involves measurement or sampling uncertainty, it is common practice to use elements from the theory of statistical hypothesis testing to provide a formal procedure. If you know the measurement procedure and if you can determine a level of uncertainty for that measurement, you can also estimate and minimize the risk of making errors in claims of conformity or non-conformity to the particular specifications.
The description of the rules was published by Christensen et al. (Christensen JM, Holst E, Olsen E, Wilrich PT. Rules for stating when a limiting value is exceeded. Accred. Qual. Assur. 7, 28-35 ).
Test for Conformity Versus Test for Non-Conformity
Different tests exist for conformity and non-conformity. Which one you use depends on the consequences of a wrong statement. An example of a test for conformity is an investigation of the amount of pesticide in a drinking water supply system that serves several hundred thousand people. A declaration that the concentration of the pesticide is below the limiting value—i.e., the point at which that water supply is deemed unsafe—should be made with great confidence. On the other hand, a test for non-conformity might involve measuring the alcohol concentration in a driver’s blood. A declaration that the blood-alcohol concentration in a particular driver exceeds the limiting value—i.e., that person is driving while drunk— should also be made with great confidence.
A test for conformity must always result in only one of the following statements:
Statement A: The measurement results have demonstrated beyond any reasonable doubt that the value of the measurand is in conformity with the requirement.
Statement B: The measurement results have demonstrated beyond any reasonable doubt that the value of the measurand is not in conformity with the requirement.
Statement C: The measurement results have not been able to demonstrate beyond any reasonable doubt whether the value of the measurand is or is not in conformity with the requirements.
The rules for testing conformity are as follows:
Rule 1: For a one-stage testing procedure, conformity with the requirements is declared, if and only if, the uncertainty interval for the value of the measurand is inside the region of conformity.
Rule 2: For a two-stage testing procedure, conformity with the requirements is declared, if and only if, the uncertainty interval for the value of the measurand is inside the region of conformity either after the first stage or after the second stage. The second stage of the test is performed if, and only if, the uncertainty interval calculated after the first stage includes a specification limit.
The power function of the conformity test can be calculated when the uncertainty is known. The power function of the test is the probability of declaring conformity and it is a function of the measurand value. For both the one-stage and the two-stage procedures, formulas for the calculation of the power function and the probability of obtaining an inconclusive result are available at <www.ami.dk/research/conformity>. At the same Web site a freeware computer program, conform1e.exe, is available for the calculations of the probabilities for statement A, B, or C.
The rules described above may assist organizations in making proposals for legislation concerning limiting values. Such organizations may be government agencies, laboratories, or others who are responsible for checking conformity to limiting values by interpreting measurements and taking into account the uncertainty of the results.
For more information, contact the Task Group Chairman Jytte Molin Christensen at <Q-International@wanadoo.fr>.
Page last modified 30 June 2003.
Copyright © 2002-2003 International Union of Pure and Applied Chemistry.
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