- Tables of repeatability and reproducibility values.
- Figure showing functional relations for the precision values.
- Histograms of the data from the precision experiment.
- Mandel plots of the data from the precision experiment.
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Estimates of repeatability and reproducibility values are given in Tables 1 and 5. The standard deviations are also shown in Figure 1.

From the figure it may be seen that the reproducibility appears to increase with the level of the results. Further, the points for reproducibility for the French experiment fall close to a straight line, so that it is reasonable to summarise these estimates using a linear functional relationship. However, the points for reproducibility from the European experiment do not fall close to a straight line, so that in this case a linear functional relationship can give only an approximate indication of the reproducibility.

The figure shows that the repeatability of the micro-Deval test does not appear to increase with the level of the results. Also, the points do not fall close to a straight line, so again linear functional relationships can give only an approximate indication of the repeatability.

Clause 10 of the draft CEN Standard gives the results of experiments carried out in France. In terms of the reproducibility standard deviation, the result given there is:

S_{R} = 0.39 + 0.089 X

(This was obtained using the earlier French method in which only one determination was obtained per test result, not two as in the CEN method. However, this difference will have a negligible effect on the reproducibility because the reproducibility of the micro-Deval test is so much larger than its repeatability.) The results for the individual levels are not available, so it is not possible to see how well they fitted the straight line given.

According to this equation, S_{R} = 0.96 when X = 6.4, S_{R} = 1.41 when X = 11.5, and S_{R} = 2.66 when X = 25.5. These values are substantially higher than those obtained in either the European or the French experiments reported here.

In terms of the repeatability standard deviation, the result given in Clause 10 of the draft CEN Standard is:

S_{r} = 0.36 + 0.039 X

According to this equation, S_{r} = 0.61 when X = 6.4, S_{r} = 0.81 when X = 11.5, and S_{r} = 1.35 when X = 25.5. Again, these values are substantially higher than those obtained in either the European or the French experiments reported here, and the difference is too large to be explained by the difference between the French and CEN methods in the number of determinations made.

Inspection of the histograms of between-determination ranges suggests that most laboratories should be able to obtain results of tests on duplicate specimens from the same laboratory sample that differ by no more than 1.0 MDE units, with any of the relatively homogeneous materials used in this experiment. This limit could be used as an easily-remembered value for the critical range W_{c}. According to the CEN method, MDE values should be rounded to the nearest whole number. If ranges of determinations are to be compared with the critical range the determinations should be rounded to the nearest 0.1 MDE.

It has been argued (*Jorck, Sym and Powell, A study of mechanical tests of aggregates. Green Land Reclamation Report GLR 3036/03a. 1994*) that the reproducibility standard deviation of a mechanical test, when expressed as a coefficient of variation, should be no more than about 8%, if the test is to be used to assess the compliance of aggregates with specifications. The results in Tables 3 and 7 show that the reproducibility of the micro-Deval test is adequate when assessed by this criterion.

The estimates of reproducibility are larger than the corresponding values for repeatability (compare values of r_{1} and R_{1} in Tables 1 or 5). Also, there are a number of laboratories that give standardised laboratory biasses that are either all positive or all negative (see the Mandel plots). These observations indicate that there are one or more factors that are having a detrimental effect on the reproducibility. Comparisons of equipment and procedures and cross-over experiments should allow these factors to be identified so that the reproducibility of the test can be improved.