Testing of industrial products - Aggregates for construction

Details of the cross-testing experiment on the Particle Size Distribution test


17 laboratories took part in the experiment from 9 European countries. The laboratories have been given numerical codes. For the purposes of this report they have also been assigned letter-codes (because single-character codes are needed in the graphs).


Samples of three sands were prepared and distributed by Partners 1 and 3. The three sands were chosen so that they would give a wide range of gradings: the average gradings found by the participants are shown in Figure A below.

Figure A. Grading curves for the sands used in the experiment.

Level 1 is a natural sand with a very narrow grading. Level 2 is a 0/2 mm Lower Rhine Valley natural sand. Level 3 is a 0/2 mm crushed limestone sand with a high fines content.

The samples were prepared, for each level of the experiment, as if they were laboratory samples all taken from one bulk sample. For Level 1 a bulk sample was divided by fractional shovelling into about 50 laboratory samples each weighing about 0.5 kg. For Levels 2 and 3 a small rotary sample divider was used to divide the bulk samples of the materials into laboratory samples of about 1 kg. The laboratory samples were sent to the participating laboratories.

The participants were required to follow the sample division plan shown in Figure B, and divide each laboratory sample into two test-portions of about 200 g (as required by the CEN method), and two test-portions of about 30 g. Hence the measures of repeatability and reproducibility given by the experiment for either the 200 g test portions or the 30 g test portions are consistent with the definitions of r1 and R1 used here.

Figure B. Sample division procedure used by the participants.


Where a participant failed to report a determination, the missing value is shown as "-.-" in the data tables. The method requires test results to be rounded to the nearest 1 % passing. However, for the purpose of the cross-testing experiment, the test results were recorded to the nearest 0.1 % passing. This was to prevent rounding of the data affecting the assessment of the repeatability and reproducibility of the test method.

All the calculations were checked and a number of errors (in the data for Laboratories 6, 42, 43, 247, 249) were corrected. It is possible that some operators were not familiar with the calculations required by the washing and sieving test.

Averages and ranges

Laboratory averages are used to calculate the reproducibility of the test method, and to assess laboratory biasses. Between-test-portion ranges are used to calculate the repeatability of the test method, and to assess the repeatability of tests from individual laboratories. The averages and ranges are shown in the histograms, and the laboratory averages are plotted in the Mandel plots. One gives the results for 200 g test portions, and shows if there are correlations between results for different sands (i.e. levels). The other shows the relations between the results for the two sizes of test portion.

The averages and ranges are also used to test for stragglers and outliers. Where these have been found, they are indicated throughout using a single question mark (?) to indicate a straggler, and a double question mark (??) to indicate an outlier.

Standardised values of the averages and ranges are shown in the Mandel plots. These figures are used to identify laboratories that give rise to large laboratory biasses, or large between-test-portion ranges, in more than one level of an experiment. The horizontal broken lines in these graphs show the critical values of the "h" and "k" statistics at the 5 % and 1 % significance levels, taken from the ISO standard on precision (ISO 5725, 1994).