ASTM E1763-98(2003)

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Designation: E 1763 – 98 (Reapproved 2003)
Standard Guide for
Interpretation and Use of Results from Interlaboratory
Testing of Chemical Analysis Methods
This standard is issued under the fixed designation E1763; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope that depend upon the method, but also are influenced by the
laboratories and test materials involved in the study. For that
1.1 This guide covers procedures to help a task group
reason,theILStaskgroupmustinterprettheseestimates,aided
interpret interlaboratory study (ILS) statistics to state precision
by this guide and using analytical judgment, to decide if the
and accuracy of a test method and make judgments concerning
method is suitable to be balloted for publication as a standard.
its range of use.
The task group may use this guide to help them prepare the
1.2 This standard does not purport to address all of the
precision and bias statements that are a required part of the
safety concerns, if any, associated with its use. It is the
method.
responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica-
5. Interlaboratory Studies
bility of regulatory limitations prior to use.
5.1 Thefollowingstatementisrequiredineachtestmethod:
2. Referenced Documents 5.1.1 This test method has been evaluated in accordance
with Practice E1601 and Guide E1763. Unless otherwise
2.1 ASTM Standards:
noted in the precision and bias section, the lower limit in the
E135 Terminology Relating to Analytical Chemistry for
scope of each method specifies the lowest analyte content that
Metals, Ores, and Related Materials
may be analyzed with acceptable error (defined as a nominal
E1601 Practice for Conducting an Interlaboratory Study to
5% risk of obtaining a 50% or larger relative difference in
Evaluate the Performance of an Analytical Method\
results on the same test sample in two laboratories).
E1763 Guide for Interpretation and Use of Results from
Interlaboratory Testing of Chemical Methods of Analysis\
6. Required Statistical Information
E1914 Practice for the Use of Terms Relating to the
6.1 A task group satisfies the requirement for statistical
Development and Evaluation of Methods for Chemical
information if the method includes a table of the ILS statistics
Analysis
prepared in accordance with 6.2 and 6.3 and a summary
3. Terminology statement selected from the model statements in Section 9.If
thetaskgroupwishestoprovidefurtherstatisticalinformation,
3.1 For definitions of terms used in this guide, refer to
it may do so in accordance with the provisions of Section 7.
Terminology E135.
6.2 Variability Data—List the variability statistics for each
3.2 For descriptions of terms used in this guide, refer to
analyte in a separate table arranged by increasing analyte
Practice E1914.
content. List the number of independent data sets used in the
4. Significance and Use
calculations and the ILS statistics calculated in accordance
with Practice E1601. Where appropriate, list the material type
4.1 Awritten test method is subjected to an ILS to evaluate
and reference material identification. Follow the examples of
its performance.The ILS produces a set of statistical estimates
Table 1, Table 2, and Table 3.
6.2.1 If the analytical method includes optional conditions
This guide is under the jurisdiction of ASTM Committee E01 on Analytical
extending the analyte range (for example, decreased sample
ChemistryforMetals,Ores,andRelatedMaterialsandisthedirectresponsibilityof
portions or multiple calibration curves,) list the ILS statistics
Subcommittee E01.22 on Statistics and Quality Control.
for each option separately as shown in Table A3.1 and Table
Current edition approved Oct. 1, 2003. Published November 2003. Originally
approved in 1995. Last previous edition approved in 1998 as E1763 – 98.
A3.3.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
6.3 Bias Data—If the ILS includes one or more test
contactASTM Customer Service at service@astm.org. ForAnnual Book ofASTM
materials having an accepted reference value, include the
Standards volume information, refer to the standard’s Document Summary page on
accepted value(s) and b-value(s) as shown in Table 3.
the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E 1763 – 98 (2003)
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
5 0.0004 0.00006 BAM 187-1 low alloyed steel
6 . . . non-alloyed steel
7. Models for Error in Analytical Methods 7 0.0015 −0.00014 BCS 456/1 mild steel
8 . . . non-alloyed steel
7.1 An estimate of the reproducibility index, R, is obtained
9 . . . non-alloyed steel
10 0.0038 −0.00018 BAM 284-1 stainless steel
in an ILS for each individual test material. These are the
11 . . . non-alloyed steel
discrete values of R listed in a statistical information table.
12 0.0041 0.00022 BAM 178-1 low alloyed steel
Users need an estimate of R at the analyte level, which may lie
13 . . . alloyed steel
14 . . . non-alloyed steel
anywhere within the range of the scope of the test method. If
15 0.0090 −0.00004 JSS 175-5 mild steel
the task group conducted the ILS properly and employed good
16 0.0118 −0.0004 BCS 459/1 carbon steel
quality test materials having compositions that cover the
application range, that information may be provided by fol-
lowing the procedures in this section.
7.1.1 If the analytical method includes sample portion or
may use the relationship to estimate R for the method at any
calibration options, treat the ILS statistics for each option as a
concentration, C, within the scope of the method.
separate method.
2 2
ˆ
R 5 =K 1 ~C 3 K /100! (1)
C R rel%
7.2 The task group must decide if the statistics for the test
The boron ILS data in Table 3 yield estimates of
materials in the ILS exhibit trends that follow one of the three
K =0.00026% boron and K =14.6%. The following
R rel%
error models included in this section. The use of a model is
equation predicts R at analyte contents from 0% to approxi-
essential if the task group intends to describe the behavior of
mately 0.012% boron.
thereproducibilityindex, R,asafunctionofanalytecontent.If
thetaskgroupcannotagreeononemodel,itshouldnotattempt 2 2
ˆ
R 5 =0.00026 1 ~%B 30.146! (2)
C
torelate Rtoanalytecontent.Thekeystoidentifyingthemodel
7.4 Constant Model for Error in Analytical Methods—The
are the trends in R and R as the analyte content increases.
rel%
ILS data follows the constant error model if, with increasing
Annex A1 includes a more detailed discussion of these
analyte concentration, R neither increases nor decreases but
analytical error models.
R continuallydecreases.ThegoldmethodILSdatainTable
rel%
7.3 General Model for Error in Analytical Methods—The
1 show this behavior. For statistics that follow this model, use
ILS data follows the general model if, with increasing analyte
Eq 3 to calculate the root-mean-square (RMS) estimate of K .
R
concentration, R increases (most noticeably at higher concen-
Thisvaluepredicts Ratallanalytecontentswithinthescopeof
trations) while R decreases (most noticeably at lower
rel%
the method:
concentrations.) Data for the boron method in Table 3 show
ˆ
this behavior. To interpret statistics that follow this model, K 5 =( R /n (3)
R
select a procedure fromAnnexA2 for calculating estimates of
where:
the constants K and K . Substituted in Eq 1, the constants
R rel%
(R = sum of the squares of R over all test materials, and
defineanequationrepresentingtheexpectedvaluesof Rforthe
n = number of test materials.
method as a function of analyte concentration. The task group
E 1763 – 98 (2003)
The six values for R, squared and added, equal 0.100901. 8.4 Set the lower limit of the method to L.
Dividing by the number of materials, n =6, and taking the
9. Interpretation of ILS Statistics
square root gives an estimate for K of 0.13%. This estimate
R
applies from 0 to 100% gold. 9.1 Aproperly conducted ILS program often provides more
7.5 Relative Model for Error in Analytical Methods—The information than is apparent from visual inspection of the
ILS data follows the relative error model, if with increasing statistics. Typically, when the test program is completed, the
analyteconcentration, R neitherincreasesnordecreasesbut participants have recent experience with the behavior of the
rel%
R continually increases. The manganese method ILS data in method as applied to different test materials. The task group
Table 2 show this behavior. For statistics that follow this may use this knowledge to clarify trends in the performance of
model, use Eq 4 to calculate an RMS estimate of K . This the method at different analyte contents. If the task group
rel%
value predicts R only within the analyte content range agrees upon an error model that is both consistent with the
rel%
tested during the ILS: observed values of R and R and representative of their
rel%
experience with the method and equipment, they may use the
ˆ
K 5 (~R ! /n (4)
=
rel% rel%
model to calculate the expected value for R at various analyte
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
9.2.1 ILS in Which No Model has Been Adopted:
n = number of test materials.
[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
Dividingbythenumberoftestmaterials, n =6,andtakingthe
[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
rel%
R 5 K 1 C 3 (6)
ΠS D
C R
con
...