ISO/TR 24857:2006

Synthetic industrial diamond grit products — Single-particle compressive failure strength — "DiaTest-SI" system

ISO/TS 24857:2006 gives the results of a study to determine the feasibility of the DiaTest-SI single particle strength tester as a system for measuring the compressive strength of synthetic industrial diamond grit products. Issues that were addressed included: the range of grit products (in terms of both size and strength) for which the DiaTest-SI system was appropriate, the choice of distribution statistics with which to describe diamond strength, and the similarities (at a statistically significant level) of the results from various test centres.

Produits en diamant synthétique industriel — Résistance à la compression des particules — Méthode "DiaTest SI"

General Information

• Status: Withdrawn
• Publication Date: 16-Mar-2006
• Withdrawal Date: 16-Mar-2006
• ICS: 25.100.70 - Abrasives
• Technical Committee: ISO/TC 29/SC 5 - Grinding wheels and abrasives
• Drafting Committee: ISO/TC 29/SC 5 - Grinding wheels and abrasives
• Current Stage: 9599 - Withdrawal of International Standard
• Start Date: 01-Mar-2021
• Completion Date: 12-Feb-2026

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 24857
First edition
2006-03-15
Synthetic industrial diamond grit
products — Single-particle compressive
failure strength — “DiaTest-SI” system
Produits en diamant synthétique industriel — Résistance à la
compression des particules — Méthode «DiaTest SI»

Reference number
©
ISO 2006
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ii © ISO 2006 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 General principles of the single particle strength testing of diamond . 2
5 Design of the experiments. 3
5.1 General conditions . 3
5.2 Additional conditions . 3
5.3 Results . 4
6 Assignable causes of variations in single particle strength. 5
7 Statistical analyses of the results . 5
8 Results and discussion. 6
8.1 Between-centre variation: all diamond types combined . 6
8.2 Between-centre variation: individual diamond types . 7
8.3 Within-centre variation. 8
8.4 Comparison of between-group and within-group variations . 9
8.5 Estimation of accuracy of the single particle strength test . 10
9 Consequences for a standard . 10
10 Conclusions . 10
Annex A (informative) Use of parametric and non-parametric statistics . 12
Annex B (informative) Statistical significance tests. 15
Annex C (informative) Between-centre variations . 16
Annex D (informative) Within-centre variations . 20
Annex E (informative) Summary of between-centre and within-centre variations. 23
Annex F (informative) Estimation of the experimental error of the single particle strength test . 25
Bibliography . 26

Foreword
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(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
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International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 24857 was prepared by Technical Committee ISO/TC 29, Small tools, Subcommittee SC 5, Grinding
wheels and abrasives.
iv © ISO 2006 – All rights reserved

Introduction
A study has been performed to evaluate the suitability of the Vollstädt “DiaTest-SI” system for the single
particle compressive strength testing of synthetic industrial diamond particles.
Four distinct saw grit diamond products were measured repeatedly by six test centres, in order that the
variation in results between the centres and the variation in results within each centre could be established.
The principal measurement examined was the median single particle strength of a sample (that is, half of the
particles in the sample have a strength below this value). It was concluded from the study that within each test
centre, the median strength of a saw grit diamond product could be measured with a high degree of
repeatability: the average “scatter” of the medians being around 2 % to 4 %. Examining variations between
test centres, there were small systematic differences in the results from each test centre's strength testing
machine, their measurement “biases” being between −2 % and +5 %. The combination of between-centre and
within-centre variations resulted in an estimated experimental error of between ±7 % and ±15 %.

TECHNICAL REPORT ISO/TR 24857:2006(E)

Synthetic industrial diamond grit products — Single-particle
compressive failure strength — “DiaTest-SI” system
1 Scope
1)
This Technical Report gives the results of a study to determine the feasibility of the “DiaTest-SI” single
particle strength tester as a system for measuring the compressive strength of synthetic industrial diamond grit
products. Issues that were addressed included: the range of grit products (in terms of both size and strength)
for which the “DiaTest-SI” system was appropriate, the choice of distribution statistics with which to describe
diamond strength, and the similarities (at a statistically significant level) of the results from various test centres.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 5725-1:1994, Accuracy (trueness and precision) of measurement methods and results — Part 1: General
principles and definitions
ISO 5725-2:1994, Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic
method for the determination of repeatability and reproducibility of a standard measurement method
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 5725-1, ISO 5725-2 and the
following apply.
3.1
analysis of variance
ANOVA
statistical method used to determine the influence of various assignable causes on experimental results
3.2
compressive failure force
CFF
force (in newtons) applied to a particle which results in its failure
3.3
single particle strength
SPS
alternative term for the compressive failure force (CFF) of a particle

1) “DiaTest-SI” is the trade name of a product supplied by Vollstädt-Diamant GmbH, Schlunkendorfer Strasse 21,
14554 Seddiner See, Germany. This information is given for the convenience of users of this Technical Report and does
not constitute an endorsement by ISO of the product named. Equivalent products may be used if they can be shown to
lead to the same results.
3.4
polycrystalline diamond
PCD
intergrown mass of randomly orientated diamond particles in a metal matrix, synthesized at high temperature
and high pressure
NOTE PCD offers very high hardness, toughness and abrasion resistance.
3.5
US mesh
size of a diamond product determined by the mesh sizes of the sieves used to separate the diamond particles
[1]
NOTE In the US mesh system, a sieve size is defined by the number of lines per inch of that sieve; see ISO 6106
for details.
4 General principles of the single particle strength testing of diamond
Industrial synthetic diamond products may be tested for strength using a variety of techniques. Perhaps the
[2]
most established of these techniques is the friability test (or friatest ), which measures the resistance of a
diamond sample contained within a capsule to multiple impacts by a steel ball. Whilst the friatest may be a
robust technique, being conceptually simple and having a high level of repeatability, it yields only one “figure
of merit” strength value, and cannot be used to describe the distribution of particle strengths within a diamond
sample.
The strength of an individual diamond particle may be measured by subjection to an increasing compressive
force, the threshold force (in newtons) at which the particle “fails” being its recorded strength. This form of
measurement, which is known as single particle strength (SPS), compressive failure force (CFF) or static
strength (as distinct from the dynamic strength of the friatest), is therefore a valuable complementary
technique to the friatest because of the information it provides on the particle strength distribution. At present,
single particle strength testing is most conveniently performed on grit sizes coarser than size D213
(70/80 US mesh).
There are two principal methods for the single particle strength testing of diamond:
[3]
⎯ particles may be either crushed between rotating cylinders , or
⎯ between vertically aligned anvils.
The second of these two methods is substantially more widespread than the first, and is commercially
[4]
available in the form of such systems as the “DiaTest-SI” by the German manufacturer Vollstädt .
In the DiaTest-SI system (and others of a similar design), diamond particles are aligned on an adhesive
“carrier” tape and are subsequently transported between the anvils. An image analysis camera may be
positioned before the anvils in order to measure the size and shape characteristics of the particle. The upper
anvil is attached to a pneumatically (or mechanically) driven piston, whilst the lower anvil is attached to a load
sensor. The anvils may be manufactured from polycrystalline cubic boron nitride (PcBN) or polycrystalline
diamond (PCD), with PCD offering a longer anvil life (this is important, as over-used anvils can have a
significant effect on results).
As the upper anvil is driven downwards, the particle is subjected to a compressive force, and this force is
transmitted through the particle to the lower anvil and the load sensor. Eventually the particle will “fail” in that
some disintegration will occur, and there will be an instantaneous reduction in the force detected by the load
sensor. The nature of this reduction in force is dependent on the defect structure of the particle: a particle with
a high perfection will tend to withstand high compressive forces before disintegrating catastrophically, whilst a
particle with numerous significant defects is more likely to break in several stages. Complex algorithms are
used to examine the force-time characteristics of a crush and to assign an appropriate failure strength value to
the particle.
2 © ISO 2006 – All rights reserved

5 Design of the experiments
5.1 General conditions
The Vollstädt “DiaTest-SI” system is capable of measuring the single particle strength distributions of virtually
all common grades of saw grit diamond in the common sizes. Experiments were therefore chosen to evaluate
the performance of the machine over a range of operating conditions in accordance with ISO 5725-1 and
ISO 5725-2.
a) Title: Synthetic industrial diamond grit products — Single-particle compressive failure strength —
“DiaTest-SI” system
b) Name and location of the laboratories:
⎯ Centre 1 Germany
⎯ Centre 2 Ireland
⎯ Centre 3 China
⎯ Centre 4 Germany
⎯ Centre 5 Austria
⎯ Centre 6 Germany
c) Measuring equipment: Vollstädt “DiaTest-SI” system using unified and optimized software
d) Anvil and (pneumatic) piston Each test laboratory received three sets processed from the same PCD
discs:
Abrasive, monocrystalline synthetic diamond macrogrit with the following sizes, properties and sievings:
1) high-strength grade, coarse grit (narrow sieving) 30/35 US-mesh
2) high-strength grade, medium-size grit (broad sieving) 40/50 US-mesh
3) medium-strength grade, medium-size grit (broad sieving) 40/50 US-mesh
4) low-strength grade, fine grit (broad sieving) 60/70 US-mesh
Each test laboratory was provided with three samples each of the particle sizes defined in 1) to 4), each
sample consisting with approximately 500 particles.
5.2 Additional conditions
A second phase of the study was performed in the same manner, with each laboratory receiving a further
three sets of PCD anvils and a further three sets of each of the four diamond samples.
For all tests to be carried out, the test laboratories appointed a measuring instrument operator.
The respective three sets of anvils (anvil and piston) were employed in such a manner that one set of anvils
was used for high-strength grade in size 30/35, and another set of anvils was used for the high-strength grade
in size 40/50. The third set of anvils was used to test both the medium-strength grade in size 40/50 and the
low-strength grade in size 60/70.
These test series were designed to evaluate the accuracy of the Vollstädt measuring equipment in terms of
the correctness and precision of strength measurements. The parameter to be tested was the so-called CFF
value (compressive failure force, in newtons).
5.3 Results
The following values were determined.
a) Mean strength, S
mean
F
∑ take out
S =
mean
n
b) Median strength, S
med
SF=
med take out, med
where
F is the compressive failure force (CFF), in newtons, remaining after all unquantifiable
take out
particle crushes (given the arbitrary strength value 9,999 N by the DiaTest-SI system)
have been removed from the data set;
F is the middle value of F when sorted in ascending order;
take out, med take out
n is the number of particles (quantifiably) tested.
NOTE If the number of F values is even, the median strength is the average of the middle pair of F
take out take out
values.
Four grades of saw grit diamond were used for the study:
• HS601: a high-strength grade, in size D601 (30/35 US mesh)
• HS427: the same high-strength grade, in size D427 (40/50 US mesh)
• MS427: a medium-strength grade, in size D427 (40/50 US mesh)
• LS251: a low-strength grade, in size D251 (60/70 US mesh)
In all four diamond grades, the particle sizing and particle strength distributions were typical of those found in
standard industrial diamond products.
For each grade, the many samples sent to the various centres were extracted from a single larger “batch”.
Each sample consisted of around 500 particles, and the sample extraction process was performed using well-
established proprietary random-splitting equipment. It is therefore believed that the best possible measures
were taken to ensure that individual samples were the same, and representative of the larger batch.
Furthermore, test centres were instructed to test all particles in a sample, rather than a fixed number, to
remove associated sample selection variations.
Six samples of each grade were analysed by each of the six centres — three samples were tested in the first
phase of the study, and the remaining three samples were tested in a subsequent second phase.
Particular efforts were made to minimise the effect of anvil variation on single particle strength results.
Polycrystalline diamond discs were carefully chosen to ensure homogeneity, processed into anvils, and
distributed to the test centres for use with specific diamond samples.
For the first phase of the study a particular disc was processed into anvils for use with the 18 samples of
HS601 (three samples for each centre), a second disc produced anvils for use with the 18 samples of HS427,
and a third disc produced anvils for the 18 samples of MS427 and the three samples of LS251. This approach
ensured that possible disc-to-disc structural variations did not affect the results either within a test centre or
4 © ISO 2006 – All rights reserved

between test centres for a particular diamond grade. Regrettably the limited size of such polycrystalline discs
necessitated the processing of new discs for the second phase of the study. However, the same method was
used for the distribution of anvils in the second phase.
6 Assignable causes of variations in single particle strength
The results of the many tests (144 in total) were analysed with the aim of determining the general variation in
[5]
the single particle strength measurement and the “assignable causes” of the variation . Assignable causes
of variation in a measurement system may be summarized in the mnemonic:
• Man: the effect of different machine operators
• Machine: different units giving different results
• Materials: differences or inhomogeneities in the materials used in the test
• Method: differences in the measurement procedure
Some of these assignable causes were investigated by the statistical analyses of the results, whilst other
assignable causes were minimized in their effect by judicious experimental design.
The contributions to test variability of man and machine were combined by ensuring that each test centre used
only one person, operating only one “DiaTest-SI” unit, for the entire study.
The category materials should perhaps be separated into two components: the test saw grit diamond samples
and the polycrystalline diamond anvils. The contributions to test variability of the test diamond samples took
the form of systematic differences in strength between different grades, and random variations in the strength
from different samples of the same grade. The contributions to test variability of the polycrystalline diamond
anvils took the form of variations in compressive strength (or other behaviour under loading) of different anvils
from the same disc, and variations in strength between discs. As mentioned earlier, the effects of between-
disc variations were eradicated within each of the two phases of the study by the use of specific discs with
specific diamond types, and the effects of within-disc variations on results from different samples of the same
diamond type were minimized by careful selection of polycrystalline diamond discs according to their structural
homogeneity.
Finally, variations in the method were addressed by each test centre using the same, strictly defined,
measurement procedure.
7 Statistical analyses of the results
[6]
A common statistical technique for analysing an experiment such as this is analysis of variance (ANOVA) .
ANOVA evaluates differences in results in terms of the various assignable causes – if there is simply one
factor that is changed between tests (e.g. machine) then one-factor ANOVA may be employed, whilst for
changes in several factors (e.g. machine, material) multi-factor ANOVA should be employed.
In the single particle strength experiment reported here, there were three factors that changed between tests:
test centre, diamond type and run (“repeat”).
However, a fundamental requirement of ANOVA that prohibits its use for this experiment is that the random
variations within each test be normally distributed. Here, these random variations correspond to variations in
strength of the particles in each “repeat”. As will be apparent, single particle strength distributions of diamond
products are not necessarily normal (Gaussian) in form, and so the form of the basic data captured in this
study invalidates the assumptions of ANOVA. Therefore, a different statistical approach was required in order
to obtain an ANOVA-type evaluation of the important factors that contribute towards variation in single particle
strength.
Non-normal single particle strength distributions are best described by non-parametric statistics, and so the
median was chosen as the descriptor of distribution location, and non-parametric significance tests were used
to determine the statistical significance of differences between distributions. An introduction to distribution
statistics and an exercise to prove the appropriateness of non-parametric statistics are presented in Annex A.
Recalling Clause 6, it is expected that the assignable cause that will have the most significant effect on
strength measurements (other than the systematic differences deriving from the different diamond types) is
man/machine – other assignable causes have been hopefully minimized by careful experimental design.
Two fundamental measurement characteristics of each test centre's man/machine are precision and bias. If a
man/machine has the ability to perform repeated measurements with little variation in results, it has high
precision. If a man/machine is able to obtain a measurement result that does not differ much from the “true”
result, it has low bias. (In this study it is difficult to know the “true” strength distribution of a diamond type, so it
is taken to be the average of the distributions from all the test centres.)
The statistical analyses performed here fall into two basic categories: analyses of between-centre variations
and analyses of within-centre variations.
Between-centre variations derive from differences in strength measurement between machines of different
test centres, and so are informative of the bias of the machines. These variations were assessed by
comparing results across test centres, having firstly combined within each test centre the results from its
repeats.
Within-centre variations derive from a single machine's ability to measure results consistently, and so are
informative of the precision of the machine. These variations were assessed by considering the six repeats for
each diamond type individually, calculating the “scatter” in their results.
Further details of the analytical approaches are given in Clause 8, together with the results and discussion.
8 Results and discussion
8.1 Between-centre variation: all diamond types combined
The effect of the factor test centre (i.e. the assignable cause man/machine) was evaluated by combining all
tests performed within each test centre. Each test centre performed 24 tests (6 repeats on each of 4 diamond
types) and, when combined with equal weighting, these formed a “master” single particle strength distribution
for the test centre with a median that can be called the overall centre median.
By comparing the six overall centre medians (both in terms of simple percentage differences, and by statistical
[7]
significance tests such as the Mann-Whitney U test , described in Annex B), an appreciation of the
fundamental differences in the results from each test centre (i.e. the underlying bias in the test centre's
man/machine) was obtained. For ease of reference, all figures associated with between-centre variations are
found in Annex C.
Table C.1 shows that the “master” distributions from each of the six centres were quite similar in terms of their
th
principal statistics (in this table and others of a similar format, “P10” is used as an abbreviation of “10
percentile”, and so on). The medians of these distributions, the six overall centre medians, all lay within
approximately ±2 % of the average overall centre median (found in the right column of the table).
Mann-Whitney U tests were performed to determine which overall centre medians were statistically
significantly different from each other. The results are presented in Table C.6. As Annex B explains, a p value
of less than 0,05 indicates a statistically significant difference (at the 95 % confidence level) between the two
medians being compared.
Here, it was found that in 5 (out of the possible 15) comparisons the two medians were statistically
significantly different. Whilst this initially seemed a surprisingly high number (given the apparent similarities
between the distributions), it was most probably due to the high number (many thousands) of strength values
6 © ISO 2006 – All rights reserved

in each “master” distribution — as the sample size increases so does the confidence in the results, and hence
even minor differences can become statistically significant.
th th th
In summary, perhaps the only notable case of bias in a test centre was that of Centre 1: the 10 , 25 and 90
percentiles of Centre 1 were higher than those of the other centres, and 4 of the 5 statistically significant
differences between medians involved the median of Centre 1.
8.2 Between-centre variation: individual diamond types
Similar analyses were performed on individual diamond types — within each test centre the six repeats on a
particular diamond type were combined to form a larger data set. By comparing the data sets from the six test
centres, the bias of each test centre as a function of diamond type was examined. In other words, perhaps a
particular test centre had a man/machine that showed systematic bias when measuring a particular diamond
type. The equivalent study in ANOVA would be the interaction between test centre and diamond type.
Tables C.2 and C.7 show the distribution statistics and Mann-Whitney U test p values respectively for the
diamond type HS601. The differences between the medians were greater here than for all diamond types
combined — the six centre medians for HS601 were within around ±4 % of the average centre median.
Centres 1 and 4 recorded generally high strength results, and Centre 3 recorded generally low strength results.
This greater scatter also increased the number of medians that were statistically significantly different to each
other (11 out of 15 comparisons).
The distribution statistics and Mann-Whitney U test results for diamond type HS427 are shown in Tables C.3
and C.8 respectively. For this diamond type, the six centre medians were within ±3 % of the average centre
median, and medians were found to be statistically significantly different in 7 of the 15 possible comparisons.
The distribution statistics and Mann-Whitney U test results for diamond type MS427 are shown in Tables C.4
and C.9 respectively, whilst the distribution statistics and Mann-Whitney U test results for diamond type LS251
are shown in Tables C.5 and C.10 respectively.
The findings for the diamond type LS251 are notable in that the strength results from Centre 1 are
substantially higher than those from the other centres. The medians from Centres 2 to 6 are very similar, and
Table C.10 shows that when comparing medians from these centres, only two pairs of medians are signifi-
cantly different. However, Centre 1's median is about 15 % higher than the average of the others, and is
statistically significantly different from the others. It was confirmed that Centre 1's median value was not
distorted by one or two “rogue” repeats; results from the six repeats were reasonably similar, and so it should
be concluded that the offset of Centre 1's median compared to the other centre medians is a “real” effect.
The tables of “p values” presented in Tables C.6 to C.10 may be conveniently summarized non-numerically in
tables of “homogeneous groups”. Tables of homogeneous groups for each of the diamond types are
presented together in Table C.11. In such a table, each centre's median is represented by an X (or a row of
Xs). Where different centres have Xs in the same column(s), there are no significant differences between their
medians.
For example, at the right-hand side of Table C.11 there is a table of homogeneous groups for diamond type
LS251. The X corresponding to Centre 1 (in the top row) does not overlap with any of the other Xs, and so this
infers that Centre 1's median is significantly different from all of the other centres' medians (this is confirmed
by the very low p values in Table C.10). The X corresponding to Centre 6 overlaps with those of Centres 2, 3
and 4, and hence their medians are not significantly different. However, Centre 6's X does not overlap with
Centre 5's X, and so these two medians are significantly different. Again, these similarities and differences
are confirmed by the p values in Table C.10. Other observations may be made in the same way.
The interaction effect between test centre and diamond type becomes evident when comparing the relation-
ships between centre medians for one diamond type, and then for another diamond type. Centre 3, for
example, recorded the lowest median strength for HS601 but the highest median strength for HS427. Centre 1,
for example, recorded a particularly high median strength for LS251 and yet a very “average” median for
HS427. That is, the respective biases of the test machines (as examined by considering all diamond types
combined) changed according to the diamond type.
This interaction is perhaps best communicated by the table and graph in Table C.12 and Figure C.1,
respectively. These show the bias (as a percentage) of a centre median from the average centre median for
each diamond type, and for all diamond types combined. The biases were calculated simply from the median
(P50) strengths in the Tables C.1 to C.5.
From Tables C.11 and C.12, two cases of centre bias are seen. Centre 1's five centre medians all lay on or
above the average centre medians (the 0 % line on the y-axis), and Centre 5's medians all lay on or below the
average centre medians. The medians of the other four centres were reasonably evenly distributed around the
0 % line.
Having gained an understanding of the measurement bias of each test centre (and the extent to which these
biases are affected by diamond type), the measurement precision of each test centre was then examined.
8.3 Within-centre variation
Within-centre variation was analysed for each diamond type by comparing the six tests (“repeats”) within each
centre. By examining only the relationship between the six repeats within a centre (without any comparison
between centres) the effect of test centre bias was eliminated, thus isolating the effect of test centre precision.
Results of the six repeats from the six centres for diamond types HS601, HS427, MS427 and LS251 are
presented in Annex D in Tables D.1, D.2, D.3 and D.4 respectively. For the purpose of brevity, only the
strength distribution medians are given (rather than the selection of percentiles given in earlier tables). The
average of the six medians for each centre is shown in the bottom row of each table.
There are two points of note here. Firstly, some values are absent from the tables. During strength testing for
this study, test centres occasionally reported measurement difficulties (e.g. computer malfunctions, equipment
faults) that either prevented completion of the test or invalidated the results. Results were only excluded from
analysis where there were reported equipment problems; unexpected results obtained whilst the equipment
was seemingly working normally have been retained in the analysis.
Secondly, during the analysis of within-centre variations it became apparent that for diamond type LS251
there was a systematic difference between the results from the first phase of the study (repeats 1 to 3) and the
second phase of the study (repeats 4 to 6). This can be seen from the median strengths in Table D.4.
The only experimental factor that changed between the two phases was the polycrystalline disc from which
the anvils were manufactured. In the specified experimental procedure, a pair of anvils used to test a sample
LS251 were previously used to test a sample of MS427. It might be the case that the set of anvils used for
these two diamond types in the second phase were more prone to chipping than those in the first phase. If so,
the testing of MS427 might have induced additional anvil damage in the form of rough surfaces, which are
known to result in lower recorded particle strengths.
As this difference was reported by most test centres (as would be expected if the anvil material was the
source of the problem) the exact procedure for analysing results for LS251 was modified to compensate
(further details of this are given shortly). It should be stressed that the systematic nature of this difference did
not compromise the findings of the between-centre variations, as all centres were affected equally.
Furthermore, statistical significance tests showed that for the other three diamond types (HS601, HS427 and
HS251) there were no significant differences between the results from the first phase and the second phase of
the study.
Statistical tests were performed to determine whether, for a particular diamond type in a particular centre, the
medians from the six “repeats” were significantly different. For this, the Kruskal-Wallis H test (a version of the
Mann-Whitney U test for multiple samples, and described briefly in Annex B) was used. The results of these
tests (expressed as p values) are tabulated in Annex D, Table D.5.
Table D.5 shows that for each of the four diamond types measured by Centre 1, the six repeats were found to
be insignificantly different. On the other hand, the p values from Centre 3 were less than 0,05 (indicating
statistically significant differences) for all four diamond types.
It is unsurprising that the p values for the repeats of LS251 were less than 0,05 for Centres 2 to 6. This
indicates that the scatter within the six repeats was high, and this was due to the systematic difference
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between the results from phase one of the study (repeats 1 to 3) and phase two (repeats 4 to 6). To
compensate, the results from these two phases were analysed separately.
Average medians and p values for LS251 from the two phases have been included in the Tables D.4 and D.5.
Table D.5 shows that the test centres generally had high consistency of results for LS251 when considering
repeats 1 to 3 and repeats 4 to 6 separately; only two of the 12 relevant p values are less than 0,05.
The precision (consistency) of the results from each centre are perhaps best communicated by the Table D.6
and in Figure D.1, respectively. For each diamond type in each centre, the differences between the median
strengths of individual repeats and the average of the six repeat medians were calculated. These six
differences were then expressed as percentages of the average median. Obviously some of these percentage
differences were negative values (for medians below the average) and the remainder were positive values (for
medians above the average). In order to prevent the average of these being 0, the absolute values of the six
differences were calculated (i.e. negatives values were converted to positives), and the mean (average) of
these was taken.
This value may be defined as the “mean deviation of the median from the average median” for a particular
diamond type in a particular centre, but has been called “scatter” for simplification. Larger numbers signify
greater scatter within the group of six medians, and so the greater the scatter, the poorer the precision.
There is a certain correlation between the p values in Table D.5 and the scatter values in Table D.6, but the
relationship is complex: six repeat medians could have a low scatter by consisting of five very similar medians,
but the presence of one “outlier” could prevent all six being deemed to be from the same population.
8.4 Comparison of between-group and within-group variations
The measurement capability of each test centre (the assignable cause man/machine) can be summarized for
all diamond types by calculating an average value for bias and an average value for scatter (inversely related
to precision).
To calculate the average bias for each test centre, the average was taken of the bias values for HS601,
HS427, MS427 and LS251. To calculate the average scatter for each test centre, the average was first taken
of the scatter values for LS251 1–3 and LS251 4–6, and then the average was taken of this and the scatter
values for HS601, HS427 and MS427 (this approach was taken to compensate for the offset in results from
LS251 from the two phases of the study, and to ensure equal weighting for the four diamond types).
The average bias and average scatter for each test centre are presented graphically in Figure E.1 in Annex E.
Overall, Centre 2 had the lowest scatter (and hence, best precision) and (together with Centre 6) the smallest
bias. Centre 1's measurement bias was significantly affected by its results on LS251; in both phases of the
study its results on this diamond type were much stronger than those of the other centres, and reasons for this
should be investigated. Excluding its results on LS251, Centre 1's average bias would be approximately 2 %.
Another interesting observation was made by calculating the average bias and scatter as a function of
diamond type (rather than centre). As the average bias for each diamond type was (by definition) 0, individual
bias values were made absolute (all positive) prior to calculation of the average. A graph of average absolute
bias against average scatter for the four diamond types is shown in Figure E.2.
There appears to be a relationship between bias and scatter: the diamond type which was measured with the
greatest repeatability (precision) within each centre (HS427) was also measured with the least bias across the
centres. Conversely, the diamond type measured with the highest within-centre variation (LS251, even
compensating for the differences between the results of the two phases) also reported the highest between-
centre variation.
It might reasonably be expected that the greatest measurement variation would derive from the diamond type
with the broadest strength distribution (HS601), because the width of the strength distribution is a possible
source of sampling variation, but that does not seem to be the case. The broader particle size distributions in
HS427 and MS427 (another source of sampling variation) do not appear to have adversely affected
measurement variation either.
Diamond type LS251 is at the edge of the “operating window” of the DiaTest-SI system (in terms of particle
size and strength), and this is perhaps the reason for its greater measurement variation.
8.5 Estimation of accuracy of the single particle strength test
A final mathematical exercise was performed to estimate the overall accuracy of the single particle strength
test for each diamond type. The aim of this was to produce a “bottom line” experimental error for each
diamond type, such that in the “everyday” scenario of two DiaTest-SI users (e.g., a diamond manufacturer and
a diamond toolmaker) comparing results, the extent to which the results are similar could be understood.
For each diamond type, the 36 medians (i.e. 6 repeats from each of 6 centres) were collected, and these
formed a sampling distribution of the median for that diamond type (the concept of the sampling distribution is
introduced in Annex A), which was theoretically normal. In a normal distribution, 95 % of the data points lie
within ±1,96 standard deviations around the mean. Therefore, by constructing the sampling distribution of the
median for a given diamond type, it is expected that (theoretically) when a sample of diamond is tested by any
of these test centres, 95 % of the time the median will fall within the mean of the sampling distribution ±1,96
standard deviations. Converted to a percentage value, this 95 % interval is an appropriate measure of the
overall experimental error of the single particle strength test according to this study.
The 95 % intervals of the sampling distributions of the medians for the four diamond types are shown in
Figure F.1 in Annex F. Again, an adjustment has been made to the medians of diamond type LS251 to
compensate for the offset in results from the two phases of the study.
The Table
...