ASTM E2056-04(2016)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E2056 − 04 (Reapproved 2016)
Standard Practice for
Qualifying Spectrometers and Spectrophotometers for Use
in Multivariate Analyses, Calibrated Using Surrogate
Mixtures
This standard is issued under the fixed designation E2056; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.3 For surrogate test methods, this practice recommends
limitations that should be placed on calibration options that are
1.1 This practice relates to the multivariate calibration of
allowed in the test method. Specifically, this practice recom-
spectrometers and spectrophotometers used in determining the
mends that the test method developer demonstrate that all
physical and chemical characteristics of materials. A detailed
calibrations that are allowed in the test method produce
description of general multivariate analysis is given in Prac-
statistically indistinguishable results.
tices E1655.This standard refers only to those instances where
surrogate mixtures can be used to establish a suitable calibra- 1.4 For surrogate test methods that reference spectrometer/
tion matrix.This practice specifies calibration and qualification spectrophotometer performance practices, such as Practices
data set requirements for interlaboratory studies (ILSs), that is, E275, E925, E932, E958, E1421, E1683,or E1944; Test
round robins, of standard test methods employing surrogate Methods E387, E388,or E579; or Guide E1866, this practice
calibration techniques that do not conform exactly to Practices recommends that instrument performance data be collected as
E1655. part of the ILS to establish the relationship between
spectrometer/spectrophotometer performance and test method
NOTE 1—For some multivariate spectroscopic analyses, interferences
precision.
andmatrixeffectsaresufficientlysmallthatitispossibletocalibrateusing
mixtures that contain substantially fewer chemical components than the
2. Referenced Documents
samples that will ultimately be analyzed. While these surrogate methods
generally make use of the multivariate mathematics described in Practices 2
2.1 ASTM Standards:
E1655, they do not conform to procedures described therein, specifically
D6277 Test Method for Determination of Benzene in Spark-
with respect to the handling of outliers.
Ignition Engine Fuels Using Mid Infrared Spectroscopy
1.2 This practice specifies how the ILS data is treated to
D6300 Practice for Determination of Precision and Bias
establish spectrometer/spectrophotometer performance qualifi-
Data for Use in Test Methods for Petroleum Products and
cation requirements to be incorporated into standard test
Lubricants
methods.
E131 Terminology Relating to Molecular Spectroscopy
NOTE 2—Spectrometer/spectrophotometer qualification procedures are
E275 Practice for Describing and Measuring Performance of
intended to allow the user to determine if the performance of a specific
Ultraviolet and Visible Spectrophotometers
spectrometer/spectrophotometer is adequate to conduct the analysis so as
E387 TestMethodforEstimatingStrayRadiantPowerRatio
to obtain results consistent with the published test method precision.
of Dispersive Spectrophotometers by the Opaque Filter
1.2.1 The spectroscopies used in the surrogate test methods
Method
would include but not be limited to mid- and near-infrared,
E388 Test Method for Wavelength Accuracy and Spectral
ultraviolet/visible, fluorescence and Raman spectroscopies.
Bandwidth of Fluorescence Spectrometers
1.2.2 The surrogate calibrations covered in this practice are:
E579 Test Method for Limit of Detection of Fluorescence of
multilinearregression(MLR),principalcomponentsregression
Quinine Sulfate in Solution
(PCR) or partial least squares (PLS) mathematics. These
E691 Practice for Conducting an Interlaboratory Study to
calibration procedures are described in detail in Practices
Determine the Precision of a Test Method
E1655.
E925 Practice for Monitoring the Calibration of Ultraviolet-
Visible Spectrophotometers whose Spectral Bandwidth
This practice is under the jurisdiction of ASTM Committee E13 on Molecular
Spectroscopy and Separation Science and is the direct responsibility of Subcom-
mittee E13.11 on Multivariate Analysis. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved April 1, 2016. Published May 2016. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1999. Last previous edition approved in 2010 as E2056 – 04(2010). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/E2056-04R16. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2056 − 04 (2016)
does not Exceed 2 nm where appropriate, to calculate the spectral data used in the
E932 Practice for Describing and Measuring Performance of calibration and analysis.
Dispersive Infrared Spectrometers
4.4 The test method should specify the exact mathematics
E958 Practice for Estimation of the Spectral Bandwidth of
that are to be used to develop the multivariate calibration.
Ultraviolet-Visible Spectrophotometers
Allowable spectral preprocessing methods should be defined.
E1421 Practice for Describing and Measuring Performance
The specific mathematics (MLR, PCR or PLS) should be
of Fourier Transform Mid-Infrared (FT-MIR) Spectrom-
specified,andtheacceptablerangeforthenumbersofvariables
eters: Level Zero and Level One Tests
should be given.
E1655 Practices for Infrared Multivariate Quantitative
4.5 When the ILS is conducted to establish the precision of
Analysis
the surrogate test method, the calibration data for all of the
E1683 Practice for Testing the Performance of Scanning
participating laboratories should be collected and used to
Raman Spectrometers
calculate a pooled standard error of calibration for the test
E1866 Guide for Establishing Spectrophotometer Perfor-
method. The pooled standard error of calibration and its
mance Tests
associated degrees of freedom should be reported in the test
E1944 Practice for Describing and Measuring Performance
of Laboratory Fourier Transform Near-Infrared (FT-NIR) method.
Spectrometers: Level Zero and Level One Tests
4.5.1 When a user is calibrating a spectrometer/
spectrophotometer, the standard error of calibration is calcu-
3. Terminology
lated and compared to the pooled standard error of calibration
from the ILS to determine if the performance of the calibrated
3.1 Definitions:
3.1.1 For definitions of terms and symbols relating to spectrometer/spectrophotometer is adequate to produce analy-
ses of the precision specified in the test method.
infrared, ultraviolet/visible and Raman spectroscopy, refer to
Terminology E131.
4.5.2 If a user is purchasing a precalibrated spectrometer/
3.1.2 For definitions of terms and symbols relating to
spectrophotometer, the instrument vendor should supply the
multivariate analysis, refer to Practices E1655.
standard error of calibration and its statistical comparison to
the pooled standard error of calibration.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 spectrometer/spectrophotometer qualification, n—the
4.6 During the ILS, each participating laboratory analyzes a
procedures by which a user demonstrates that the performance
set of qualification samples and reports both the compositions
of a specific spectrometer/spectrophotometer is adequate to
of the qualification set and the estimates made using the
conduct a multivariate analysis so as to obtain precision
multivariate analysis. A pooled error of qualification is calcu-
consistent with that specified in the test method.
lated and reported as part of the test method along with its
corresponding degrees of freedom.
3.2.2 surrogate calibration, n—a multivariate calibration
that is developed using a calibration set which consists of
4.6.1 Before a user may use the spectrometer/
mixtureswithpre-specifiedandreproduciblecompositionsthat spectrophotometer, it must be qualified to perform the surro-
contain substantially fewer chemical components than the
gate test method. The qualification set is analyzed, and a
samples that will ultimately be analyzed. standard error of qualification is calculated. The standard error
of qualification is statistically compared with the pooled
3.2.3 surrogate test method, n—a standard test method that
standard error of qualification to determine if the performance
is based on a surrogate calibration.
ofthecalibratedspectrometer/spectrophotometerisadequateto
4. Summary of Practice produce analyses of the precision specified in the test method.
4.6.2 Spectrometer/spectrophotometer qualification is re-
4.1 Asurrogatetestmethodmustspecifythecompositionof
quiredregardlessofwhetherthecalibrationisperformedbythe
two sets of samples. One set is used to calibrate the
vendor or the user.
spectrometers/spectrophotometers. The second set of samples
4.6.3 Spectrometer/spectrophotometer qualification should
is used to qualify the spectrometer/spectrophotometer to per-
berepeatedaftermajormaintenancehasbeenperformedonthe
form the analysis. The compositions of both sets are expressed
spectrometer/spectrophotometer so as to determine whether
in terms of weight or volume fraction depending on whether
recalibration is required.
thesamplesarepreparedgravimetricallyorvolumetrically.The
compositions of both sets should be specified in the surrogate
test method. If the surrogate test method is being used to 5. Significance and Use
estimate a physical property, then the test method should
5.1 This practice should be used by the developer of
indicate what value of the property is to be assigned to each of
standard test methods that employ surrogate calibrations.
the calibration and qualification samples.
5.1.1 This practice assists the test method developer in
4.2 The surrogate test method should specify the minimum
setting and documenting requirements for the spectrometer/
spectrometer/spectrophotometer requirements for instruments
spectrophotometers that can perform the test method.
that can be used to perform the test method.
5.1.2 This practice assists the test method developer in
4.3 The spectrometer/spectrophotometer test method should setting and documenting spectral data collection and compu-
specify the exact conditions that are to be used to collect and, tation parameters for the test method.
E2056 − 04 (2016)
5.1.3 This practice assists the test method developer in 6.2.1 Thesetsofsurrogatesamplesthatareusedtocalibrate
selecting among possible multivariate analysis procedures that the spectrometers/spectrophotometers should satisfy the re-
could be used to establish the surrogate calibration. The quirements of Practices E1655.If k is the number of variables
practice describes statistical tests that should be performed to (MLR wavelengths or frequencies, PCR principal components
ensurethatallmultivariateanalysisproceduresthatareallowed or PLS latent variables) used in the model, then the minimum
within the scope of the test method produce statistically number of calibration samples should be the greater of 24 or
indistinguishable results. 6k. If the calibration set is derived from an experimental
5.1.4 This practice describes statistical calculations that the design, and if the spectra have been shown to be linear
functions of the component concentrations, then fewer calibra-
test method developer should perform on the calibration and
qualification data that should be collected as part of the ILS tion samples can be used, but in all cases the minimum number
of calibration samples should be the greater of 24 or 4k. The
that establishes the test method precision. These calculations
establish the level of performance that spectrometers/ experimental design must independently vary all components
over the desired analysis range.
spectrophotometers must meet in order to perform the test
method.
6.2.2 When calibrating for a single component, the calibra-
tion set should uniformly span the range over which the
5.2 This practice describes how the person who calibrates a
analysis of that component is to be conducted. Additional
spectrometer/spectrophotometer can test the performance of
components that are present in the calibration set to simulate
said spectrometer/spectrophotometer to determine if the per-
interferences should be independently and uniformly varied
formance is adequate to conduct the test method.
over a range at least as large as is likely to be encountered
5.3 This practice describes how the user of a spectrometer/
during actual application of the test method.
spectrophotometer can qualify the spectrometer/
6.2.3 When calibrating for a property that depends on more
spectrophotometer to conduct the test method.
than one chemical component, the calibration set should
uniformly span the range over which the property analysis is to
6. Surrogate Calibrations
be conducted, and all components that contribute to the
6.1 Practices E1655 assumes that the calibration set used to property should be varied independently.
develop a multivariate model contains samples of the same 6.2.4 The test method should specify the compositions of
type as those that are to eventually be analyzed using the
the calibration samples, including components and target
model. Practices E1655 requires use of outlier statistics to concentrations. The purity of materials to be used in preparing
ensure that samples being analyzed are sufficiently similar to
the calibration samples should also be specified in the test
the calibration samples to produce meaningful results. For method.
some spectroscopic analyses, however, it is possible to cali-
6.3 Qualification Sets:
brate using gravimetrically or volumetrically prepared mix-
6.3.1 The sets of surrogate samples that are used to qualify
tures that contain significantly fewer components than the
the spectrometers/spectrophotometers should satisfy the vali-
samples that will ultimately be analyzed. For these surrogate
dation requirements of Practices E1655.If k is the number of
test methods, the outlier statistics described in Practices E1655
variables (MLR wavelengths or frequencies, PCR principal
arenotappropriatesinceallsamplesareexpectedtobeoutliers
components or PLS latent variables) used in the model, then
relative to the simplified calibrations. Thus, surrogate test
the minimum number of qualification samples should be the
methods cannot fulfill the requirements of Practices E1655.
greater of 20 or 5k. If the qualification set is derived from an
While surrogate test methods may make use of the mathemat-
experimental design, and if the spectra have been shown to be
ics described in Practices E1655, they should not claim to
linear functions of the component concentrations, then fewer
follow the procedures described in that practice.
qualificationsamplescanbeused,butinallcasestheminimum
6.1.1 Indevelopingsurrogatetestmethods,itisnecessaryto
number of qualification samples should be the greater of 20 or
thoroughly understand and account for potential spectral inter-
3k. The experimental design must independently vary all
ferences. Typically, the spectral range used in surrogate cali-
components over the entire calibration range.
brations will be limited so as to minimize interferences. For
6.3.2 The compositions of the qualification samples should
those interferences that cannot be eliminated through limiting
span the same ranges as did the calibration samples.
the spectral range, representative components that mimic the
6.3.3 The test method should specify the compositions of
interference should be included in the calibration mixtures.
the qualification samples, including components and target
6.1.2 Test Method D6277 provides an example of a surro-
concentrations. The purity of materials to be used in preparing
gate test method. The FT-MIR analysis of benzene in gasoline
the qualification samples should also be specified in the test
is calibrated using mixtures of benzene, isooctane, toluene and
method.
xylenes and PLS mathematics. The calibration mixtures con-
tain far fewer components than gasoline, but the spectral range
6.4 Precision of Surrogate Calibration Test Methods:
used in the analysis is limited to a narrow range about a
6.4.1 An ILS determines the precision of a surrogate test
relatively interference-free benzene peak. Toluene and xylenes
method.Theinterlaboratorystudymustconformtotherequire-
are used in the calibration mixtures to adequately mimic the
mentsofPracticeE691,andtoanyotherrelevantpractices.For
interferences that are present in gasolines.
example, a test method applicable to petroleum products
6.2 Calibration Sets: should conform to Practice D6300.
E2056 − 04 (2016)
6.4.2 The standard error of calibration (SEC ) and the pating laboratories should report a complete set of calibration
surrogate
standarderrorofqualification(SEQ )forasurrogatetest results consisting of the following:
surrogate
th
method cannot be used reliably to infer the precision that can
7.2.1.1 The component concentration or property for the i
th
be expected for the analysis of actual samples. However, calibration sample from the j laboratory, denoted as y ,
ij
th
SEC and SEQ arerepresentativeofthenecessary
7.2.1.2 The estimate of the concentration of the i calibra-
surrogate surrogate
th
spectrometer/spectrophotometer performance that must be
tion sample from the j laboratory obtained using the multi-
achieved in order to obtain precision comparable to that
variate model to analyze the calibration spectrum, denoted as
established by the ILS.
ŷ ,
ij
th
7.2.1.3 The number of calibration samples for the j
7. Requirements for Test Methods Using Surrogate
laboratory, denoted as n, and
j
Calibrations
7.2.1.4 The number of variables used in the multivariate
th
model for the j laboratory, denoted as k.
j
7.1 Surrogate Calibrations of Individual Spectrometers/
7.2.2 The pooled standard error of calibration is calculated
Spectrophotometers:
as:
7.1.1 The multivariate spectroscopic analysis is calibrated
using a set of surrogate mixtures. These mixtures are prepared
m n
i
yˆ 2 y
volumetrically or gravimetrically to compositions defined by ~ !
( ( ij ij
j51 i51
the test method. Spectra of the mixtures are collected under PSEC 5 (2)
m
surrogate
conditions defined by the test method. The spectral data is !
n 2 k 2 δ
( j j j
j51
pretreated as prescribed in the test method, and a multivariate
calibrationmodelisdevelopedasprescribedinthetestmethod. The sum with index j is over the m laboratories, and δ is 1
j
7.1.1.1 The y values that are used in the development of the for labs that use a mean-centered calibration and 0 for labs
whose calibration is not mean-centered.
model can be the concentrations of individual components in
the surrogate mixtures, or the sum of component concentra-
7.2.3 The degrees of freedom for the pooled standard error
tions depending on the application. of calibration, DOF(PSEC ), is calculated as:
surrogate
7.1.1.2 For some applications, the y values that are used in m
DOF~PSEC ! 5 n 2 k 2 δ (3)
the calibration may be property values that can be calculated
surrogate ( j j j
j51
from the compositions of the mixtures.
7.2.4 The surrogate test method should document both
NOTE 3—For some surrogate calibrations, it may be possible to
PSEC and DOF(PSEC ).
surrogate surrogate
establish a correlation equation that relates the surrogate analyses to
results from another analytical test method. It is recommended that
7.3 Determining Adequacy of Spectrometer/
multiplicative or additive factors determined from such a correlation not
Spectrophotometer Calibrations—The surrogate test method
be incorporated into the y values of the surrogate calibration. Instead, the
should indicate that, when a spectrometer/spectrophotometer is
y values should consist of the actual component concentrations, the
calibrated either by an end user or a vendor, the adequacy of
surrogate test method results should be reported in terms of these
concentrations, and the test method should contain a separate section that the calibration is tested by comparing SEC with
surrogate
compares the two test methods and gives the correlation equation.
PSEC . The comparison is done using an F-test. The
surrogate
F value is calculated as:
7.1.2 A standard error of calibration for the surrogate
calibration
calibration is calculated as:
SEC
surrogate
F 5 (4)
calibration 2
PSEC
n surrogate
yˆ 2 y
~ !
( i i
The calculated F value is compared to the critical F
i51
calibration
SEC 5 (1)
!
surrogate
DOF value from Table 1 for DOF (see 6.1.2) degrees of freedom in
the numerator and DOF(PSEC ) (see 6.2.3)inthe
surrogate
where:
denominator.
DOF = the number of degrees of freedom for the calibration
7.3.1 If the calculated F value is less than or equal
calibration
and is n–k–1 if the model is mean centered, and n–k
to the critical F value, then the calibration of the spectrometer/
otherwise,
spectrophotometer is comparable to or better than those that
n = the number of surrogate mixtures used in the
participated in the ILS, and the user may continue with the
calibration,
qualification of the spectrometer/spectrophotometer.
k = the number of variables (MLR wavelengths or
7.3.2 If the calculated F value is greater than the
calibration
frequencies, PCR principal components, or PLS
critical F value, then the calibration is poorer than those that
latent variables) used in the model,
th participated in the ILS. The cause of the poorer performance
y = the component concentration for the i calibration
i
should be identified and corrected, and the spectrometer/
sample, and
th
spectrophotometer should be recalibrated.
ŷ = theestimateoftheconcentrationofthe i calibration
i
sample.
NOTE 4—The F-test in 7.3.1 is a one-sided test conducted at the 95 %
level. The test is one-sided since it is only necessary to show that the
7.2 Pooled Standard Error of Calibration:
variance for the current calibration (SEC ) is not worse than that
surrogate
7.2.1 During the interlaboratory study that establishes the
for the calibrations used in the interlaboratory study (PSEC ). If
surrogate
2 2
precision of the surrogate test method, each of the m partici- SEC and PSEC come from the same population, then
surrogate surrogate
E2056 − 04 (2016)
TABLE 1 95 Percentiles of the F Statistic (One-Sided Test)
Denominator, Numerator
Degrees of Freedom 7 8 9 101214 16182025 304050 100
7 3.79 3.73 3.68 3.64 3.57 3.53 3.49 3.47 3.44 3.40 3.38 3.34 3.32 3.27
8 3.50 3.44 3.39 3.35 3.28 3.24 3.20 3.17 3.15 3.11 3.08 3.04 3.02 2.97
9 3.29 3.23 3.18 3.14 3.07 3.03 2.99 2.96 2.94 2.89 2.86 2.83 2.80 2.76
10 3.14 3.07 3.02 2.98 2.91 2.86 2.83 2.80 2.77 2.73 2.70 2.66 2.64 2.59
11 3.01 2.95 2.90 2.85 2.79 2.74 2.70 2.67 2.65 2.60 2.57 2.53 2.51 2.46
12 2.91 2.85 2.80 2.75 2.69 2.64 2.60 2.57 2.54 2.50 2.47 2.43 2.40 2.35
13 2.83 2.77 2.71 2.67 2.60 2.55 2.51 2.48 2.46 2.41 2.38 2.34 2.31 2.26
14 2.76 2.70 2.65 2.60 2.53 2.48 2.44 2.41 2.39 2.34 2.31 2.27 2.24 2.19
15 2.71 2.64 2.59 2.54 2.48 2.42 2.38 2.35 2.33 2.28 2.25 2.20 2.18 2.12
16 2.66 2.59 2.54 2.49 2.42 2.37 2.33 2.30 2.28 2.23 2.19 2.15 2.12 2.07
17 2.61 2.55 2.49 2.45 2.38 2.33 2.29 2.26 2.23 2.18 2.15 2.10 2.08 2.02
18 2.58 2.51 2.46 2.41 2.34 2.29 2.25 2.22 2.19 2.14 2.11 2.06 2.04 1.98
19 2.54 2.48 2.42 2.38 2.31 2.26 2.21 2.18 2.16 2.11 2.07 2.03 2.00 1.94
20 2.51 2.45 2.39 2.35 2.28 2.22 2.18 2.15 2.12 2.07 2.04 1.99 1.97 1.91
25 2.40 2.34 2.28 2.24 2.16 2.11 2.07 2.04 2.01 1.96 1.92 1.87 1.84 1.78
30 2.33 2.27 2.21 2.16 2.09 2.04 1.99 1.96 1.93 1.88 1.84 1.79 1.76 1.70
35 2.29 2.22 2.16 2.11 2.04 1.99 1.94 1.91 1.88 1.82 1.79 1.74 1.70 1.63
40 2.25 2.18 2.12 2.08 2.00 1.95 1.90 1.87 1.84 1.78 1.74 1.69 1.66 1.59
45 2.22 2.15 2.10 2.05 1.97 1.92 1.87 1.84 1.81 1.75 1.71 1.66 1.63 1.55
50 2.20 2.13 2.07 2.03 1.95 1.89 1.85 1.81 1.78 1.73 1.69 1.63 1.60 1.52
60 2.17 2.10 2.04 1.99 1.92 1.86 1.82 1.78 1.75 1.69 1.65 1.59 1.56 1.48
70 2.14 2.07 2.02 1.97 1.89 1.84 1.79 1.75 1.72 1.66 1.62 1.57 1.53 1.45
80 2.13 2.06 2.00 1.95 1.88 1.82 1.77 1.73 1.70 1.64 1.60 1.54 1.51 1.43
90 2.11 2.04 1.99 1.94 1.86 1.80 1.76 1.72 1.69 1.63 1.59 1.53 1.49 1.41
thereisonlya5 %chancethatthe F willbegreaterthanthevalue
7.5.3 The number of qualification samples analyzed by the
calibration
th
in Table 1.
j laboratory, denoted as q.
j
7.4 Standard Error of Qualification for Individual
7.5.4 Thepooledstandarderrorofqualificationiscalculated
Spectrometers/Spectrophotometers:
as:
7.4.1 Before a spectrophotometer can be used to analyze
m q
j
actual samples, it must be qualified. A qualification set of
yˆ 2 y
~ !
( ( ij ij
surrogate mixtures are prepared volumetrically or gravimetri-
j51 i51
PSEQ 5 (6)
surrogate m
callytocompositionsdefinedbythetestmethod.Spectraofthe
!
q
( j
qualification mixtures are collected under conditions defined
j51
bythetestmethod.Thespectraldataispretreatedasprescribed
7.5.5 The degrees of freedom for the pooled standard error
in the test method, and analyzed using the multivariate cali-
of calibration, DOF(PSEC ), is calculated as:
surrogate
bration model as described in the test method.
m
7.4.2 A standard error of qualification is calculated as:
DOF~PSEQ ! 5 q (7)
surrogate ( j
j51
q
~yˆ 2 y !
( i i
i51 7.5.6 The surrogate test method should document both
SEQ 5 (5)
!
surrogate
q
PSEQ and DOF(PSEQ ).
surrogate surrogate
where:
7.6 Qualification of an Individual Spectrometer/
q = the number of surrogate qualification mixtures, Spectrophotometer—The surrogate test method should indicate
th
y = the component concentration for the i qualification that, when a spectrometer/spectrophotometer is qualified by an
i
sample, and
end user, the performance of the calibrated spec
...