ASTM E1763-98

NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
Designation: E 1763 – 98
Standard Guide for
Interpretation and Use of Results from Interlaboratory
Testing of Chemical Analysis Methods
This standard is issued under the fixed designation E 1763; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope The task group may use this guide to help them prepare the
precision and bias statements that are a required part of the
1.1 This guide covers procedures to help a task group
method.
interpret interlaboratory study (ILS) statistics to state precision
and accuracy of a test method and make judgments concerning
5. Interlaboratory Studies
its range of use.
5.1 The following statement is required in each test method:
1.2 This standard does not purport to address all of the
5.1.1 This test method has been evaluated in accordance
safety concerns, if any, associated with its use. It is the
with Practice E 1601 and Guide E 1763. Unless otherwise
responsibility of the user of this standard to establish appro-
noted in the precision and bias section, the lower limit in the
priate safety and health practices and determine the applica-
scope of each method specifies the lowest analyte content that
bility of regulatory limitations prior to use.
may be analyzed with acceptable error (defined as a nominal
2. Referenced Documents 5 % risk of obtaining a 50 % or larger relative difference in
results on the same test sample in two laboratories).
2.1 ASTM Standards:
E 135 Terminology Relating to Analytical Chemistry for
6. Required Statistical Information
Metals, Ores, and Related Materials
6.1 A task group satisfies the requirement for statistical
E 1601 Practice for Conducting an Interlaboratory Study to
2 information if the method includes a table of the ILS statistics
Evaluate the Performance of an Analytical Method
prepared in accordance with 6.2 and 6.3 and a summary
E 1763 Guide for Interpretation and Use of Results from
statement selected from the model statements in Section 9. If
Interlaboratory Testing of Chemical Methods of Analysis
the task group wishes to provide further statistical information,
E 1914 Practice for the Use of Terms Relating to the
it may do so in accordance with the provisions of Section 7.
Development and Evaluation of Methods for Chemical
3 6.2 Variability Data—List the variability statistics for each
Analysis
analyte in a separate table arranged by increasing analyte
3. Terminology content. List the number of independent data sets used in the
calculations and the ILS statistics calculated in accordance
3.1 For definitions of terms used in this guide, refer to
with Practice E 1601. Where appropriate, list the material type
Terminology E 135.
and reference material identification. Follow the examples of
3.2 For descriptions of terms used in this guide, refer to
Table 1, Table 2, and Table 3.
Practice E 1914.
6.2.1 If the analytical method includes optional conditions
4. Significance and Use
extending the analyte range (for example, decreased sample
portions or multiple calibration curves,) list the ILS statistics
4.1 A written test method is subjected to an ILS to evaluate
for each option separately as shown in Table A3.1 and Table
its performance. The ILS produces a set of statistical estimates
A3.3.
that depend upon the method, but also are influenced by the
6.3 Bias Data—If the ILS includes one or more test
laboratories and test materials involved in the study. For that
materials having an accepted reference value, include the
reason, the ILS task group must interpret these estimates, aided
accepted value(s) and b-value(s) as shown in Table 3.
by this guide and using analytical judgment, to decide if the
method is suitable to be balloted for publication as a standard.
7. Models for Error in Analytical Methods
7.1 An estimate of the reproducibility index, R, is obtained
This guide is under the jurisdiction of ASTM Committee E-1 on Analytical
in an ILS for each individual test material. These are the
Chemistry for Metals, Ores, and Related Materials and is the direct responsibility of
discrete values of R listed in a statistical information table.
Subcommittee E01.22 on Statistics and Quality Control.
Current edition approved May 10, 1998. Published July 1998. Originally
Users need an estimate of R at the analyte level, which may lie
published as E 1763 – 95. Last previous edition E 1763 – 95.
anywhere within the range of the scope of the test method. If
Annual Book of ASTM Standards, Vol 03.05.
3 the task group conducted the ILS properly and employed good
Annual Book of ASTM Standards, Vol 03.06.
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NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 1763
TABLE 1 Gold in Bullion by the Fire Assay Method TABLE 3 Boron in Steel by the Curcumin Spectrophotometric
Method
Repro- Repro-
Number of Minimum
Test Gold ducibility ducibility
Repro- Repro-
Labor- SD (s , R
M rel% Number of Minimum
Material found, % SD (s , Index (R,
R Test Boron ducibility ducibility
atories E 1601)
Labora- SD (s , R
M rel%
E 1601) E 1601)
Material found, % SD (s , Index (R,
R
tories E 1601)
E 1601) E 1601)
6 7 26.350 0.0089 0.0318 0.089 0.34
4 10 65.744 0.0236 0.0439 0.123 0.25
1–D1,1 14 0.00023 0.000036 0.000064 0.00018 78.3
2 10 73.831 0.0261 0.0296 0.083 0.20 2–B1,2 21 0.00023 0.000082 0.000102 0.00028 124
3 10 76.484 0.0275 0.0543 0.152 0.19
3–B1,1 21 0.00026 0.000046 0.000084 0.00024 90.4
1 10 78.392 0.0200 0.0689 0.193 0.11
4–D1,7 14 0.00045 0.000046 0.000150 0.00042 63.3
5 7 99.060 0.0189 0.0368 0.103 0.10
5–B1,3 21 0.00046 0.000061 0.000107 0.00030 65.2
6–D1,2 14 0.00108 0.000054 0.000100 0.00028 25.9
7–B1,4 21 0.00136 0.000068 0.000189 0.00053 39.0
8–D1,3 14 0.00275 0.000104 0.000129 0.00036 12.1
TABLE 2 Manganese in Iron Ores by the Permanganate
9–D1,4 14 0.00315 0.000104 0.000129 0.00036 11.4
Titrimetric method
10–B1,5 21 0.00362 0.000111 0.000214 0.00060 13.3
11–D1,5 14 0.00378 0.000104 0.000257 0.00072 19.0
Repro- Repro-
Number Man Minimum
12–B1,6 21 0.00432 0.000143 0.000189 0.00053 12.3
Test ducibility ducibility
of Labora- ganese SD (s , R
M rel%
13–D1,8 14 0.00432 0.000096 0.000171 0.00048 11.1
Material SD (s , Index (R,
R
tories found, % E 1601)
14–D1,6 14 0.00639 0.000132 0.000471 0.00132 15.2
E 1601) E 1601)
15–B1,7 21 0.00904 0.000179 0.000482 0.00135 14.9
1 8 0.62 0.0047 0.0069 0.0193 3.11
16–B1,8 21 0.0114 0.00035 0.000625 0.00175 15.4
2 8 1.17 0.0189 0.0219 0.0614 5.25
Certified Material Identification
3 8 1.72 0.0237 0.0244 0.0683 3.97
B-value, % Description
Boron, % (Source)
4 8 2.83 0.0218 0.0244 0.0683 2.41
5 8 3.73 0.0218 0.0360 0.1007 2.70
1 . . . non-alloyed steel
6 8 5.55 0.0275 0.0724 0.2026 3.65
2 0.0003 −0.00007 ERMC 097-1 high purity iron
3 0.0003 −0.00007 ERMC 283-1 high speed steel
4 . . . alloyed steel
quality test materials having compositions that cover the
5 0.0004 0.00006 BAM 187-1 low alloyed steel
application range, that information may be provided by fol- 6 . . . non-alloyed steel
7 0.0015 −0.00014 BCS 456/1 mild steel
lowing the procedures in this section.
8 . . . non-alloyed steel
7.1.1 If the analytical method includes sample portion or
9 . . . non-alloyed steel
calibration options, treat the ILS statistics for each option as a 10 0.0038 −0.00018 BAM 284-1 stainless steel
11 . . . non-alloyed steel
separate method.
12 0.0041 0.00022 BAM 178-1 low alloyed steel
7.2 The task group must decide if the statistics for the test
13 . . . alloyed steel
14 . . . non-alloyed steel
materials in the ILS exhibit trends that follow one of the three
15 0.0090 −0.00004 JSS 175-5 mild steel
error models included in this section. The use of a model is
16 0.0118 −0.0004 BCS 459/1 carbon steel
essential if the task group intends to describe the behavior of
the reproducibility index, R, as a function of analyte content. If
the task group cannot agree on one model, it should not attempt ILS data follows the constant error model if, with increasing
to relate R to analyte content. The keys to identifying the model
analyte concentration, R neither increases nor decreases but
are the trends in R and R as the analyte content increases. R continually decreases. The gold method ILS data in Table
rel% rel%
Annex A1 includes a more detailed discussion of these
1 show this behavior. For statistics that follow this model, use
analytical error models. Eq 3 to calculate the root-mean-square (RMS) estimate of K .
R
7.3 General Model for Error in Analytical Methods—The This value predicts R at all analyte contents within the scope of
ILS data follows the general model if, with increasing analyte the method:
concentration, R increases (most noticeably at higher concen-
ˆ
K 5 =( R /n (3)
R
trations) while R decreases (most noticeably at lower
rel%
concentrations.) Data for the boron method in Table 3 show
where:
this behavior. To interpret statistics that follow this model,
(R = sum of the squares of R over all test materials, and
select a procedure from Annex A2 for calculating estimates of
n = number of test materials.
the constants K and K . Substituted in Eq 1, the constants
The six values for R, squared and added, equal 0.100901.
R rel%
define an equation representing the expected values of R for the
Dividing by the number of materials, n = 6, and taking the
method as a function of analyte concentration. The task group
square root gives an estimate for K of 0.13 %. This estimate
R
may use the relationship to estimate R for the method at any
applies from 0 to 100 % gold.
concentration, C, within the scope of the method.
7.5 Relative Model for Error in Analytical Methods—The
ILS data follows the relative error model, if with increasing
2 2
ˆ
R 5 K 1 ~C 3 K /100! (1)
=
C R rel%
analyte concentration, R neither increases nor decreases but
rel%
The boron ILS data in Table 3 yield estimates of
R continually increases. The manganese method ILS data in
K = 0.00026 % boron and K = 14.6 %. The following
R rel%
Table 2 show this behavior. For statistics that follow this
equation predicts R at analyte contents from 0 % to approxi-
model, use Eq 4 to calculate an RMS estimate of K . This
rel%
mately 0.012 % boron.
value predicts R only within the analyte content range
rel%
2 2
tested during the ILS:
ˆ
R 5 0.00026 1 ~%B 3 0.146! (2)
=
C
ˆ
7.4 Constant Model for Error in Analytical Methods—The K 5 =(~R ! /n (4)
rel% rel%
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 1763
contents within the scope of the method as a guide to users.
where:
9.2 Precision Statements—Select a statement from the fol-
((R ) = sum of the squares of R over all test
rel% rel%
lowing example formats:
materials, and
n = number of test materials. 9.2.1 ILS in Which No Model has Been Adopted:
[Insert the number of laboratories with data used in the ILS]
The six values for R , squared and added, equal 79.4161.
rel%
laboratories participated in testing this method, providing
Dividing by the number of test materials, n = 6, and taking the
[number of data sets actually used] sets of data. Table ____
square root gives an estimate for K of 3.7 %. This estimate
rel%
summarizes the precision information.
applies from approximately 0.5 % to 6 % manganese.
9.2.2 ILS in Which Constant Error Model has Been
8. Calculation of the Low Scope Limit of the Method
Adopted:
[Insert the number of laboratories with data used in the ILS]
NOTE 1—Refer to Annex A4.
laboratories participated in testing this method, providing
8.1 A method is always written for a nominal analyte
[number of data sets actually used] sets of data. Table ____
concentration range expected to cover the anticipated applica-
summarizes the precision information. Within the scope of the
tions. If the low scope limit calculated from the ILS statistics
method, the reproducibility index, R, is approximately [insert
is lower than the low limit specified in the draft method, the
the estimated K from 7.4].
R
task group need not lower the scope of the method unless it
9.2.3 ILS in Which Relative Error Model has Been Adopted:
wishes to do so. However, if the calculated low limit is higher
[Insert the number of laboratories with data used in the ILS]
than the value specified in the draft method, the task group
laboratories participated in testing this method, providing
shall raise the low limit to the calculated value. For methods
[number of data sets actually used] sets of data. Table ____
with sample portion or calibration options, calculate the low
summarizes the precision information. Within the scope of the
scope limit from the data for the option covering the lowest
method, the relative reproducibility index, R is approxi-
rel%
range.
mately [insert the estimated K from 7.5.]
rel%
8.2 The task group must establish the appropriate value for
9.2.4 ILS in Which General Analytical Error Model has
R , the lowest estimated reproducibility index from the ILS
L
been Adopted:
and select e , the maximum allowable percent relative error.
max
[Insert the number of laboratories with data used in the ILS]
These constants are used to calculate L, the lowest analyte
laboratories participated in testing this method, providing
content for which the method is expected to give quantitative
[number of data sets actually used] sets of data. Table ____
results.
summarizes the precision information. The following equation
8.2.1 R —For an ILS evaluated in accordance with the
L
predicts the approximate value of R at any concentration, C,
general error model (7.3) or the constant error model (7.4), set
within the scope of the method:
R equal to the estimate of K . Otherwise, set R equal to the
L R L
estimated R for the test material with the lowest analyte K
2 rel%
R 5 K 1 C 3 (6)
˛ S D
C R
content. If several have nearly equal values for R, set R equal
L
to the square root of the sum of their squares.
Insert values for K and K obtained in 7.3#
R rel%
8.2.2 Maximum Allowable Error, e —Set e equal to
max max
9.2.5 For 9.2.3 or 9.2.4, the task group may also wish to
50 %, a value that has been found satisfactory for most
show and refer to a table of expected values for R, calculated
methods used to test materials at low analyte contents.
for various analyte contents by K or Eq 1,
...