ASTM E1345-98(2008)e1

Standard Practice for Reducing the Effect of Variability of Color Measurement by Use of Multiple Measurements

SIGNIFICANCE AND USE
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.
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 Analysis ).
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.

General Information

• Status: Historical
• Publication Date: 31-May-2008
• ICS: 17.180.20 - Colours and measurement of light
• Technical Committee: E12 - Color and Appearance
• Drafting Committee: E12.04 - Color and Appearance Analysis

Relations

• Replaces: ASTM E1345-98(2008) - Standard Practice for Reducing the Effect of Variability of Color Measurement by Use of Multiple Measurements
• Effective Date: 01-Jun-2008
• Replaced By: ASTM E1345-98(2014) - Standard Practice for Reducing the Effect of Variability of Color Measurement by Use of Multiple Measurements
• Effective Date: 01-Nov-2014
• Referred By: ASTM E1477-98a(2022) - Standard Test Method for Luminous Reflectance Factor of Acoustical Materials by Use of Integrating-Sphere Reflectometers
• Effective Date: 01-Jun-2008
• Referred By: ASTM D1746-23 - Standard Test Method for Transparency of Plastic Sheeting
• Effective Date: 01-Jun-2008
• Referred By: ASTM D5531-17(2023) - Standard Guide for Preparation, Maintenance, and Distribution of Physical Product Standards for Color and Geometric Appearance of Coatings
• Effective Date: 01-Jun-2008
• Referred By: ASTM E2539-14(2021) - Standard Test Method for Multiangle Color Measurement of Interference Pigments
• Effective Date: 01-Jun-2008
• Referred By: ASTM D5382-02(2017) - Standard Guide to Evaluation of Optical Properties of Powder Coatings
• Effective Date: 01-Jun-2008
• Referred By: ASTM E313-20 - Standard Practice for Calculating Yellowness and Whiteness Indices from Instrumentally Measured Color Coordinates
• Effective Date: 01-Jun-2008
• Referred By: ASTM D3134-15(2019) - Standard Practice for Establishing Color and Gloss Tolerances
• Effective Date: 01-Jun-2008
• Referred By: ASTM D6631-05(2019) - Standard Guide for Committee D01 for Conducting an Interlaboratory Study for the Purpose of Determining the Precision of a Test Method
• Effective Date: 01-Jun-2008
• Referred By: ASTM E991-21 - Standard Practice for Color Measurement of Fluorescent Specimens Using the One-Monochromator Method
• Effective Date: 01-Jun-2008
• Referred By: ASTM D7195-21 - Standard Guide for Setting Object Color Specifications
• Effective Date: 01-Jun-2008
• Referred By: ASTM E1349-06(2022) - Standard Test Method for Reflectance Factor and Color by Spectrophotometry Using Bidirectional (45°:0° or 0°:45°) Geometry
• Effective Date: 01-Jun-2008
• Referred By: ASTM E2194-14(2021) - Standard Test Method for Multiangle Color Measurement of Metal Flake Pigmented Materials
• Effective Date: 01-Jun-2008
• Referred By: ASTM E805-22 - Standard Practice for Identification of Instrumental Methods of Color or Color-Difference Measurement of Materials
• Effective Date: 01-Jun-2008

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
´1
Designation: E1345 − 98 (Reapproved2008)
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.
´ 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 E308 PracticeforComputingtheColorsofObjectsbyUsing
the CIE System
1.1 Reduction of the variability associated with average
E456 Terminology Relating to Quality and Statistics
color or color-difference measurements of object-color speci-
E1164 PracticeforObtainingSpectrometricDataforObject-
mens is achieved by statistical analysis of the results of
Color Evaluation
multiple measurements on a single specimen, or by measure-
2.2 Other Standard:
ment of multiple specimens, whichever is appropriate.
SAE J 1545 Recommended Practice for Instrumental Color
1.2 This practice provides a means for the determination of
Difference Measurement for Exterior Finishes, Textiles
the number of measurements required to reduce the variability
and Colored Trim
to a predetermined fraction of the relevant color or color-
difference tolerances.
3. Terminology
1.3 This practice is general in scope rather than specific as
3.1 DefinitionsofappearancetermsinTerminologyE284or
to instrument or material.
statistical terms in Terminology E456 are applicable to this
practice.
2. Referenced Documents
3.2 Definitions of Terms Specific to This Standard:
2.1 ASTM Standards:
3.2.1 box and whisker plot, n—a nonparmetric data analysis
D2244 Practice for Calculation of Color Tolerances and
diagram that illustrates the 25, 50, and 75 % cumulative
Color Differences from Instrumentally Measured Color
distribution of values in a data set (the box) and the expected
Coordinates
range of values, defined by distance outside the box ends; see
D3134 Practice for Establishing Color and Gloss Tolerances
whiskers, see Fig. 1.
E178 Practice for Dealing With Outlying Observations
3.2.2 extreme value, n—a single reading, selected from a
E284 Terminology of Appearance
series of readings, whose value is farther from the nearer box
end than 3.0 times the hinge length.
This practice is under the jurisdiction of ASTM Committee E12 on Color and
3.2.2.1 Discussion—A box and whiskers plot is normally
Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
usedtofindoutliersandextremevalues.Suchvaluesshouldbe
Appearance Analysis.
Current edition approved June 1, 2008. Published June 2008. Originally
eliminated from a series before calculating the series mean,
approved in 1990. Last previous edition approved in 2003 as E1345 - 98 (2003).
standard deviation, and confidence intervals.
DOI: 10.1520/E1345-98R08E01.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at [e-mail]. 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
´1
E1345 − 98 (2008)
3.2.9 standard error of the estimated mean, s,n—standard
e
deviation of color or color-difference measurement divided by
the 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
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
FIG. 1 Schematic Description of a Box and Whisker Plot
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
tested, this same colinearity problem may also be observed in 1960 u, v
3.2.3 hinges, n—the 25 and 75 % cumulative distribution
and 1976 u', v' coordinates. Table 1 provides a listing of the appropriate
points in a set of readings taken during a measurement.
and inappropriate color coordinates for use with this practice.
3.2.3.1 Discussion—Hinges represent the values in which
4.3 The successive steps in the procedure are as follows:
25 % of the readings are less than the lower hinge and 75 % of
4.3.1 Determine the standard deviation of instrument.
the readings are less than the upper hinge. See also hinge
4.3.1.1 Screen the measurement data for outliers and ex-
length.
treme values.
3.2.3.2 Discussion—Hinges are sometimes called the lower
4.3.2 Determine the standard deviation of color or color-
(Q ) and upper (Q ) quartile values.
1 1
difference measurement.
3.2.4 hinge length, H, n—the range of values between the
4.3.2.1 Screen the measurement data for outliers and ex-
lower and upper hinges.
treme values.
3.2.4.1 Discussion—The hinge length is sometimes called
4.3.3 Determinethestandarderroroftheestimatedmeanfor
the box width or the interquartile range Q to Q .
3 1
a sampling number of one.
3.2.5 outlier, n—a single reading, selected from a series of
4.3.4 Determine the final sampling number that reduces the
readings, whose value is further from the nearer box end then standard error of the estimated mean to less than the standard
1.5 times the hinge length; see 3.2.2.1.
error goal for each scale value.
4.3.5 Determine the final standard error goal values.
3.2.6 sampling number, N, n—number of multiple measure-
ments,ornumberofmultiplespecimens,requiredtoreducethe
NOTE 2—When the standard error of the estimated mean for a sampling
variability of color or color-difference measurement to a 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
desired level.
three color-difference-scale values, a sampling number greater than one is
3.2.7 standard deviation of color or color-difference mea-
required.
surement, s—standard deviation of the color scale or color-
4.4 Screening for and Elimination of Outliers and Extreme
difference-scale value, x, being considered:
i
Values in Measured Data:
0.5
s 5 @ x 2 x / n 2 1 # (1)
$ ~ ! % ~ !
( i avg
where:
TABLE 1 Appropriate and Inappropriate Color Coordinates for
Use in This Practice
x =(∑ x)/n, and
avg i
n = the number of replicate measurements made. Color Coordinates Appropriate Inappropriate
CIE Yxy =
3.2.8 standard deviation of instrument, s,n—standard de-
i
CIE LCH =
viation of a color-scale or color-difference-scale value due to
CIE LAB =
instrument variability alone: CIE LUV =
CIE Lu'v' =
0.5
s 5 @$ x 2 x %/ n 2 1 # (2)
~ ! ~ !
i i avg
(
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E1345 − 98 (2008)
TABLE 2 Official Values for T (One-Sided Test) for Outliers
4.4.1 Box and whisker test—This test is best carried out by
computer. Many programs for the box and whisker technique Number of Upper 0.1% Upper 1.0%
Observations Significance Significance
are available.
n Level Level
4.4.1.1 Orderthereadingsfromlowesttohighestvalue.The
3 1.155 1.155
reading whose value is half way between the minimum and
4 1.499 1.492
5 1.780 1.749
maximum values is the median. Fig. 1 illustrates the following
6 2.011 1.944
steps.
7 2.201 2.097
4.4.1.2 Thereadingwhosevalueisjustlessthan75 %ofthe
8 2.358 2.221
other readings is the lower hinge. The readings whose value is 9 2.492 2.323
10 2.606 2.410
just higher than 75 % of the other readings is the upper hinge.
11 2.705 2.485
The difference between these two is the hinge length H.
12 2.791 2.550
13 2.867 2.607
4.4.1.3 If the smallest value of any reading is less than the
14 2.935 2.659
lower hinge value minus 1.5 times the hinge length, it may be
15 2.997 2.705
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.
are adequate to allow an unambiguous decision as to whether
4.4.1.4 If the smallest (largest) value of any reading is less
or not the mean results are within tolerance.
(greater) than the lower (upper) hinge value minus (plus) 3.0
times the hinge length, it may be considered an extreme value.
5.2 This practice is based on portions of SAE J 1545, as it
4.4.2 Practice E178 Procedure—The test for outliers in
appli
...