Estimates of repeatability and reproducibility are given in Tables 1 and 4. The standard deviations (for determinations made using 5.00 mm sieves) are also shown in Figure 1. These estimates have been calculated by excluding the following data:
The pattern of the points in Figure 1 suggests that the repeatability and reproducibility standard deviations both decrease as the level of the results increases. This is contrary to what would be expected normally, so it does not seem advisable to fit functional relations to these results.
The results of the cross-testing experiments reveal a number of cases where laboratories obtained erratic results. This shows that there is a need for laboratories to have some means of checking the accuracy of their results. The KOAC laboratories in the Netherlands, in co-operation with the State Road Laboratory, started a system of proficiency testing in 1978. Packages of samples were prepared and distributed to the participants, and the results analysed statistically. Initially the laboratories were sent eight packages a year, and were asked to carry out about 200 tests per package - a total of about 1600 tests per laboratory per year. Nowadays the frequency has been reduced to three packages a year because the laboratories are also subject to accreditation, and some of the test methods have changed, but not the number of tests per package.
The system has proved to be successful. Table X shows the improvement that has been achieved in the precision of the DSC test since the proficiency testing was started.
|Repeatability standard deviation
|Reproducibility standard deviation|
|1978 to 1979||1.6||2.2|
|1995 to 1996||1.3||1.4|
Figure 1 also contains horizontal lines that represent the precision achieved by participants in recent proficiency tests (the results for 1995 - 1996 shown in Table X). In these proficiency tests the participants are required to obtain only a single test result on each sample, so the data cannot be used to calculate a repeatability standard deviation that is equivalent to that derived from the cross-testing experiment. Instead, a repeatability-like value is derived from the results obtained in successive rounds of the proficiency scheme. This value, called an "intermediate precision standard deviation", measures the variation that occurs under repeatability conditions together with additional variations that can occur within a laboratory between tests carried out at different times. It is to be expected that the intermediate precision standard deviation will be larger than the repeatability standard deviation, as is the case in Figure 1.
The reproducibility standard deviation from the proficiency tests is close to the intermediate precision standard deviation, indicating that laboratory biasses have largely been eliminated from the participants in the proficiency scheme. The reproducibility for the strongest aggregate in the cross-testing experiment exceeds that from the proficiency tests.
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. The results in Table 2 show that the reproducibility of the DSC test easily meets this criterion for Levels 2 and 3 (the weaker materials) but fails to meet the criterion, by a small margin, for Level 1.
The same three materials were used in the cross-testing experiment reported here as in a similar experiment on the Los Angeles test conducted earlier in this programme. Figure A below shows the results for the DSC test from Table 1 plotted against the corresponding values taken from the report on the Los Angeles test (Sym, 1994. The proposed CEN method for the Los Angeles test: results of the 1993/4 cross-testing experiments. Green Land Reclamation Ltd Report GLR 3036/05.). All these tests were carried out on the 10.0/14.0 mm fraction of the samples, so a 5.00 mm sieve was used to determine the DSC test result.
The figure also shows results obtained in a Dutch study of crushing tests (KOAC-VUGHT, 1991. Vergelijkend Verbrijzelingsonderzoek; Definitief Rapport = Comparative investigation on crushing tests; Final Report. KOAC, Vught, Holland.) that involved tests on 26 different rocks. These DSC tests were carried out on the 11.2/16.0 mm fraction of the samples, so that a 5.60 mm sieve was used to determine the DSC test result. Further details of the Dutch study may be found in the report on a study of mechanical tests carried out as part of this programme (J»rck, Sym and Powell, 1994).
The results obtained in the Dutch study showed that a reasonable degree of correlation exists between the DSC test and the Los Angeles test. The figure also shows that, even though a slightly different size fraction was used in the experiment reported here, the results obtained (using the 5.00 mm sieve) are consistent with those obtained in the Dutch study.
However, examination of the points for the three materials used in the cross-testing experiments reveals that they do not fall on a straight line. With the Los Angeles test, the difference between the materials used for Levels 1 and 2 is similar to that between the materials used for Levels 2 and 3. With the DSC test, the difference between Levels 1 and 2 is much larger than that between Levels 2 and 3. This indicates that the relation between the DSC test and the Los Angeles is not simple. If the DSC test is to be used as an alternative to the Los Angeles test, further work is required to establish specification limits for the DSC test that are equivalent to those that are applied to the results of Los Angeles tests.
Such further work should be directed towards identifying the factors that cause the scatter that can be seen in Figure A. Examination of the particle size distributions produced by the two tests may help identify these factors. During the DSC test, the aggregate is confined in mould, so that once compaction has reached the point where the air void content is small, increasing the load will not cause further fragmentation of the aggregate. This may be the reason why the DSC test is not able to discriminate very well between Levels 2 and 3.
Figure A also shows the results for the DSC test from Table 4 plotted against the Los Angeles test results. In this case, the 1.60 mm sieve was used to determine the DSC test result (the same size sieve as is used in the Los Angeles test), and the three points fall closer to a straight line than those obtained using the 5.00 mm sieve in the DSC test. Tests on only three materials do not provide enough evidence to be able to conclude that a better correlation between the Los Angeles and DSC tests would be obtained if a 1.60 mm sieve were to be used in the DSC test, but it does show that the 1.60 mm sieve should be included in further work to compare the tests.
The histograms of laboratory averages are brought together in Figures B and C below, in a form that allows the reproducibility of the DSC test to be compared with that of the Los Angeles test illustrated by Figure D.
Figure B shows that the histograms for Levels 2 and 3 overlap, so that when the tests are carried out in different laboratories, the results usually show that the Level 3 material gives a higher DSC result than the Level 2 material, but sometimes the results show that the Level 2 material gives a higher result than the Level 3 material. Thus the DSC test (using a 5.00 mm sieve) is not able to discriminate reliably between these two materials. This arises because the reproducibility achieved in the cross-testing experiment is large in comparison with the difference between the materials used for Levels 2 and 3. The sensitivity ratio is a coefficient that indicates how well the reproducibility of a test method allows the test method to discriminate between two materials. In Table Y it can be seen that a low value of 1.8 is obtained in this case.
The results obtained for Levels 2 and 3, using the 1.60 mm sieve to determine the result of the DSC test, give a higher sensitivity ratio of 3.3 than the 1.8 achieved with the DSC test using the 5.00 mm sieve. The Los Angeles test gave an even higher sensitivity ratio of 5.3 for these two materials. In Figure C it can be seen that there is less overlap between the histograms for Levels 2 and 3 for the DSC test using the 1.60 mm sieve than for the results obtained for the 5.00 mm sieve, and in Figure D there is no overlap between the results obtained for Levels 2 and 3 using the Los Angeles test.
Examination of the results in Figures B, C and D for Levels 1 and 2 shows that there is no overlap between the histograms for either the Los Angeles test, or for either version of the DSC test, so that all three are able to discriminate reliably between these two materials. However, in Table Y the sensitivity ratio for the DSC test using the 1.60 mm sieve is lower than that achieved by the other two tests. The conclusion to be drawn from this is that for stronger materials in the range covered by Levels 1 and 2 the Los Angeles and DSC test (using the 5.00 mm sieve) give equivalent levels of reproducibility, whereas for weaker materials in the range covered by Levels 2 and 3 the Los Angeles test gives better discrimination than the DSC test (using the 5.00 mm sieve).
|Level 2 - Level 1||Level 3 - Level 2||Level 3 - Level 1|
|Los Angeles test||9.2||5.9||12.2|
|DSC test (5.00 mm sieve)||8.6||1.9||10.2|
|DSC test (1.60 mm sieve)||6.6||3.3||10.1|
D (67) D (66) D (67) 56.0 ¦ . . . ¦ . . . 54.0 ¦ . . .Level 3 ¦ . . .laboratory averages 52.0 ¦ . . . ¦ . . BEL 50.0 ¦ . . AJW ¦ . Y HISU 48.0 ¦ . E FGMNQTVYZ ¦ . . R 46.0 ¦ . ABQ P ¦ . HLUVW 44.0 ¦ . FIJMNRS ¦ . GPTZ 42.0 ¦ . . ¦ . .Level 2 40.0 ¦ . .laboratory averages ¦ . 38.0 ¦ . ¦ . 36.0 ¦ . ¦ . 34.0 ¦ . ¦ . 32.0 ¦ . ¦ . 30.0 ¦ . ¦ . Level 1 28.0 ¦ . laboratory averages ¦ . 26.0 ¦ J ¦ Y 24.0 ¦ EFU ¦ AHMR 22.0 ¦ BLW ¦ IQTZ 20.0 ¦ GSV ¦ N 18.0 ¦ P
34.0 ¦ ¦ 32.0 ¦ .Level 3 ¦ .laboratory averages 30.0 ¦ . ¦ . 28.0 ¦ BY ¦ .Level 2 TUW 26.0 ¦ .laboratory EGJN ¦ .averages I 24.0 ¦ F RSV ¦ . F 22.0 ¦ Y . ¦ BW . 20.0 ¦ ENU . ¦ GIJSTV . 18.0 ¦ R . ¦ . . 16.0 ¦ H . ¦ F H 14.0 ¦ . ¦ . 12.0 ¦ . ¦ . 10.0 ¦ H ¦ JY 8.0 ¦ BEU ¦ GRTVW 6.0 ¦ INS ¦ . 4.0 ¦ .Level 1 ¦ .laboratory averages 2.0 ¦ ¦ 0.0 ¦
46.0 ¦ ¦ 44.0 ¦ ¦ b 42.0 ¦ ¦ Ta 40.0 ¦ XYZ ¦ V 38.0 ¦ LOPQS ¦ HIMNRUW Level 3 laboratory averages 36.0 ¦ EFJK ¦ G 34.0 ¦ BC ¦ D 32.0 ¦ ¦ A 30.0 ¦ ¦ 28.0 ¦ ¦ 26.0 ¦ ¦ 24.0 ¦ Wb ¦ UVYZa 22.0 ¦ JKNOPQRSX Level 2 laboratory averages ¦ DEGILM 20.0 ¦ ACFHT ¦ B 18.0 ¦ ¦ 16.0 ¦ ¦ 14.0 ¦ ¦ 12.0 ¦ ¦ 10.0 ¦ Level 1 laboratory averages ¦ DGKMNRWab 8.0 ¦ ABCFHIJLOPQSTUVXYZ ¦ E 6.0 ¦