1、Designation: E2867 13E2867 14Standard Practice forEstimating Uncertainty of Test Results Derived fromSpectrophotometry1This standard is issued under the fixed designation E2867; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the y
2、ear of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice describes a protocol to be utilized by measurement laboratories for estimating and reporting the
3、uncertaintyof a measurement result when the result is derived from a measurand that has been obtained by spectrophotometry.1.2 This practice is specifically limited to the reporting of uncertainty of color measurement results that are reported ascolor-differences in E format, even though the measure
4、ment itself may be reported in other units such as percent reflectance ortransmittance.1.3 The procedures defined here are not intended to be applicable to national standardizing laboratories or transfer laboratories.1.4 This standard does not purport to address all of the safety concerns, if any, a
5、ssociated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use. Some specific hazards statements are given in Section 7 on Hazards.2. Referenced Documents2.1 ASTM
6、Standards:2D2244 Practice for Calculation of Color Tolerances and Color Differences from Instrumentally Measured Color CoordinatesE29 Practice for Using Significant Digits in Test Data to Determine Conformance with SpecificationsE284 Terminology of Appearance2.2 ISO Standards:3ISO 9001 Quality Manag
7、ement SystemsRequirementsISO/IEC 17025 General Requirements for the Competence of Calibration and Testing Laboratories2.3 Other Standard:4QS 9000 Quality Systems Requirements Chrysler Corporation, Ford Motor Company, General Motors Corporation3. Terminology3.1 Definitions: For definitions of terms u
8、sed in this standard refer to Terminology E284.3.2 Definitions of Terms Specific to This Standard:3.2.1 uncertainty, na parameter associated with a measurement result or test result that reasonably characterizes the dispersionof results attributable to the particular quantity being measured of the p
9、articular characteristic being tested.3.2.2 instrument uncertainty conditions, nof a measurement, conditions wherein the measurements are made repetitively andcarefully over a short timescale, without replacement of the specimen being measured in the specimen port of the instrument.NOTE 1Instrument
10、uncertainty conditions always include potential specimen drift due to causes such as theromchromism, photochromism, orbleaching of the specimen. While these may be thought of as characteristics of the specimen, their effects will be picked up here under instrumentuncertainty conditions.1 This practi
11、ce is under the jurisdiction of ASTM Committee E12 on Color and Appearance and is the direct responsibility of Subcommittee E12.04 on Color andAppearance Analysis.Current edition approved Jan. 1, 2013May 1, 2014. Published February 2013May 2014. Originally approved in 2013. Last previous edition app
12、roved in 2013 as E2867 13. DOI: 10.1520/E2867-13.10.1520/E2867-14.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM web
13、site.3 Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http:/www.ansi.org.4 Available from Automotive Industry Action Group (AIAG), 26200 Lahser Rd., Suite 200, Southfield, MI 48033, http:/www.aiag.org.This document is not an ASTM standard
14、and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases onl
15、y the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.3 operator uncertainty conditions, nof a measurement, conditions wherein the measu
16、rements are made repetitively andcarefully over a short timescale, with replacement of the specimen being measured by the operator completely withdrawing thespecimen from the specimen port and replacing the specimen back in the specimen port prior to the ensuing measurement so thatthe specimen apert
17、ure samples the same location on the specimen, and the specimen has the same orientation as previous, to thebest of the operators ability to accomplish.3.2.4 uniformity uncertainty conditions, nof a measurement, conditions wherein the measurements are made repetitively andcarefully over a short time
18、scale, with replacement of the specimen being measured to an entirely new location on the face of thespecimen with the intent of sampling the entire surface of the specimen, or as much of the surface as is practical, by the end ofthe repetitive sampling run.3.2.5 instrument uncertainty, nthe results
19、 of an uncertainty analysis of a measurement system made under instrumentuncertainty conditions.3.2.6 operator uncertainty, nthe results of an uncertainty analysis of a measurement system made under operator uncertaintyconditions.3.2.7 uniformity uncertainty, nthe results of an uncertainty analysis
20、of a measurement system made under uniformityuncertainty conditions.3.2.8 expanded uncertainty, nuncertainty reported as a multiple of the standard uncertainty.3.2.9 measurement system, nthe entirety of variable factors that could affect the precision, accuracy, or uncertainty of ameasurement result
21、. These include the instrument, the operator, the environmental conditions, the quality of the transfer standard,the specimen aperture size, as well as other factors.3.2.10 standard uncertainty, nuncertainty reported as the standard deviation of the estimated value of the quantity subject tomeasurem
22、ent.3.2.11 95 % confidence interval, nthe 95 percentile value of an ascending-ordered distribution of differences between multiplemeasurement results of a derived parameter characterized by a color measurement system.3.2.11.1 DiscussionThis value is the cumulative distribution between zero and the s
23、tated value of the measurand that contains 95 % of all themeasurement results made by this procedure.4. Summary of Practice4.1 This practice establishes a protocol for measurement laboratories to assess the uncertainty of their measurement system fromtest specimens or from control samples of materia
24、ls similar in both first-surface characteristics and color to those being measuredand reported.4.2 Where control samples are used, the process will be to establish control samples representative of the type of materials tobe measured. Control samples will be processed to assess the various uncertain
25、ty components of measurement results, the resultsretained in a control chart, and the rolling average of the uncertainty components of the control samples used as a surrogate forassessing the uncertainty of a similar specimen.4.3 Some of the components of uncertainty for color measurement result are
26、 instrument uncertainty, operator uncertainty, anduniformity (of the specimen) uncertainty.5. Significance and Use5.1 Many competent measurement laboratories comply with accepted quality system requirements such as ISO 9001, QS 9000,or ISO 17025. When using standard test methods, the measurement res
27、ults should agree with those from other similar laboratorieswithin the combined uncertainty limits of the laboratories measurement systems. It is for this reason that quality systemrequirements demand that a statement of the uncertainty of the test results accompany every test result.5.2 Preparation
28、 of uncertainty estimates is a requirement for laboratory certification under ISO 17025. This practice describesthe procedures by which such uncertainty estimates may be calculated.6. Concepts in Reporting Uncertainty of Test Results6.1 Acommonly cited definition (1,2)5 paraphrased to form a single
29、citation defines uncertainty as “a parameter, associated withthe measurement result, or test result, that characterizes the dispersion of values that could reasonably be attributed to the quantity5 The boldface numbers in parentheses refer to a list of references at the end of this standard.E2867 14
30、2subject to measurement or characteristic subject to test.” This definition emphasizes uncertainty as an attribute of an individual testresult, not as a property defining statistical variation of test results.6.2 The methodology for classification of uncertainty types has been classified as TypeAand
31、 Type B as discussed in references(2) and (3). TypeAestimates of uncertainty include estimates based upon knowledge of the statistical character of the measurementresults, or estimates based upon statistical analysis of replicate measurement results. The latter may include results from controlsample
32、 monitoring programs, or proficiency testing. Type B estimates of uncertainty include estimates from calibration certificatesand manufacturers specifications. Type A are evaluated by statistical methods and Type B by non-statistical methods.6.3 The goal of reporting uncertainty is to account for all
33、 potential causes contributing to uncertainty in the measurement result.Uncertainty for a single measurement result is thens121s221.1sn2!1/2where s1 is the estimate of the uncertainty of the first factor contributing to variance, s2 the second, and so on, through all ncomponents of variance.6.4 Unce
34、rtainty in this practice shall be reported as the 95% confidence interval of the largest component of all the componentsof uncertainty assessed.6.5 The minimum components contributing to variance shall be the instrument uncertainty, the operator uncertainty, theuniformity uncertainty, and the uncert
35、ainty of the traceability scheme.7. Procedure7.1 Measure the test specimen a minimum of 20 times, and preferably as many as 30 times, under instrument uncertaintyconditions. Make all measurements in compliance with the manufacturers recommendations including prior standardization of theinstrument us
36、ing a white tile, a black tile, or light trap, and a grey tile, if required.7.2 There will be n* (n - 1) / 2 possible differencescolor-differences between the n measurement results taken two-at-a-time inall possible combinations.7.3 Calculate the absolute value of the differencescolor-differences be
37、tween each of these combinations and retain the resultsin a list. Calculate these color-differences in accordance with a color-difference equation chosen from Practice D2244.7.4 Sort the list in ascending order. The member of the sorted list whose index is Int 0.95 * n * (n-1) / 2 contains the value
38、of the 95 % confidence interval of the instrument uncertainty s1. The symbol Int means the integer value of the expression inbrackets.7.5 Measure the test specimen a minimum of 20 times, and preferably as many as 30 times, under operator uncertaintyconditions. Follow the operations of 7.1 7.3 using
39、this data set to calculate the 95 % confidence interval of operator uncertaintys2.7.6 Measure the test specimen a minimum of 20 times, and preferably as many as 30 times, under uniformity uncertaintyconditions. Follow the operations of 7.1 7.3 using this data set to calculate the 95 % confidence int
40、erval of uniformity uncertaintys3.7.7 Sort the uncertainties obtained from Sections 7.1 7.6 s1,s2,s3 in ascending order with the smallest of the three in s1 andthe next larger in s2, and so forth. Lets 1 5 s1 (1)s1 5 s1 (1)s2 5s222s12!1/2 (2)s2 5s222s12!1/2 (2)s 3 5 s322s22!1/2 (3)s 3 5 s322s22!1/2
41、(3)The value of s2 used in Eq 3 is the original experimentally assessed value, not that value which results from the calculation ofEq 2 which is s22. This isolates the uncertainties, each of which has been until now included in each of the measured uncertainties,into a separate uncertainty contribut
42、ion attributable to each subsequent type of uncertainty considered. However, consult thecautionary remarks in Appendix X1 to this Practice at X2.1 X2.4.7.8 Calculate the combined uncertaintyU 5 s1 2 1s 2 21 s 3 2!1/2 (4)U 5 s12 1s 221 s 32!1/2 (4)where the elements s1,s2, and s3 are the uncertaintie
43、s from 7.4.E2867 143The combined uncertainty may be expressed in the form mean value 6 U to a 95 % confidence interval.The value of U shallbe expressed to no greater number of significant digits than are expressed in the mean, and shall be rounded in accordance withPractice E29. All calculations sho
44、uld be carried out with the full precision of the machine employed at all times and rounded onlywhen the final values, seen in the worked example in the table in X1.2.1, are calculated.7.9 In some infrequently occurring instances, the length of time required to make a measurement may make it impossi
45、ble tomake as many as 30 measurements. Under those circumstances it is permissible to reduce the number of measurements made toa smaller number providing that it can be demonstrated that the results are sufficient to the intended purpose.8. The Substitution of Control Samples8.1 Under circumstances
46、where it would prove a hardship, or is infeasible to utilize the test specimen for this determination,it is permissible to substitute control samples of a like material for the material being considered in the test result.8.2 Values quoted using control samples shall be rolling averages of the last
47、four determinations of the uncertainty by theoperations of 7.1 7.8 using the same control sample in each of the four determinations. Each of the four determinations mustbe demonstrated to be in-control by maintenance of control charts of the uncertainty determinations.8.3 The control samples should
48、be chosen to be as alike the material being reported as possible and special attention should bepaid to the matter of uniformity uncertainty when control samples are chosen. Uniformity uncertainty is the most likely componentto be discrepant between a control sample and a test specimen.8.4 The first
49、 surface of control samples involved in measurements of reflection properties should be as nearly identical aspossible to the first surface of the test sample.8.5 Reports of uncertainty where a control sample is substituted for a test sample shall state the facts of the substitution andidentify the control sample utilized.9. Reporting Statement9.1 Form of the Reporting StatementIn reporting uncertainty, a statement such as the following may be useful: “Theuncertainty of the value reported was found to be X.XX (here repo
