ASTM E1345-98(2003)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation:E1345–98(Reapproved2003)
Standard Practice for
Reducing the Effect of Variability of Color Measurement by
Use of Multiple Measurements
This standard is issued under the fixed designation E 1345; 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 (e) 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 E 1164 Practice for Obtaining Spectrophotometric Data for
Object-Color Evaluation
1.1 Reduction of the variability associated with average
2.2 Other Standard:
color or color-difference measurements of object-color speci-
SAE J 1545 Recommended Practice for Instrumental Color
mens is achieved by statistical analysis of the results of
Difference Measurement for Exterior Finishes, Textiles
multiple measurements on a single specimen, or by measure-
and Colored Trim
ment of multiple specimens, whichever is appropriate.
1.2 This practice provides a means for the determination of
3. Terminology
the number of measurements required to reduce the variability
3.1 Definitions of appearance terms in Terminology E 284
to a predetermined fraction of the relevant color or color-
or statistical terms in Terminology E 456 are applicable to this
difference tolerances.
practice.
1.3 This practice is general in scope rather than specific as
3.2 Definitions of Terms Specific to This Standard:
to instrument or material.
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
D 2244 Practice for Calculation of Color Differences from
whiskers, see Fig. 1.
Instrumentally Measured Color Coordinates
3.2.2 extreme value, n—a single reading, selected from a
D 3134 PracticeforEstablishingRetroreflectanceColorand
series of readings, whose value is farther from the nearer box
Gloss Tolerances
end than 3.0 times the hinge length.
E 178 Practice for Dealing With Outlying Observations
3.2.2.1 Discussion—A box and whiskers plot is normally
E 284 Terminology of Appearance
usedtofindoutliersandextremevalues.Suchvaluesshouldbe
E 308 Practice for Computing the Colors of Objects by
eliminated from a series before calculating the series mean,
Using the CIE System
standard deviation, and confidence intervals.
E 456 Terminology Relating to Quality and Statistics
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
This practice is under the jurisdiction of ASTM Committee E12 on Color and
25 % of the readings are less than the lower hinge and 75 % of
Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
Appearance Analysis. the readings are less than the upper hinge. See also hinge
Current edition approved Dec. 1, 2003. Published December 2003. Originally
length.
approved in 1990. Last previous edition approved in 1998 as E 1345 - 98.
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.
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E1345–98 (2003)
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 Lu8v8 =
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 D 3134).
4.2 For convenience, the numerical example in the Appen-
FIG. 1 Schematic Description of a Box and Whisker Plot
dix uses CIELAB LCH (lightness, chroma, hue) color differ-
ence scales DL*, DC* , and DH* (see Practice D 2244 and
ab ab
Practice E 308), but this is not meant to be restrictive.
3.2.3.2 Discussion—Hinges are sometimes called the lower
NOTE 1—Some coordinates, such as CIE x, y, Y, do not follow the
(Q ) and upper (Q ) quartile values.
1 1
theoriesofthisstandardduetoexcessivecolinearity.Whileithasnotbeen
3.2.4 hinge length, H, n—the range of values between the
tested, this same colinearity problem may also be observed in 1960 u, v
lower and upper hinges. and 1976 u8,v8 coordinates. Table 1 provides a listing of the appropriate
and inappropriate color coordinates for use with this practice.
3.2.4.1 Discussion—The hinge length is sometimes called
the box width or the interquartile range Q to Q . 4.3 The successive steps in the procedure are as follows:
3 1
4.3.1 Determine the standard deviation of instrument.
3.2.5 outlier, n—a single reading, selected from a series of
4.3.1.1 Screen the measurement data for outliers and ex-
readings, whose value is further from the nearer box end then
treme values.
1.5 times the hinge length; see 3.2.2.1.
4.3.2 Determine the standard deviation of color or color-
3.2.6 sampling number, N, n—number of multiple measure-
difference measurement.
ments,ornumberofmultiplespecimens,requiredtoreducethe
4.3.2.1 Screen the measurement data for outliers and ex-
variability of color or color-difference measurement to a
treme values.
desired level.
4.3.3 Determinethestandarderroroftheestimatedmeanfor
3.2.7 standard deviation of color or color-difference mea-
a sampling number of one.
surement, s—standard deviation of the color scale or color-
4.3.4 Determine the final sampling number that reduces the
difference-scale value, x, being considered:
i
standard error of the estimated mean to less than the standard
2 0.5
s 5 @ (~x 2 x ! /~n 2 1!# (1)
$ %
i avg
error goal for each scale value.
4.3.5 Determine the final standard error goal values.
where:
x =(( x)/n, and
NOTE 2—Whenthestandarderroroftheestimatedmeanforasampling
avg i
n = the number of replicate measurements made. 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
3.2.8 standard deviation of instrument, s, n—standard de-
i
three color-difference-scale values, a sampling number greater than one is
viation of a color-scale or color-difference-scale value due to
required.
instrument variability alone:
4.4 Screening for and Elimination of Outliers and Extreme
2 0.5
s 5 @ (~x 2 x ! /~n 2 1!# (2)
$ %
i i avg
Values in Measured Data:
4.4.1 Box and whisker test—This test is best carried out by
3.2.9 standard error of the estimated mean, s , n—standard
e
computer. Many programs for the box and whisker technique
deviation of color or color-difference measurement divided by
are available.
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 See for example, Schaefer, R. L. and Anderson, R. B., The Student Edition of
standard error of the estimated mean is to be reduced. Minitab, Addison-Wesley, New York, 1989.
E1345–98 (2003)
4.4.1.1 Orderthereadingsfromlowesttohighestvalue.The 4.4.4 Recalculate the mean, standard deviation and confi-
reading whose value is half way between the minimum and dence limits of the remaining dataset.
maximum values is the median. Fig. 1 illustrates the following
5. Significance and Use
steps.
4.4.1.2 Thereadingwhosevalueisjustlessthan75 %ofthe 5.1 This practice should be used whenever measured color-
other readings is the lower hinge. The readings whose value is scale or color-difference-scale values are to be compared to an
just higher than 75 % of the other readings is the upper hinge. established tolerance. In this way it can be demonstrated
quantitatively that the sampling and measurement procedures
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 are adequate to allow an unambiguous decision as to whether
or not the mean results are within tolerance.
lower hinge value minus 1.5 times the hinge length, it may be
considered an outlier. Likewise, if the largest value of any 5.2 This practice is based on portions of SAE Practice
J 1545, as it applies to painted or plastic automotive parts. It is
reading is greater than the upper hinge value plus 1.5 times the
hinge length, it may be considered an outlier. generally applicable to object colors in various ma
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