Estimates of repeatability and reproducibility are given in Table 1. The standard deviations are also shown in Figure 1. These estimates have been calculated by excluding the data for Laboratories Q and c. In the case of Laboratory Q (Number code 129), their data give outlying laboratory averages in Levels 1 and 2, and a straggling laboratory average in Level 3. With Laboratory c (Number code 251), their data give several outliers and stragglers, in both the laboratory averages and the between-specimen and between-test-portion ranges. Laboratory O (Number code 112) gave a straggling laboratory average in Level 1, but no other stragglers or outliers, so their data have been included in the calculation of the precision values.
Experiments carried out in France on the current French methods for the Sand Equivalent test (AFNOR 1990, P 18-597 Détermination de la propreté des sables: équivalent de sable à 10 % de fines (ES10); AFNOR, 1991. P 18-598 Equivalent de sable (ES).) give estimates of the repeatability and reproducibility standard deviations of:
Sr = 1.5 SE units
SR = 2.5 SE units.
Comparing these values with those given in Table 1, it is seen that the repeatability achieved in the cross-testing experiment is better that that reported for the French methods. However, the reproducibility of the CEN method is worse than that of the French methods, particularly in Level 1. It is possible that this is because some laboratories had little experience with the test method before the cross-testing experiment, or because the materials were difficult to test as noted in the description of the experiment.
In Figure 1 it can be seen that the three materials give average Sand Equivalent values rather close together, so that functional relations fitted to the results will be valid only over this narrow range.
With a very clean sand, the two measurements h1 and h2 will be close together, and the repeatability and reproducibility should be close to zero. However, because the measurements are made to the nearest 1 mm, rounding errors will cause the repeatability and reproducibility to be non-zero. Rounding to 1 mm will give rise to a repeatability standard deviation of 1/12½ mm in each measurement of h1 and h2, so the smallest value the repeatability standard deviation of the Sand Equivalent test can take is:Sr1 = (SE/12½) × ( 1/h12 + 1/h22 )½
For a clean sand, both h1 and h2 will be close to 80 mm and SE will be close to 100 , giving:
Sr1 = 0.5 SE units
Linear functional relations have been fitted to the repeatability and reproducibility standard deviations in Table 1, constraining them to pass through the point SE = 100 , Sr1 (or SR1) = 0.5 .
It has been argued (J»rck, Sym and Powell, 1994. A study of mechanical tests of aggregates. Green Land Reclamation Ltd Report GLR 3036/03a.) 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 method is to be used to assess the compliance of aggregates with specifications. At the present time it has not been decided how the Sand Equivalent test will be called up in specifications. However, if a specification does impose a limiting value on the Sand Equivalent test, then the value will be a lower limit. The above criterion may then be applied to the Sand Equivalent test provided that the coefficient of variation is calculated as shown in the formulae.
The results in Table 3 show that the reproducibility of the Sand Equivalent test does not meet this criterion with Level 1, and lies on the borderline of acceptability with Levels 2 and 3. Hence if it is to be called up in specifications it would be desirable for laboratories to implement techniques for improving precision (such as repeatability checks and proficiency testing).
From an examination of the readings made by the participants it is clear that it is variations in the measurement of h1 (the height of the upper level of the flocculant above the base of the cylinder) that is the major cause of the between-laboratory variation of the method. The Mandel plots show strong evidence of correlations between results for the three materials. This indicates that the cause of the variations in the measurement of h1 is a factor or factors that affects all the tests in a laboratory consistently, such as the preparation of the flocculant, or ageing of the flocculant. Another possibility is the irrigation of the sand - several participants reported having difficulty with this. If it is not done thoroughly the value of h1 will be reduced, giving a higher SE value than with thorough irrigation.