ASTM E1345-98(2019)

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: E1345 − 98 (Reapproved 2019)
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 D2244 Practice for Calculation of Color Tolerances and
Color Differences from Instrumentally Measured Color
1.1 Reduction of the variability associated with average
Coordinates
color or color-difference measurements of object-color speci-
D3134 Practice for Establishing Color and Gloss Tolerances
mens is achieved by statistical analysis of the results of
E178 Practice for Dealing With Outlying Observations
multiple measurements on a single specimen, or by measure-
E284 Terminology of Appearance
ment of multiple specimens, whichever is appropriate.
E308 PracticeforComputingtheColorsofObjectsbyUsing
1.2 This practice provides a means for the determination of
the CIE System
the number of measurements required to reduce the variability
E456 Terminology Relating to Quality and Statistics
to a predetermined fraction of the relevant color or color-
2.2 Other Standard:
difference tolerances.
SAE J 1545 Recommended Practice for Instrumental Color
1.3 This practice is general in scope rather than specific as Difference Measurement for Exterior Finishes, Textiles
to instrument or material. and Colored Trim
1.4 This international standard was developed in accor-
3. Terminology
dance with internationally recognized principles on standard-
3.1 DefinitionsofappearancetermsinTerminologyE284or
ization established in the Decision on Principles for the
statistical terms in Terminology E456 are applicable to this
Development of International Standards, Guides and Recom-
practice.
mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 box and whisker plot, n—a nonparmetric data analysis
2. Referenced Documents
diagram that illustrates the 25, 50, and 75 % cumulative
distribution of values in a data set (the box) and the expected
2.1 ASTM Standards:
range of values, defined by distance outside the box ends; see
whiskers, see Fig. 1.
1 3.2.2 extreme value, n—a single reading, selected from a
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 series of readings, whose value is farther from the nearer box
Appearance Analysis.
end than 3.0 times the hinge length.
Current edition approved May 1, 2019. Published May 2019. Originally
3.2.2.1 Discussion—A box and whiskers plot is normally
approved in 1990. Last previous edition approved in 2014 as E1345 – 98 (2014).
usedtofindoutliersandextremevalues.Suchvaluesshouldbe
DOI: 10.1520/E1345-98R19.
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 (2019)
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
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-
FIG. 1 Schematic Description of a Box and Whisker Plot
ence scales ∆L*, ∆C* , and ∆H* (see Practice D2244 and
ab ab
Practice E308), but this is not meant to be restrictive.
eliminated from a series before calculating the series mean,
NOTE 1—Some coordinates, such as CIE x, y, Y, do not follow the
standard deviation, and confidence intervals.
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
measurements, or number of multiple specimens, required to
NOTE 2—When the standard error of the estimated mean for a sampling
reduce the variability of color or color-difference measurement
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
to a desired level.
three color-difference-scale values, a sampling number greater than one is
3.2.7 standard deviation of color or color-difference
required.
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 TABLE 1 Appropriate and Inappropriate Color Coordinates for
(
Use in This Practice
where:
Color Coordinates Appropriate Inappropriate
x =(∑ x)/n, and
avg i
CIE Yxy =
n = the number of replicate measurements made.
CIE LCH =
CIE LAB =
3.2.8 standard deviation of instrument, s,n—standard de-
i
CIE LUV =
viation of a color-scale or color-difference-scale value due to
CIE Lu'v' =
instrument variability alone:
E1345 − 98 (2019)
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
4.4 Screening for and Elimination of Outliers and Extreme
or not the mean results are within tolerance.
Values in Measured Data:
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
...