ASTM E1345-98(2014)
(Practice)Standard Practice for Reducing the Effect of Variability of Color Measurement by Use of Multiple Measurements
Standard Practice for Reducing the Effect of Variability of Color Measurement by Use of Multiple Measurements
SIGNIFICANCE AND USE
5.1 This practice should be used whenever measured color-scale or color-difference-scale values are to be compared to an established tolerance. In this way it can be demonstrated quantitatively that the sampling and measurement procedures are adequate to allow an unambiguous decision as to whether or not the mean results are within tolerance.
5.2 This practice is based on portions of SAE J 1545, as it applies to painted or plastic automotive parts. It is generally applicable to object colors in various materials. Textured materials, such as textiles, may require special consideration (see SAE J 1545 and STP 15D Manual on Presentation of Data and Control Chart Analysis5).
5.3 While Practice E178 deals with outliers, it does not include definitions relating to the box and whisker technique. The definition of an outlier is operational and a little vague because there is still considerable disagreement about what constitutes an outlier. In any normally distributed population, there will be members that range from minus to plus infinity. Theoretically, one should include any member of the population in any sample based on estimates of the population parameters. Practically, including a member that is found far from the mean within a small sample, most members of which are found near the mean, will introduce a systematic bias into the estimate of the population parameters (mean, standard deviation, standard error). Such a bias is in direct contrast with the goal of this practice, namely, to reduce the effects of variability of measurement. For the purposes of this practice, no distinction is made between errors of sampling and members of the tails of the distribution. Practice E178 has several methods and significance tables to attempt to differentiate between these two types of extreme values.
SCOPE
1.1 Reduction of the variability associated with average color or color-difference measurements of object-color specimens is achieved by statistical analysis of the results of multiple measurements on a single specimen, or by measurement of multiple specimens, whichever is appropriate.
1.2 This practice provides a means for the determination of the number of measurements required to reduce the variability to a predetermined fraction of the relevant color or color-difference tolerances.
1.3 This practice is general in scope rather than specific as to instrument or material.
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Designation: E1345 − 98 (Reapproved 2014)
Standard Practice for
Reducing the Effect of Variability of Color Measurement by
Use of Multiple Measurements
This standard is issued under the fixed designation E1345; 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.
INTRODUCTION
Recent improvements in the precision and bias of color-measuring instruments have been
accompanied by more widespread use of numerical color tolerances based on instrumental measure-
ments. As tighter tolerances are specified, they begin to approach the limits of visual perception. In
many cases, the instrument user has found it difficult to prepare and measure specimens with adequate
repeatability. This practice provides procedures for reducing variability in the mean results of color
measurement by the use of multiple measurements, and it indicates how many measurements are
required for a specific reduction.
1. Scope E456 Terminology Relating to Quality and Statistics
E1164 PracticeforObtainingSpectrometricDataforObject-
1.1 Reduction of the variability associated with average
Color Evaluation
color or color-difference measurements of object-color speci-
2.2 Other Standard:
mens is achieved by statistical analysis of the results of
SAE J 1545 Recommended Practice for Instrumental Color
multiple measurements on a single specimen, or by measure-
Difference Measurement for Exterior Finishes, Textiles
ment of multiple specimens, whichever is appropriate.
and Colored Trim
1.2 This practice provides a means for the determination of
the number of measurements required to reduce the variability
3. Terminology
to a predetermined fraction of the relevant color or color-
3.1 DefinitionsofappearancetermsinTerminologyE284or
difference tolerances.
statistical terms in Terminology E456 are applicable to this
1.3 This practice is general in scope rather than specific as
practice.
to instrument or material.
3.2 Definitions of Terms Specific to This Standard:
2. Referenced Documents
3.2.1 box and whisker plot, n—a nonparmetric data analysis
diagram that illustrates the 25, 50, and 75 % cumulative
2.1 ASTM Standards:
distribution of values in a data set (the box) and the expected
D2244 Practice for Calculation of Color Tolerances and
range of values, defined by distance outside the box ends; see
Color Differences from Instrumentally Measured Color
whiskers, see Fig. 1.
Coordinates
D3134 Practice for Establishing Color and Gloss Tolerances
3.2.2 extreme value, n—a single reading, selected from a
E178 Practice for Dealing With Outlying Observations
series of readings, whose value is farther from the nearer box
E284 Terminology of Appearance
end than 3.0 times the hinge length.
E308 PracticeforComputingtheColorsofObjectsbyUsing
3.2.2.1 Discussion—A box and whiskers plot is normally
the CIE System
usedtofindoutliersandextremevalues.Suchvaluesshouldbe
eliminated from a series before calculating the series mean,
This practice is under the jurisdiction of ASTM Committee E12 on Color and
standard deviation, and confidence intervals.
Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
3.2.3 hinges, n—the 25 and 75 % cumulative distribution
Appearance Analysis.
Current edition approved Nov. 1, 2014. Published November 2014. Originally points in a set of readings taken during a measurement.
ε1
approved in 1990. Last previous edition approved in 2008 as E1345 – 98 (2008) .
3.2.3.1 Discussion—Hinges represent the values in which
DOI: 10.1520/E1345-98R14.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on Available from Society of Automotive Engineers (SAE), 400 Commonwealth
the ASTM website. Dr., Warrendale, PA 15096-0001, http://www.sae.org.
Copyright ©ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA19428-2959. United States
E1345 − 98 (2014)
0.5
s 5 s/ N (3)
~ !
e
3.2.10 standard error goal, s ,n—level to which the
e,g
standard error of the estimated mean is to be reduced.
3.2.11 tolerance, n—the upper tolerance limit minus the
lower tolerance limit; the total allowable range of the color-
scale or color-difference-scale value considered.
3.2.12 whiskers, n—lines extending out from the box ends
to the largest and smallest observations lying within 1.5 times
the hinge length, measured from the box ends.
4. Summary of Practice
4.1 This practice assumes that, for the material under
consideration and a specified set of color scales, relevant color
or color-difference tolerances have been established (see Prac-
tice D3134).
4.2 For convenience, the numerical example in the Appen-
dix uses CIELAB LCH (lightness, chroma, hue) color differ-
ence scales ∆L*, ∆C* , and ∆H* (see Practice D2244 and
ab ab
Practice E308), but this is not meant to be restrictive.
NOTE 1—Some coordinates, such as CIE x, y, Y, do not follow the
theoriesofthisstandardduetoexcessivecolinearity.Whileithasnotbeen
FIG. 1 Schematic Description of a Box and Whisker Plot
tested, this same colinearity problem may also be observed in 1960 u, v
and 1976 u', v' coordinates. Table 1 provides a listing of the appropriate
and inappropriate color coordinates for use with this practice.
25 % of the readings are less than the lower hinge and 75 % of
4.3 The successive steps in the procedure are as follows:
the readings are less than the upper hinge. See also hinge
4.3.1 Determine the standard deviation of instrument.
length.
4.3.1.1 Screen the measurement data for outliers and ex-
3.2.3.2 Discussion—Hinges are sometimes called the lower
treme values.
(Q ) and upper (Q ) quartile values.
1 1
4.3.2 Determine the standard deviation of color or color-
3.2.4 hinge length, H, n—the range of values between the
difference measurement.
lower and upper hinges.
4.3.2.1 Screen the measurement data for outliers and ex-
3.2.4.1 Discussion—The hinge length is sometimes called
treme values.
the box width or the interquartile range Q to Q .
3 1
4.3.3 Determinethestandarderroroftheestimatedmeanfor
3.2.5 outlier, n—a single reading, selected from a series of
a sampling number of one.
readings, whose value is further from the nearer box end then
4.3.4 Determine the final sampling number that reduces the
1.5 times the hinge length; see 3.2.2.1.
standard error of the estimated mean to less than the standard
3.2.6 sampling number, N, n—number of multiple
error goal for each scale value.
measurements, or number of multiple specimens, required to
4.3.5 Determine the final standard error goal values.
reduce the variability of color or color-difference measurement
NOTE 2—When the standard error of the estimated mean for a sampling
to a desired level.
number of one is larger than a specified fraction of the tolerance or a
3.2.7 standard deviation of color or color-difference
specified multiple of the standard deviation of instrument for any of the
measurement, s—standard deviation of the color scale or three color-difference-scale values, a sampling number greater than one is
required.
color-difference-scale value, x, being considered:
i
0.5
4.4 Screening for and Elimination of Outliers and Extreme
s 5 @ x 2 x / n 2 1 # (1)
$ ~ ! % ~ !
( i avg
Values in Measured Data:
where:
x =(∑ x)/n, and
avg i
n = the number of replicate measurements made.
3.2.8 standard deviation of instrument, s,n—standard de- TABLE 1 Appropriate and Inappropriate Color Coordinates for
i
Use in This Practice
viation of a color-scale or color-difference-scale value due to
instrument variability alone: Color Coordinates Appropriate Inappropriate
CIE Yxy =
0.5
s 5 @$ x 2 x %/ n 2 1 # (2)
~ ! ~ !
i i avg
( CIE LCH =
CIE LAB =
3.2.9 standard error of the estimated mean, s,n—standard
e
CIE LUV =
deviation of color or color-difference measurement divided by
CIE Lu'v' =
the square root of the sampling number:
E1345 − 98 (2014)
TABLE 2 Official Values for T (One-Sided Test) for Outliers
4.4.2.4 If T (T ) is larger than the critical value for n
l n
Number of Upper 0.1% Upper 1.0% readingsatthe1 %levelofsignificance,Readings1(n)maybe
Observations Significance Significance
considered an extreme value.
n Level Level
4.4.3 If any outliers or extreme values were found, consider
3 1.155 1.155
carefully whether they should be dropped or retained. Drop
4 1.499 1.492
5 1.780 1.749
those readings not considered to be part of the desired dataset,
6 2.011 1.944
by whatever consistent criteria are accepted. See 5.3.
7 2.201 2.097
4.4.4 Recalculate the mean, standard deviation and confi-
8 2.358 2.221
9 2.492 2.323 dence limits of the remaining dataset.
10 2.606 2.410
11 2.705 2.485
5. Significance and Use
12 2.791 2.550
13 2.867 2.607
5.1 This practice should be used whenever measured color-
14 2.935 2.659
scale or color-difference-scale values are to be compared to an
15 2.997 2.705
established tolerance. In this way it can be demonstrated
quantitatively that the sampling and measurement procedures
are adequate to allow an unambiguous decision as to whether
or not the mean results are within tolerance.
4.4.1 Box and whisker test—This test is best carried out by
5.2 This practice is based on portions of SAE J 1545, as it
computer. Many programs for the box and whisker technique
applies to painted or plastic automotive parts. It is generally
are available.
applicable to object colors in various materials. Textured
4.4.1.1 Orderthereadingsfromlowesttohighestvalue.The
materials, such as textiles, may require special consideration
reading whose value is half way betw
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
´1
Designation: E1345 − 98 (Reapproved 2008) E1345 − 98 (Reapproved 2014)
Standard Practice for
Reducing the Effect of Variability of Color Measurement by
Use of Multiple Measurements
This standard is issued under the fixed designation E1345; 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.
ε NOTE—Equation 6 was corrected editorially in March 2010.
INTRODUCTION
Recent improvements in the precision and bias of color-measuring instruments have been
accompanied by more widespread use of numerical color tolerances based on instrumental measure-
ments. As tighter tolerances are specified, they begin to approach the limits of visual perception. In
many cases, the instrument user has found it difficult to prepare and measure specimens with adequate
repeatability. This practice provides procedures for reducing variability in the mean results of color
measurement by the use of multiple measurements, and it indicates how many measurements are
required for a specific reduction.
1. Scope
1.1 Reduction of the variability associated with average color or color-difference measurements of object-color specimens is
achieved by statistical analysis of the results of multiple measurements on a single specimen, or by measurement of multiple
specimens, whichever is appropriate.
1.2 This practice provides a means for the determination of the number of measurements required to reduce the variability to
a predetermined fraction of the relevant color or color-difference tolerances.
1.3 This practice is general in scope rather than specific as to instrument or material.
2. Referenced Documents
2.1 ASTM Standards:
D2244 Practice for Calculation of Color Tolerances and Color Differences from Instrumentally Measured Color Coordinates
D3134 Practice for Establishing Color and Gloss Tolerances
E178 Practice for Dealing With Outlying Observations
E284 Terminology of Appearance
E308 Practice for Computing the Colors of Objects by Using the CIE System
E456 Terminology Relating to Quality and Statistics
E1164 Practice for Obtaining Spectrometric Data for Object-Color Evaluation
2.2 Other Standard:
SAE J 1545 Recommended Practice for Instrumental Color Difference Measurement for Exterior Finishes, Textiles and Colored
Trim
3. Terminology
3.1 Definitions of appearance terms in Terminology E284 or statistical terms in Terminology E456 are applicable to this
practice.
This practice is under the jurisdiction of ASTM Committee E12 on Color and Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
Appearance Analysis.
Current edition approved June 1, 2008Nov. 1, 2014. Published June 2008November 2014. Originally approved in 1990. Last previous edition approved in 20032008 as
ε1
E1345 - 98 (2003).E1345 – 98 (2008) . DOI: 10.1520/E1345-98R08E01. 10.1520/E1345-98R14.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’sstandard’s Document Summary page on the ASTM website.
Available from Society of Automotive Engineers (SAE), 400 Commonwealth Dr., Warrendale, PA 15096-0001, http://www.sae.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1345 − 98 (2014)
3.2 Definitions of Terms Specific to This Standard:
3.2.1 box and whisker plot, n—a nonparmetric data analysis diagram that illustrates the 25, 50, and 75 % cumulative distribution
of values in a data set (the box) and the expected range of values, defined by distance outside the box ends; see whiskers, see Fig.
1.
3.2.2 extreme value, n—a single reading, selected from a series of readings, whose value is farther from the nearer box end than
3.0 times the hinge length.
3.2.2.1 Discussion—
A box and whiskers plot is normally used to find outliers and extreme values. Such values should be eliminated from a series before
calculating the series mean, standard deviation, and confidence intervals.
3.2.3 hinges, n—the 25 and 75 % cumulative distribution points in a set of readings taken during a measurement.
3.2.3.1 Discussion—
Hinges represent the values in which 25 % of the readings are less than the lower hinge and 75 % of the readings are less than
the upper hinge. See also hinge length.
3.2.3.2 Discussion—
Hinges are sometimes called the lower (Q ) and upper (Q ) quartile values.
1 1
3.2.4 hinge length, H, n—the range of values between the lower and upper hinges.
3.2.4.1 Discussion—
The hinge length is sometimes called the box width or the interquartile range Q to Q .
3 1
3.2.5 outlier, n—a single reading, selected from a series of readings, whose value is further from the nearer box end then 1.5
times the hinge length; see 3.2.2.1.
3.2.6 sampling number, N, n—number of multiple measurements, or number of multiple specimens, required to reduce the
variability of color or color-difference measurement to a desired level.
FIG. 1 Schematic Description of a Box and Whisker Plot
E1345 − 98 (2014)
3.2.7 standard deviation of color or color-difference measurement, s—standard deviation of the color scale or color-difference-
scale value, x , being considered:
i
0.5
s 5@$ ~x 2 x ! %/~n 2 1!# (1)
( i avg
where:
x = (∑ x )/n, and
avg i
n = the number of replicate measurements made.
where:
x = (∑ x )/n, and
avg i
n = the number of replicate measurements made.
3.2.8 standard deviation of instrument, s , n—standard deviation of a color-scale or color-difference-scale value due to
i
instrument variability alone:
0.5
s 5@$ ~x 2 x ! %/~n 2 1!# (2)
i ( i avg
3.2.9 standard error of the estimated mean, s , n—standard deviation of color or color-difference measurement divided by the
e
square root of the sampling number:
0.5
s 5 s/~N ! (3)
e
3.2.10 standard error goal, s , n—level to which the standard error of the estimated mean is to be reduced.
e,g
3.2.11 tolerance, n—the upper tolerance limit minus the lower tolerance limit; the total allowable range of the color-scale or
color-difference-scale value considered.
3.2.12 whiskers, n—lines extending out from the box ends to the largest and smallest observations lying within 1.5 times the
hinge length, measured from the box ends.
4. Summary of Practice
4.1 This practice assumes that, for the material under consideration and a specified set of color scales, relevant color or
color-difference tolerances have been established (see Practice D3134).
4.2 For convenience, the numerical example in the Appendix uses CIELAB LCH (lightness, chroma, hue) color difference
scales ΔL*, ΔC* , and ΔH* (see Practice D2244 and Practice E308), but this is not meant to be restrictive.
ab ab
NOTE 1—Some coordinates, such as CIE x, y, Y, do not follow the theories of this standard due to excessive colinearity. While it has not been tested,
this same colinearity problem may also be observed in 1960 u, v and 1976 u', v' coordinates. Table 1 provides a listing of the appropriate and inappropriate
color coordinates for use with this practice.
4.3 The successive steps in the procedure are as follows:
4.3.1 Determine the standard deviation of instrument.
4.3.1.1 Screen the measurement data for outliers and extreme values.
4.3.2 Determine the standard deviation of color or color-difference measurement.
4.3.2.1 Screen the measurement data for outliers and extreme values.
4.3.3 Determine the standard error of the estimated mean for a sampling number of one.
4.3.4 Determine the final sampling number that reduces the standard error of the estimated mean to less than the standard error
goal for each scale value.
4.3.5 Determine the final standard error goal values.
NOTE 2—When the standard error of the estimated mean for a sampling number of one is larger than a specified fraction of the tolerance or a specified
multiple of the standard deviation of instrument for any of the three color-difference-scale values, a sampling number greater than one is required.
4.4 Screening for and Elimination of Outliers and Extreme Values in Measured Data:
TABLE 1 Appropriate and Inappropriate Color Coordinates for
Use in This Practice
Color Coordinates Appropriate Inappropriate
CIE Yxy =
CIE LCH =
CIE LAB =
CIE LUV =
CIE Lu'v' =
E1345 − 98 (2014)
TABLE 2 Official Values for T (One-Sided Test) for Outliers
Number of Upper 0.1 % Upper 1.0 %
Observations Significance Significance
n Level Level
3 1.155 1.155
4 1.499 1.492
5 1.780 1.749
6 2.011 1.944
7 2.201 2.097
8 2.358 2.221
9 2.492 2.323
10 2.606 2.410
11 2.705 2.485
12 2.791 2.550
13 2.867 2.607
14 2.935 2.659
15 2.997 2.705
4.4.1 Box and whisker test—This test is best carried out by computer. Many programs for the box and whisker technique are
available.
4.4.1.1 Order the readings from lowest to highest value. The reading whose value is half way between the minimum and
maximum values is the median. Fig. 1 illustrates the following steps.
4.4.1.2 The reading whose value is just less than 75 % of the other readings is the lower hinge. The readings whose value is
just higher than 75 % of the other readings is the upper hinge. The difference between these two is the hinge length H.
4.4.1.3 If the smallest value of any reading is less than the lower hinge value minus 1.5 times the hinge length, it may be
considered an outlier. Likewise, if the largest value of any reading is greater than the upper hinge value plus 1.5 times the hinge
length, it may be considered an outlier.
4.4.1.4 If the smallest (largest) value of any reading is less (greater) than the lower (upper) hinge value minus (plus) 3.0 times
the hinge length, it may be considered an extreme value.
4.4.2 Practice E1
...
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