ISO 5725-5:1998 pdf download – Accuracy (trueness and precision) of measurement methodsand results – Part 5: Alternative methods for the determination of the precision of astandard measurement method
ISO 5725-5:1998 pdf download – Accuracy (trueness and precision) of measurement methodsand results – Part 5: Alternative methods for the determination of the precision of astandard measurement method.
There are situations in which it can be desirable to produce identical “samples” by some special process designed to eliminate, as far as possible, the variability of the material (for example, for a proficiency test, or when a precision expenment is used as part of a programme of work during the development of a measurement method). However, when the aim of the precision experiment is to discover the variability that will be experienced in practice (for example, when vendors and purchasers test samples of the same product) then it is necessary for the variability arising as a consequence of the heterogeneity of the material to be included in the measures of the precision of the measurement method.
Care should also be taken to ensure that each test result in an experiment is obtained by carrying out the test procedure independently of other tests. This will not be so if some stages of the specimen preparation are shared by several specimens, so that a bias or deviation introduced by the preparation will have a common influence on the test results derived from these specimens.
5.1.4 The design for heterogeneous materials proposed in this clause yields information about the variability between samples that is not obtainable from the uniform level design described in ISO 5725-2. There is, inevitably, a cost associated with obtaining extra information: the proposed design requires more samples to be tested. This extra information may be valuable. In the leather example discussed in 5.1.1, information about the variability between hides could be used to decide how many hides to test when assessing the quality of a consignment, or to decide between testing more hides with fewer specimens per hide or fewer hides with more specimens per hide. In the sand example discussed in 5.1.2, information about the variability between bulk samples could be used to decide if the procedure for taking bulk samples is satisfactory or in need of improvement.
5.1.5 The design described in this clause is applicable to experiments involving three factors arranged in a hierarchy: with a factor “laboratories” at the highest level in the hierarchy, a factor “samples within laboratories” as the next level in the hierarchy, and a factor “test results within samples” as the lowest level of the hierarchy. Another case that can be encountered in practice is of a three-factor hierarchy with “laboratories” at the highest level, “test results within laboratories” as the next level, and “determinations within test results” as the lowest level. This would arise if the participating laboratories in a precision experiment were each sent a single sample of a homogeneous material, were asked to carry out two (or perhaps more) tests per sample, and if each test involved a number of determinations and the test result is calculated as the average of the determinations. The formulae given in 5.5, 5.6 and 5.9 may be applied to data obtained in such an experiment, but the repeatability and reproducibility standard deviations have to be calculated in a slightly different manner to that given here (see NOTE 2 to 5.5.5). It is also necessary to specify the number of determinations that are to be averaged to give a test result, because this affects the values of the repeatability and reproducibility standard deviations.
5.2 Layout of the design for a heterogeneous material
5.2.1 The layout of the design for a heterogeneous material is shown in table 9.
The p partIcipating laboratories are each provided with two samples at q levels, and obtain two test results on each sample. Thus each cell in the experiment contains four test results (two test results for each of two samples).
It is possible to generalize this simple design, by allowing for more than two samples per laboratory per level, or for more than two test results per sample. The calculations required by the more general design are much more complicated than those required by the case with two test results per sample and two samples per laboratory per level. However, the principles of the more general design are the same as for the simple design, so the calculations will be set out in detail here for the simple design. Formulae for calculating values for the repeatability and reproducibility standard deviations for the general design are given below in 5.9, and an example of their application in 5.10.
5.2.2 The data from the design for a heterogeneous material are represented by.