- 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.
- Return to Particle Size Distribution test Summary Page.
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Estimates of repeatability and reproducibility are given in Table 1 for 200 g test portions and in Table 3 for 30 g test portions. The standard deviations are also shown in Figure 1. These estimates have been calculated by excluding the data listed in Table A below.

Statistical theory may be used to derive a formula that predicts, reasonably well, the repeatability of sieve tests on coarse aggregates from the particle size distribution and the test portion mass (Sym, 1992. *An investigation into the relationship between test portion mass and repeatability for quantitative petrographic examination of aggregates.* Building Research Establishment Note N 194/92, October 1992.), but the formula does not appear to fit the results of tests on sands. However, the theory does suggest that the repeatability standard deviation should follow, approximately, the function (X (100.0 - X) )^{½} , where X is the percentage passing. The lines in Figure 1 show the results obtained by fitting functions of this form to the repeatability and reproducibility standard deviations.

For Level 1, the experimental points for the 200 g test portions fit the functions for the repeatability and reproducibility standard deviations, except in the case of the reproducibility standard deviation for the 0.250 mm sieve. This material has a very narrow grading with most of the particles having a size concentrated around 0.250 mm, so this sieve is heavily loaded during the test. In the corresponding histogram, the laboratory averages for the 0.250 mm sieve are seen to be widely spread, with Laboratories M H F and E giving a long tail towards lower percentages passing. This suggests that the unusually high reproducibility standard deviation for the 0.250 mm sieve arose because of incomplete sieving in some laboratories when using 200 g test portions. If the results in the histogram for 200 g test portions are compared with those in the corresponding histogram for 30 g test portions, it will be seen that the 30 g test portions give laboratory averages that are less widely spread, which is to be expected as there is less risk of overloading sieves with smaller test portions.

For Level 2, the experimental points for both sizes of test portion are in reasonable agreement with the fitted functions.

For Level 3, for both sizes of test portion, the experimental points for the smaller sieve sizes fall below the fitted functions. This material had a high percentage of fines, but otherwise a rather flat grading curve over the smaller sieves. Most of the fines would have been removed during the washing operation, so the smaller sieves would have been lightly loaded by this material.

Hence the functional relations given in Tables 2 and 4 may be used to describe the precision of the determination of particle size distribution, provided that it is noted that they will underestimate the repeatability and reproducibility when sieves are overloaded, and overestimate the repeatability and reproducibility when sieves are lightly loaded.

Level | Test portion | Laboratory | Sieves |
---|---|---|---|

1 | 200 g | E | 0.500 mm |

I | 0.250 mm | ||

O | 0.063 mm | ||

1 | 30 g | D | 0.250 mm, 0.125 mm, 0.063 mm |

F | 0.063 mm | ||

I | 0.250 mm | ||

O | 0.063 mm | ||

2 | 200 g | E | 0.500 mm |

I | 0.500 mm, 0.250 mm | ||

2 | 30 g | E | 2.00 mm, 1.00 mm, 0.500 mm, 0.250 mm, 0.125 mm, 0.063 mm |

I | 2.00 mm, 1.00 mm, 0.500 mm, 0.250 mm, 0.125 mm, 0.063 mm | ||

M | 0.063 mm | ||

3 | 200 g | E | 0.500 mm, 0.125 mm, 0.063 mm |

F | 0.250 mm, 0.125 mm, 0.063 mm | ||

M | 0.063 mm | ||

3 | 30 g | I | 0.500 mm, 0.125 mm |

F | 0.125 mm, 0.063 mm |

There is only one method for determining the particle size distribution of sands using sieves, with its associated precision, but there are several specifications contain requirements for the particle size distribution of sands, so a method is proposed here that will allow a common approach to be applied for ensuring that the reproducibility of the sieve test is adequate in all cases. Consider the relations:

T > 0.30 (X (100.0 - X) )^{½} % passing

S_{R} < 0.05 (X (100.0 - X) )^{½} % passing

Here T is a tolerance in a specification (a measured value should fall within ±T % of a specified value).

According to these relations, S_{R} is always smaller than T by a factor of at least 0.30/0.05 = 6.0 , so if both S_{R} and T satisfy these relations there will be only a small risk that testing variation will cause non-compliance.

The factor of 0.30 in the relation for T may be justified as follows. Table 3 of the draft CEN specification for aggregates for concrete (CEN, 1994a. *Aggregates for concrete.* CEN/TC 154/SC 2 working document, November, 1994.) imposes a tolerance of ±15 % around the declared grading for the results of tests using the mid-sized sieve. At X = 50 % passing, which is approximately what is to be expected with the mid-size sieve, the relation gives T >15 %. Hence the relation is equivalent to the tolerance that is allowed in this particular specification.

If the experimental results in Figure 1 are compared with the above relation for S_{R} it will be seen that the experimental results generally fall below the line S_{R} = 0.05 (X (100.0 - X) )^{½}, so that in most cases the reproducibility is satisfactory according to this criterion (both for 200 g and for 30 g test portions). However, this is not so in Level 1 with the 0.250 mm sieve (which the data suggest was overloaded in several laboratories). Also, if specification limits are fixed close to 0 % passing or 100 % passing then one should check that the reproducibility is adequate in the circumstances to which the specification is to be applied.

Hence if the tolerances for particle size distribution satisfy the above relation for T then the reproducibility of the sieve test should be generally satisfactory, except in the special cases just mentioned.

The sieve test is very widely used with aggregates. On the conservative assumption that one sieve test is applied to each 1000 tonnes of aggregates produced, more than one million sieve tests are carried out on aggregates in Europe every year. Any modification to the test that improves its precision or reduces its cost will be of significant benefit to the industry.

It should be possible to calculate a functional relation for the repeatability of the sieve test using statistical theory. This would be of value because it would allow the factors that influence the repeatability to be understood properly so that the test could be designed to give adequate precision at minimum cost. Also, laboratories would be able to use it to check that they are achieving a satisfactory level of repeatability.

However, it was not possible to use the results of the experiments reported here to establish a functional relation for the repeatability of the determination of the particle size distribution of sands that gives a good fit to the experimental results. In previous work it has been found that relations derived from statistical theory do not agree with experimental results obtained on sands, but it is not clear whether this is because of faults in the derivation of the theoretical formula or because the practical work was not carried out with sufficient care. In the experiments reported here it is clear (from the number of mistakes made in the calculations, and the number of stragglers and outliers) that several of the participants were not familiar with the test method, so there is no point trying to use the results to match theory and practice.

Further work is therefore required to establish a functional relation for the repeatability of the sieve test. As a first step it would be of interest to establish the repeatability that can be achieved when using either fractional shovelling or a good quality rotary sample divider to sub-divide clean sands.

With 200 g test portions there is a risk that some of the finer sieves will be overloaded. The draft CEN method contains a rule that is intended to prevent this happening, although in practice this rule may not always be applied. Small test portions reduce the risk of overloading, and may give satisfactory precision generally. Small test portions will also be easier to wash to remove fines and will pass through the sieves quicker, and so will reduce the time needed for the test.

The X-Y plots show results for the 30 g test portions plotted against the results for the 200 g test portions. In each graph there are two points for each laboratory (following the sample reduction plan, test 3 is plotted against test 1, and test 4 is plotted against test 2).

The most obvious feature of these graphs is the wide scatter of the points for the stragglers and outliers already noted on the histograms and in Table A above. This illustrates that, at the present time, the first priority for laboratories should be for them to make sure that they are carrying out the test correctly, for example, by taking part in proficiency tests.

If a sieve is overloaded with a 200 g test portion, but not with a 30 g test portion, then one would expect to see higher percentages passing with the smaller test portion, giving points above the line of equality in these graphs. The graph for the 0.250 mm sieve for Level 1 shows this pattern, but as the Laboratories responsible for the lowest results with the 200 g test portions (E and F) gave rise to outliers at other times in the experiment, it is risky to place too much weight on this graph.

According to statistical theory, the repeatability standard deviation should be related to 1/M^{½}, where M is the test portion mass, so that, other factors being equal, 200 g test portions should give repeatability standard deviations smaller by a factor of (30/200) ^{½} = 0.39 than those given by 30 g test portions. In Figure 1 it can be seen that 200 g test portions do give the smaller repeatability standard deviations, but only by a factor of 0.0151/0.0251 = 0.60 . Hence the experimental results are not consistent with what would be expected from statistical theory.