1 Scope
This International Standard covers the calculation of precision estimates and their application to specifications. In particular, it contains definitions of relevant statistical terms (Clause 3), the procedures to be adopted in the planning of an inter-laboratory test programme to determine the precision of a test method (Clause 4), the method of calculating the precision from the results of such a programme (Clauses 5 and 6), and the procedure to be followed in the interpretation of laboratory results in relation both to precision of the test methods and to the limits laid down in specifications (Clauses 7 to 10).
The procedures in this International Standard have been designed specifically for petroleum and petroleum-related products, which are normally homogeneous. However, the procedures described in this International Standard can also be applied to other types of homogeneous products. Careful investigations are necessary before applying this International Standard to products for which the assumption of homogeneity can be questioned.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 5725-2:1994, Accuracy (trueness and precision) of measurement methods and results - Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1 analysis of variance
technique that enables the total variance of a method to be broken down into its component factors.
3.2 between-laboratory variance
element of the total variance attributable to the difference between the mean values of different laboratories.
NOTE 1 When results obtained by more than one laboratory are compared, the scatter is usually wider than when the same number of tests are carried out by a single laboratory, and there is some variation between means obtained by different laboratories. These give rise to the between-laboratory variance which is that component of the overall variance due to the difference in the mean values obtained by different laboratories.
NOTE 2 There is a corresponding definition for between-operator variance.
NOTE 3 The term "between-laboratory" is often shortened to "laboratory" when used to qualify representative parameters of the dispersion of the population of results, for example as "laboratory variance".
3.3 bias
difference between the true value (related to the method of test) and the known value, where this is available.
NOTE For a definition of "true value" and "known value", see 3.26 and 3.8, respectively.
3.4 blind coding
assignment of a different number to each sample so that no other identification or information on any sample is given to the operator.
3.5 check sample
sample taken at the place where the product is exchanged, i.e. where the responsibility for the product quality passes from the supplier to the recipient.
3.6 degrees of freedom
divisor used in the calculation of variance; one less than the number of independent results.
NOTE The definition applies strictly only in the simplest cases. Complete definitions are beyond the scope of this International Standard.
3.7 determination
process of carrying out the series of operations specified in the test method, whereby a single value is obtained.
3.8 known value
actual quantitative value implied by the preparation of the sample.
NOTE The known value does not always exist, for example for empirical tests such as flash point.
3.9 mean
arithmetic mean
sum of the results divided by their number for a given set of results.
3.10 mean square
sum of squares divided by the degrees of freedom.
3.11 normal distribution
probability distribution of a continuous random variable, x, such that, if x is any real number, the probability density is
NOTE µ is the true value and σ is the standard deviation of the normal distribution (σ > 0).
3.12 operator
person who normally and regularly carries out a particular test.
3.13 outlier
result far enough in magnitude from other results to be considered not a part of the set.
3.14 precision
closeness of agreement between the results obtained by applying the experimental procedure several times on identical materials and under prescribed conditions.
NOTE The smaller the random part of the experimental error, the more precise is the procedure.
3.15 random error
chance variation encountered in all test work despite the closest control of variables.
3.16 recipient
any individual or organization who receives or accepts the product delivered by the supplier.
3.17 repeatability
(qualitatively) closeness of agreement between independent results obtained in the normal and correct operation of the same method on identical test material, in a short interval of time, and under the same test conditions (same operator, same apparatus, same laboratory).
NOTE The representative parameters of the dispersion of the population that can be associated with the results are qualified by the term "repeatability", for example, repeatability standard deviation or repeatability variance. It is important that the term "repeatability" not be confused with the terms "between repeats" or "repeats" when used in this way (see 3.19). Repeatability refers to the state of minimum random variability of results. The period of time during which repeated results are to be obtained should therefore be short enough to exclude time-dependent errors, for example, environmental and calibration errors.
3.18 repeatability
(quantitatively) value equal to or below which the absolute difference between two single test results obtained in the conditions specified that can be expected to lie with a probability of 95 %.
NOTE For the details of the conditions specified, see 3.17.
3.19 replication
execution of a test method more than once so as to improve precision and to obtain a better estimation of testing error.
NOTE Replication should be distinguished from repetition in that the former implies that repeated experiments are carried out at one place and, as far as possible, within one period of time. The representative parameters of the dispersion of the population that can be associated with repeated experiments are qualified by the term "between repeats", or in shortened form "repeats", for example, "repeats standard deviation".
3.20 reproducibility
(qualitatively) closeness of agreement between individual results obtained in the normal and correct operation of the same method on identical test material but under different test conditions (different operators, different apparatus and different laboratories).
NOTE The representative parameters of the dispersion of the population that can be associated with the results are qualified by the term "reproducibility", for example, reproducibility standard deviation or reproducibility variance.
3.21 reproducibility
(quantitatively) value equal to or below which the absolute difference between two single test results on identical material obtained by operators in different laboratories, using the standardized test method, may be expected to lie with a probability of 95 %.
3.22 result
final value obtained by following the complete set of instructions in the test method; it may be obtained from a single determination or from several determinations depending on the instructions in the method.
NOTE It is assumed that the result is rounded off according to the procedure specified in Annex G.
3.23 standard deviation
measure of the dispersion of a series of results around their mean, equal to the positive square root of the variance and estimated by the positive square root of the mean square.
3.24 sum of squares
sum of squares of the differences between a series of results and their mean.
3.25 supplier
any individual or organization responsible for the quality of a product just before it is taken over by the recipient.
3.26 true value
for practical purposes, the value towards which the average of single results obtained by n laboratories tends, as n tends towards infinity.
NOTE 1 Such a true value is associated with the particular method of test.
NOTE 2 A different and idealized definition is given in ISO 3534-2.
3.27 variance
mean of the squares of the deviation of a random variable from its mean, estimated by the mean square.