Testing of industrial products -
Aggregates for construction

Cross-testing experiments

Return to Home Page.

The cross-testing experiments in MAT 1 - CT 93 - 0040 all followed the same design, shown in Figure 1.

Laboratories
15 (or more) laboratories took part in each experiment. Usually, one or two laboratories came from each country. With some test methods, some countries were not able to take part because they did not have the equipment.

Levels
Each experiment involved three levels (three different aggregates). The three aggregates were chosen to give a wide range of results in the test.

Laboratory samples
Samples were prepared using a rotating sample divider or by fractional shovelling.

Test portion preparation
Laboratories were asked to prepare test portions from their laboratory samples by following the instructions given in prEN 932-2.

Tests
Each laboratory was asked to obtain two results on each laboratory sample.

Determinations
With some test methods, the test procedure requires a test result to be obtained as the average of the results of two (or more) determinations.


Figure 1. The design of the cross-testing experiments.
Laboratory Level 1 Level 2 Level 3
A Test 1Test 2 Test 1Test 2 Test 1Test 2
B Test 1Test 2 Test 1Test 2 Test 1Test 2
C Test 1Test 2 Test 1Test 2 Test 1Test 2
... ...... ...... ......
... ...... ...... ......
... ...... ...... ......
Z Test 1Test 2 Test 1Test 2 Test 1Test 2

An example of a cross-testing experiment: the Los Angeles test.

The results of the cross-testing experiment on the Los Angeles (LA) test are shown in Figures 2 and 3, and Tables 1 to 3.

Laboratories
28 laboratories took part (they are represented by the letters A, B, C, ... , Z, a, b in Figure 2).

Levels
Level 1 is a very strong aggregate. Level 3 is a very weak aggregate (just strong enough to make concrete, not strong enough to go in the wearing course of a road).

Laboratory samples
15 kg samples were prepared by fractional shovelling.

Test portion preparation
Laboratories were asked to prepare two 5 kg test portions from each of their laboratory samples.

Tests
Each laboratory was asked to obtain two results on each laboratory sample.

Test method
In the Los Angeles test, a 5000 +/- 5 g test portion of 10/14 mm aggregate is rolled in a steel drum together with 11 steel balls of total mass 4775 +/- 85 g. The drum has an internal diameter of 710 +/- 3 mm and rotates at 32 +/- 1 r/min. A projecting plate inside the drum lifts some of the steel balls and aggregate each time the drum rotates, so that the steel balls fall, causing the aggregate to be fragmented. The rolling continues for 500 revolutions, after which the percentage of the test portion that passes a 1.60 mm sieve is determined by washing then sieving. This percentage is the Los Angeles coefficient, measured in "LA units".

Statistical analysis
The data are analysed by applying the formulae given in ISO 5725-2 (ISO, 1994).

Remarks
It is common to find stragglers and outliers in the results of cross-testing experiments (see the points with ? or ?? in Figure 2), particularly when some laboratories are not experienced with the test method. The usual practice in the statistical analysis is to exclude the outliers but include the stragglers. The data are used to calculate the repeatability and reproducibility standard deviations (Sr1 and SR1 ) following ISO 5725-2, and these statistics are used to calculate the repeatability and reproducibility limits (r1 and R1) and the coefficients of variation (Cr1 and CR1).


Figure 2. Results of the cross-testing experiment on the Los Angeles test.

LA units (percentages passing the test sieve).


Repeatability illustrated by between-test-result ranges
?  = straggler   ?? = outlier
     ¦              ¦          7.8 ¦ A  ??
     ¦              ¦              ¦
     ¦              ¦              ¦

     ¦              ¦              ¦
     ¦              ¦          4.9 ¦ X  ??
     ¦              ¦              ¦
 2.0 ¦          2.0 ¦          2.0 ¦
     ¦              ¦ L            ¦ FK ?
     ¦              ¦              ¦ B  ?
     ¦              ¦              ¦
     ¦              ¦              ¦
 1.5 ¦          1.5 ¦          1.5 ¦
     ¦              ¦ AB           ¦
     ¦              ¦              ¦
     ¦              ¦              ¦ T
     ¦              ¦              ¦
 1.0 ¦          1.0 ¦          1.0 ¦
     ¦              ¦ Xb           ¦
     ¦ B            ¦              ¦
     ¦              ¦ P            ¦ L
     ¦              ¦ GKY          ¦ V
 0.5 ¦ H        0.5 ¦ Ua       0.5 ¦ P
     ¦ ALNSV        ¦ FT           ¦ DESUab
     ¦ T            ¦ E            ¦ HJNZ
     ¦ EGIJKPQXYZb  ¦ HJMQR        ¦ GR
     ¦ DFMa         ¦ DINV         ¦ IQ
 0.0 ¦ RU       0.0 ¦ SZ       0.0 ¦ M
     ¦ Level 1      ¦ Level 2      ¦ Level 3

Reproducibility illustrated by Laboratory averages 10.0 ¦ 27.5 ¦ 45.0 ¦ ¦ ¦ ¦ ¦ ¦ ¦ b ¦ ¦ ¦ ¦ ¦ ¦ Ta 9.0 ¦ 25.0 ¦ 40.0 ¦ XYZ ¦ DGMNR ¦ ¦ V ¦ KWab ¦ Wb ¦ LOPQS ¦ AHILUVXZ ¦ Ua ¦ HIMNRUW ¦ BJOSY ¦ YZ ¦ EFJK 8.0 ¦ C 22.5 ¦ QRV 35.0 ¦ G ¦ PT ¦ JKPSX ¦ BC ¦ F ¦ MNO ¦ D ¦ Q ¦ DIL ¦ ¦ E ¦ CEG ¦ A 7.0 ¦ 20.0 ¦ FHT 30.0 ¦ ¦ ¦ AB ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ 6.0 ¦ 17.5 ¦ 25.0 ¦ ¦ Level 1 ¦ Level 2 ¦ Level 3

Table 1. Repeatability and reproducibility for the Los Angeles test.
Level 1Level 2Level 3
Number of laboratories included N 282826
General Average XLA units 8.321.637.5
Repeatability standard deviation Sr1LA units 0.2130.4870.572
Reproducibility standard deviation SR1LA units 0.4591.3642.348
Repeatability limit r1LA units 0.61.41.6
Reproducibility limit R1LA units 1.33.86.6

Table 2. Functional relations for the Los Angeles test.
Functional relationship
Repeatability standard deviation LA unitsSr1 = 0.021 X
Reproducibility standard deviation LA unitsSR1 = 0.060 X
Repeatability limit LA unitsr1 = 0.06 X
Reproducibility limit LA unitsR1 = 0.17 X

Table 3. Repeatability and reproducibility standard deviations, for the Los Angeles test, expressed as coefficients of variation.
Level 1Level 2Level 3
Repeatability coefficient of variation Cr1 %2.52.31.5
Reproducibility coefficient of variation CR1 %5.56.36.3

Figure 3. Repeatability and reproducibility standard deviations for the Los Angeles test.