ASTM E2867-14(2023)

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: E2867 − 14 (Reapproved 2023)
Standard Practice for
Estimating Uncertainty of Test Results Derived from
Spectrophotometry
This standard is issued under the fixed designation E2867; 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 E29 Practice for Using Significant Digits in Test Data to
Determine Conformance with Specifications
1.1 This practice describes a protocol to be utilized by
E284 Terminology of Appearance
measurement laboratories for estimating and reporting the
2.2 ISO Standards:
uncertainty of a measurement result when the result is derived
ISO 9001 Quality Management Systems—Requirements
from a measurand that has been obtained by spectrophotom-
ISO/IEC 17025 General Requirements for the Competence
etry.
of Calibration and Testing Laboratories
1.2 This practice is specifically limited to the reporting of
2.3 Other Standard:
uncertainty of color measurement results that are reported as
QS 9000 Quality Systems Requirements Chrysler
color-differences in ΔE format, even though the measurement
Corporation, Ford Motor Company, General Motors Cor-
itself may be reported in other units such as percent reflectance
poration
or transmittance.
1.3 The procedures defined here are not intended to be 3. Terminology
applicable to national standardizing laboratories or transfer
3.1 Definitions—For definitions of terms used in this stan-
laboratories.
dard refer to Terminology E284.
1.4 This standard does not purport to address all of the
3.2 Definitions of Terms Specific to This Standard:
safety concerns, if any, associated with its use. It is the
3.2.1 uncertainty, n—a parameter associated with a mea-
responsibility of the user of this standard to establish appro-
surement result or test result that reasonably characterizes the
priate safety, health, and environmental practices and deter-
dispersion of results attributable to the particular quantity being
mine the applicability of regulatory limitations prior to use.
measured of the particular characteristic being tested.
1.5 This international standard was developed in accor-
3.2.2 instrument uncertainty conditions, n—of a
dance with internationally recognized principles on standard-
measurement, conditions wherein the measurements are made
ization established in the Decision on Principles for the
repetitively and carefully over a short timescale, without
Development of International Standards, Guides and Recom-
replacement of the specimen being measured in the specimen
mendations issued by the World Trade Organization Technical
port of the instrument.
Barriers to Trade (TBT) Committee.
NOTE 1—Instrument uncertainty conditions always include potential
2. Referenced Documents specimen drift due to causes such as theromchromism, photochromism, or
bleaching of the specimen. While these may be thought of as character-
2.1 ASTM Standards:
istics of the specimen, their effects will be picked up here under instrument
D2244 Practice for Calculation of Color Tolerances and
uncertainty conditions.
Color Differences from Instrumentally Measured Color
3.2.3 operator uncertainty conditions, n—of a
Coordinates
measurement, conditions wherein the measurements are made
repetitively and carefully over a short timescale, with replace-
ment of the specimen being measured by the operator com-
This practice is under the jurisdiction of ASTM Committee E12 on Color and pletely withdrawing the specimen from the specimen port and
Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
replacing the specimen back in the specimen port prior to the
Appearance Analysis.
ensuing measurement so that the specimen aperture samples
Current edition approved June 1, 2023. Published July 2023. Originally approved
in 2013. Last previous edition approved in 2019 as E2867 – 14 (2019). DOI:
10.1520/E2867-14R23.
2 3
For referenced ASTM standards, visit the ASTM website, www.astm.org, or Available from American National Standards Institute (ANSI), 25 W. 43rd St.,
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM 4th Floor, New York, NY 10036, http://www.ansi.org.
Standards volume information, refer to the standard’s Document Summary page on Available from Automotive Industry Action Group (AIAG), 26200 Lahser Rd.,
the ASTM website. Suite 200, Southfield, MI 48033, http://www.aiag.org.
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E2867 − 14 (2023)
the same location on the specimen, and the specimen has the 5. Significance and Use
same orientation as previous, to the best of the operator’s
5.1 Many competent measurement laboratories comply with
ability to accomplish.
accepted quality system requirements such as ISO 9001, QS
3.2.4 uniformity uncertainty conditions, n—of a
9000, or ISO 17025. When using standard test methods, the
measurement, conditions wherein the measurements are made measurement results should agree with those from other similar
repetitively and carefully over a short timescale, with replace-
laboratories within the combined uncertainty limits of the
ment of the specimen being measured to an entirely new laboratories’ measurement systems. It is for this reason that
location on the face of the specimen with the intent of sampling
quality system requirements demand that a statement of the
the entire surface of the specimen, or as much of the surface as uncertainty of the test results accompany every test result.
is practical, by the end of the repetitive sampling run.
5.2 Preparation of uncertainty estimates is a requirement for
3.2.5 instrument uncertainty, n—the results of an uncer-
laboratory certification under ISO 17025. This practice de-
tainty analysis of a measurement system made under instru-
scribes the procedures by which such uncertainty estimates
ment uncertainty conditions.
may be calculated.
3.2.6 operator uncertainty, n—the results of an uncertainty
6. Concepts in Reporting Uncertainty of Test Results
analysis of a measurement system made under operator uncer-
tainty conditions. 6.1 A commonly cited definition (1, 2) paraphrased to form
a single citation defines uncertainty as “a parameter, associated
3.2.7 uniformity uncertainty, n—the results of an uncertainty
with the measurement result, or test result, that characterizes
analysis of a measurement system made under uniformity
the dispersion of values that could reasonably be attributed to
uncertainty conditions.
the quantity subject to measurement or characteristic subject to
3.2.8 expanded uncertainty, n—uncertainty reported as a
test.” This definition emphasizes uncertainty as an attribute of
multiple of the standard uncertainty.
an individual test result, not as a property defining statistical
3.2.9 measurement system, n—the entirety of variable fac- variation of test results.
tors that could affect the precision, accuracy, or uncertainty of
6.2 The methodology for classification of uncertainty types
a measurement result. These include the instrument, the
has been classified as Type A and Type B as discussed in
operator, the environmental conditions, the quality of the
references (2) and (3). Type A estimates of uncertainty include
transfer standard, the specimen aperture size, as well as other
estimates based upon knowledge of the statistical character of
factors.
the measurement results, or estimates based upon statistical
3.2.10 standard uncertainty, n—uncertainty reported as the
analysis of replicate measurement results. The latter may
standard deviation of the estimated value of the quantity include results from control sample monitoring programs, or
subject to measurement.
proficiency testing. Type B estimates of uncertainty include
estimates from calibration certificates and manufacturer’s
3.2.11 95 % confidence interval, n—the 95 percentile value
specifications. Type A are evaluated by statistical methods and
of an ascending-ordered distribution of differences between
Type B by non-statistical methods.
multiple measurement results of a derived parameter charac-
terized by a color measurement system.
6.3 The goal of reporting uncertainty is to account for all
3.2.11.1 Discussion—This value is the cumulative distribu- potential causes contributing to uncertainty in the measurement
tion between zero and the stated value of the measurand that result. Uncertainty for a single measurement result is then
contains 95 % of all the measurement results made by this
2 2 2 1/2
~s 1s 1 .1 s !
1 2 n
procedure.
where s is the estimate of the uncertainty of the first factor
contributing to variance, s the second, and so on, through all
4. Summary of Practice 2
n components of variance.
4.1 This practice establishes a protocol for measurement
6.4 Uncertainty in this practice shall be reported as the 95 %
laboratories to assess the uncertainty of their measurement
confidence interval of the largest component of all the compo-
system from test specimens or from control samples of
nents of uncertainty assessed.
materials similar in both first-surface characteristics and color
to those being measured and reported.
6.5 The minimum components contributing to variance
shall be the instrument uncertainty, the operator uncertainty,
4.2 Where control samples are used, the process will be to
the uniformity uncertainty, and the uncertainty of the traceabil-
establish control samples representative of the type of materials
ity scheme.
to be measured. Control samples will be processed to assess the
various uncertainty components of measurement results, the
7. Procedure
results retained in a control chart, and the rolling average of the
7.1 Measure the test specimen a minimum of 20 times, and
uncertainty components of the control samples used as a
preferably as many as 30 times, under instrument uncertainty
surrogate for assessing the uncertainty of a similar specimen.
4.3 Some of the components of uncertainty for color mea-
surement result are instrument uncertainty, operator
The boldface numbers in parentheses refer to a list of references at the end of
uncertainty, and uniformity (of the specimen) uncertainty. this standard.
E2867 − 14 (2023)
conditions. Make all measurements in compliance with the to make as many as 30 measurements. Under those circum-
manufacturer’s recommendations including prior standardiza- stances it is permissible to reduce the number of measurements
tion of the instrument using a white tile, a black tile, or light made to a smaller number providing that it can be demon-
trap, and a grey tile, if required. strated that the results are sufficient to the intended purpose.
7.2 There will be n* (n - 1) / 2 possible color-differences
8. The Substitution of Control Samples
between the n measurement results taken two-at-a-time in all
8.1 Under circumstances where it would prove a hardship,
possible combinations.
or is infeasible to utilize the test specimen for this
7.3 Calculate the absolute value of t
...