Vol.
25 No. 4
July - August 2003
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 [2002]).
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 <[email protected]>.
www.iupac.org/projects/1993/720_4_93.html
Page
last modified 30 June 2003.
Copyright © 2002-2003 International Union of Pure and
Applied Chemistry.
Questions regarding the website, please contact [email protected]
|