1、Designation: E2867 13Standard 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 year of l
2、ast 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 bymeasurement laboratories for estimating and reporting theuncertaint
3、y of a measurement result when the result is derivedfrom a measurand that has been obtained by spectrophotom-etry.1.2 This practice is specifically limited to the reporting ofuncertainty of color measurement results that are reported ascolor-differences in E format, even though the measurementitself
4、 may be reported in other units such as percent reflectanceor transmittance.1.3 The procedures defined here are not intended to beapplicable to national standardizing laboratories or transferlaboratories.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with
5、 its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use. Some specifichazards statements are given in Section 7 on Hazards.2. Referenced Documents2.1 ASTM Standards:2E
6、29 Practice for Using Significant Digits in Test Data toDetermine Conformance with SpecificationsE284 Terminology of Appearance2.2 ISO Standards:3ISO 9001 Quality Management SystemsRequirementsISO/IEC 17025 General Requirements for the Competenceof Calibration and Testing Laboratories2.3 Other Stand
7、ard:4QS 9000 Quality Systems Requirements ChryslerCorporation, Ford Motor Company, General Motors Cor-poration3. Terminology3.1 Definitions: For definitions of terms used in this stan-dard refer to Terminology E284.3.2 Definitions of Terms Specific to This Standard:3.2.1 uncertainty, na parameter as
8、sociated with a mea-surement result or test result that reasonably characterizes thedispersion of results attributable to the particular quantity beingmeasured of the particular characteristic being tested.3.2.2 instrument uncertainty conditions, nof ameasurement, conditions wherein the measurements
9、 are maderepetitively and carefully over a short timescale, withoutreplacement of the specimen being measured in the specimenport of the instrument.NOTE 1Instrument uncertainty conditions always include potentialspecimen drift due to causes such as theromchromism, photochromism, orbleaching of the s
10、pecimen. While these may be thought of as character-istics of the specimen, their effects will be picked up here under instrumentuncertainty conditions.3.2.3 operator uncertainty conditions, nof ameasurement, conditions wherein the measurements are maderepetitively and carefully over a short timesca
11、le, with replace-ment of the specimen being measured by the operator com-pletely withdrawing the specimen from the specimen port andreplacing the specimen back in the specimen port prior to theensuing measurement so that the specimen aperture samplesthe same location on the specimen, and the specime
12、n has thesame orientation as previous, to the best of the operatorsability to accomplish.3.2.4 uniformity uncertainty conditions, nof ameasurement, conditions wherein the measurements are maderepetitively and carefully over a short timescale, with replace-ment of the specimen being measured to an en
13、tirely newlocation on the face of the specimen with the intent of sampling1This practice is under the jurisdiction of ASTM Committee E12 on Color andAppearance and is the direct responsibility of Subcommittee E12.93 on Precisionand Bias.Current edition approved Jan. 1, 2013. Published February 2013.
14、 DOI: 10.1520/E2867-13.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from American National Stan
15、dards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.4Available from Automotive Industry Action Group (AIAG), 26200 Lahser Rd.,Suite 200, Southfield, MI 48033, http:/www.aiag.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken,
16、PA 19428-2959. United States1the entire surface of the specimen, or as much of the surface asis practical, by the end of the repetitive sampling run.3.2.5 instrument uncertainty, nthe results of an uncer-tainty analysis of a measurement system made under instru-ment uncertainty conditions.3.2.6 oper
17、ator uncertainty, nthe results of an uncertaintyanalysis of a measurement system made under operator uncer-tainty conditions.3.2.7 uniformity uncertainty, nthe results of an uncertaintyanalysis of a measurement system made under uniformityuncertainty conditions.3.2.8 expanded uncertainty, nuncertain
18、ty reported as amultiple of the standard uncertainty.3.2.9 measurement system, nthe entirety of variable fac-tors that could affect the precision, accuracy, or uncertainty ofa measurement result. These include the instrument, theoperator, the environmental conditions, the quality of thetransfer stan
19、dard, the specimen aperture size, as well as otherfactors.3.2.10 standard uncertainty, nuncertainty reported as thestandard deviation of the estimated value of the quantitysubject to measurement.3.2.11 95 % confidence interval, nthe 95 percentile valueof an ascending-ordered distribution of differen
20、ces betweenmultiple measurement results of a derived parameter charac-terized by a color measurement system.3.2.11.1 DiscussionThis value is the cumulative distribu-tion between zero and the stated value of the measurand thatcontains 95 % of all the measurement results made by thisprocedure.4. Summa
21、ry of Practice4.1 This practice establishes a protocol for measurementlaboratories to assess the uncertainty of their measurementsystem from test specimens or from control samples ofmaterials similar in both first-surface characteristics and colorto those being measured and reported.4.2 Where contro
22、l samples are used, the process will be toestablish control samples representative of the type of materialsto be measured. Control samples will be processed to assess thevarious uncertainty components of measurement results, theresults retained in a control chart, and the rolling average of theuncer
23、tainty components of the control samples used as asurrogate for assessing the uncertainty of a similar specimen.4.3 Some of the components of uncertainty for color mea-surement result are instrument uncertainty, operatoruncertainty, and uniformity (of the specimen) uncertainty.5. Significance and Us
24、e5.1 Many competent measurement laboratories comply withaccepted quality system requirements such as ISO 9001, QS9000, or ISO 17025. When using standard test methods, themeasurement results should agree with those from other similarlaboratories within the combined uncertainty limits of thelaboratori
25、es measurement systems. It is for this reason thatquality system requirements demand that a statement of theuncertainty of the test results accompany every test result.5.2 Preparation of uncertainty estimates is a requirement forlaboratory certification under ISO 17025. This practice de-scribes the
26、procedures by which such uncertainty estimatesmay be calculated.6. Concepts in Reporting Uncertainty of Test Results6.1 Acommonly cited definition (1, 2)5paraphrased to forma single citation defines uncertainty as “a parameter, associatedwith the measurement result, or test result, that characterize
27、sthe dispersion of values that could reasonably be attributed tothe quantity subject to measurement or characteristic subject totest.” This definition emphasizes uncertainty as an attribute ofan individual test result, not as a property defining statisticalvariation of test results.6.2 The methodolo
28、gy for classification of uncertainty typeshas been classified as Type A and Type B as discussed inreferences (2) and (3). Type A estimates of uncertainty includeestimates based upon knowledge of the statistical character ofthe measurement results, or estimates based upon statisticalanalysis of repli
29、cate measurement results. The latter mayinclude results from control sample monitoring programs, orproficiency testing. Type B estimates of uncertainty includeestimates from calibration certificates and manufacturersspecifications. Type A are evaluated by statistical methods andType B by non-statist
30、ical methods.6.3 The goal of reporting uncertainty is to account for allpotential causes contributing to uncertainty in the measurementresult. Uncertainty for a single measurement result is thens121s221 .1 sn2!1/2where s1is the estimate of the uncertainty of the first factorcontributing to variance,
31、 s2the second, and so on, through alln components of variance.6.4 Uncertainty in this practice shall be reported as the 95%confidence interval of the largest component of all the compo-nents of uncertainty assessed.6.5 The minimum components contributing to varianceshall be the instrument uncertaint
32、y, the operator uncertainty,the uniformity uncertainty, and the uncertainty of the traceabil-ity scheme.7. Procedure7.1 Measure the test specimen a minimum of 20 times, andpreferably as many as 30 times, under instrument uncertaintyconditions. Make all measurements in compliance with themanufacturer
33、s recommendations including prior standardiza-tion of the instrument using a white tile, a black tile, or lighttrap, and a grey tile, if required.7.2 There will be n*(n - 1) / 2 possible differences betweenthe n measurement results taken two-at-a-time in all possiblecombinations.5The boldface number
34、s in parentheses refer to a list of references at the end ofthis standard.E2867 1327.3 Calculate the absolute value of the differences betweeneach of these combinations and retain the results in a list.7.4 Sort the list in ascending order. The member of thesorted list whose index is Int 0.95*n*(n-1)
35、 / 2 contains thevalue of the 95 % confidence interval of the instrumentuncertainty s1. The symbol Int means the integer value of theexpression in brackets.7.5 Measure the test specimen a minimum of 20 times, andpreferably as many as 30 times, under operator uncertaintyconditions. Follow the operati
36、ons of 7.1-7.3 using this data setto calculate the 95 % confidence interval of operator uncer-tainty s2.7.6 Measure the test specimen a minimum of 20 times, andpreferably as many as 30 times, under uniformity uncertaintyconditions. Follow the operations of 7.1-7.3 using this data setto calculate the
37、 95 % confidence interval of uniformityuncertainty s3.7.7 Sort the uncertainties obtained from Sections 7.1-7.6 s1,s2, s3in ascending order with the smallest of the three in s1andthe next larger in s2, and so forth. Lets15 s1(1)s25 s222 s12!1/2(2)s35 s322 s22!1/2(3)The value of s2used in Eq 3 is the
38、 original experimentallyassessed value, not that value which results from the calcula-tion of Eq 2 which is s2. This isolates the uncertainties, eachof which has been until now included in each of the measureduncertainties, into a separate uncertainty contribution attribut-able to each subsequent ty
39、pe of uncertainty considered.However, consult the cautionary remarks in Appendix X1 tothis Practice at X2.1-X2.4.7.8 Calculate the combined uncertaintyU 5 s121 s221 s32!1/2(4)where the elements s1, s2, and s3are the uncertainties from7.4.The combined uncertainty may be expressed in the formmean valu
40、e 6 U to a 95 % confidence interval. The value ofU shall be expressed to no greater number of significant digitsthan are expressed in the mean, and shall be rounded inaccordance with Practice E29. All calculations should becarried out with the full precision of the machine employed atall times and r
41、ounded only when the final values, seen in theworked example in the table in X1.2.1, are calculated.7.9 In some infrequently occurring instances, the length oftime required to make a measurement may make it impossibleto make as many as 30 measurements. Under those circum-stances it is permissible to
42、 reduce the number of measurementsmade to a smaller number providing that it can be demon-strated that the results are sufficient to the intended purpose.8. The Substitution of Control Samples8.1 Under circumstances where it would prove a hardship,or is infeasible to utilize the test specimen for th
43、isdetermination, it is permissible to substitute control samples ofa like material for the material being considered in the testresult.8.2 Values quoted using control samples shall be rollingaverages of the last four determinations of the uncertainty bythe operations of 7.1-7.8 using the same contro
44、l sample in eachof the four determinations. Each of the four determinationsmust be demonstrated to be in-control by maintenance ofcontrol charts of the uncertainty determinations.8.3 The control samples should be chosen to be as alike thematerial being reported as possible and special attention shou
45、ldbe paid to the matter of uniformity uncertainty when controlsamples are chosen. Uniformity uncertainty is the most likelycomponent to be discrepant between a control sample and a testspecimen.8.4 The first surface of control samples involved in mea-surements of reflection properties should be as n
46、early identicalas possible to the first surface of the test sample.8.5 Reports of uncertainty where a control sample is sub-stituted for a test sample shall state the facts of the substitutionand identify the control sample utilized.9. Reporting Statement9.1 Form of the Reporting StatementIn reporti
47、nguncertainty, a statement such as the following may be useful:“The uncertainty of the value reported was found to be X.XX(here report the uncertainty value.) This value was determinedusing XX (here report the number of measurements made inthe assessment of uncertainty; ninety, for instance) measure
48、-ments categorizing the instrument, operator and uniformityuncertainty. This value is the combined expanded standarduncertainty in color difference units according to the (herename the color-difference equation used) equation calculatedfrom D65 and the CIE 10 Observer, which defines theuncertainty o
49、f the measured value to a confidence level of 95percent.”9.2 The following measurement parameters shall be definedand specified in the uncertainty expression: (1) the identity ofthe measured sample being reported, (2) the color differenceequation used in the uncertainty assessment, (3) the values ofl and c, only for DECMC,(4) the IlluminantObserver combi-nation used, (5) the number of measurements in each of theuncertainty component assessments, (6) the level expressed asa percentage to which the coverage factor raises the confi-dence.10. Ap
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