1、AN ASME TECHNICAL REPORTMeasurement Uncertainty and Conformance Testing: Risk AnalysisASME B89.7.4.1-2005(Technical Report)ASME B89.7.4.1-2005(Technical Report)MeasurementUncertainty andConformance Testing:Risk AnalysisAN ASME TECHNICAL REPORTThree Park Avenue New York, NY 10016Date of Issuance: Feb
2、ruary 3, 2006This Technical Report will be revised when the Society approves the issuance of a new edition. Therewill be no addenda issued to this edition.ASME is the registered trademark of The American Society of Mechanical Engineers.ASME does not “approve,” “rate,” or “endorse” any item, construc
3、tion, proprietary device, or activity.ASME does not take any position with respect to the validity of any patent rights asserted in connection with anyitems mentioned in this document, and does not undertake to insure anyone utilizing a standard against liability forinfringement of any applicable le
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5、 affiliated with industry is not to be interpreted asgovernment or industry endorsement of this code or standard.No part of this document may be reproduced in any form,in an electronic retrieval system or otherwise,without the prior written permission of the publisher.The American Society of Mechani
6、cal EngineersThree Park Avenue, New York, NY 10016-5990Copyright 2006 byTHE AMERICAN SOCIETY OF MECHANICAL ENGINEERSAll rights reservedPrinted in U.S.A.CONTENTSForeword ivCommittee Roster . v1 Scope 12 Definitions and Terminology . 13 Inspection Measurements and Pass/Fail Decisions 24 Frequency Dist
7、ributions: Variable Production Processes and NoisyMeasurements 35 Probability Densities: Prior Information and Standard Uncertainty 66 Workpiece Inspection: Measurements and Measurement Uncertainty . 87 Gauging (or Test) Limits and Guard Bands 108 Controlling the Quality of Individual Workpieces 129
8、 Controlling the Average Quality of Workpieces 15References 18Figures1 Tolerance Zone . 32 Frequency Distribution of a Sample of Spacers 33 Fraction of Workpieces Conforming Versus Process Capability Index . 54 Process Probability Density for the Length of a Randomly Chosen Workpiece 75 Probability
9、Density for the Lengths of a Measured Workpiece 96 Measurement Capability Index Versus Scaled Measurement Result . 117 Stringent Acceptance Zone 128 Relaxed Acceptance Zone . 129 Desired Level of Confidence Defines an Acceptance Zone . 1310 Guard Band Chosen to Reduce the Probability of Accepting a
10、Workpiece That IsToo Long 1411 Stringent Acceptance Zone for Symmetric Two-Sided Guard Banding 1412 Contingency Table for an Inspection Measurement 1613 Contingency Table for the Worked Example . 1714 Producers and Consumers Risks for the Worked Example 1915 Producers Risk Versus Consumers Risk for
11、the Worked Example WithCpp 0.55 and Cmp 2.5 2016 Producers Risk Versus Consumers Risk for Cpp 1.5 . 2117 Producers Risk Versus Consumers Risk for Cpp 1 . 2218 Producers Risk Versus Consumers Risk for Cpp232319 Producers Risk Versus Consumers Risk for Cpp1324Tables1 Fraction Conforming Versus Process
12、 Capability Index . 62 Conformance Probability Versus Guard Band Multiplier . 14Mandatory AppendicesI Properties of Gaussian Probability Densities . 25II Risk Calculations . 27iiiFOREWORDThe ISO Guide to the Expression of Uncertainty in Measurement (GUM) is now the internation-ally accepted method o
13、f expressing measurement uncertainty 1. The U.S. has adopted the GUMas a national standard 2. The evaluation of measurement uncertainty has been applied forsome time at national measurement institutes; more recently, increasingly stringent laboratoryaccreditation requirements have increased the use
14、of measurement uncertainty analysis in indus-trial calibration laboratories. In some cases, measurement uncertainty calculations have even beenapplied to factory floor measurements.Given the potential impact to business practices, national and international standards commit-tees are working to publi
15、sh new standards and technical reports that will facilitate the integrationof the GUM approach and the consideration of measurement uncertainty in product conformancedecisions. In support of this effort, the ASME B89 Committee for Dimensional Metrology hasformed Subcommittee 7 Measurement Uncertaint
16、y.Measurement uncertainty has important economic consequences for calibration and inspectionactivities. In calibration reports, the magnitude of the uncertainty is often taken as an indicationof the quality of the laboratory, and smaller uncertainty values generally are of higher value andcost. In i
17、ndustrial measurements, uncertainty has an economic impact through the decision ruleemployed in accepting and rejecting products. ASME B89.7.3.1, Guidelines for Decision Rules:Considering Measurement Uncertainty in Determining Conformance to Specifications, addressesthe role of measurement uncertain
18、ty when accepting or rejecting products based on a measurementresult and a product specification.With significant economic interests at stake, it is advisable that manufacturers guard againstaccepting bad products and rejecting good ones. Even with a very good measurement system,there will be some r
19、isk of decision errors, with cost impacts that vary depending upon the natureof the product and its intended end use. While the evaluation of measurement uncertainty is atechnical activity well-described in the GUM, the selection of a decision rule is a business decisionthat involves cost considerat
20、ions.ASME B89.7.3.1 provides uniform, unambiguous terminology for documenting a decision rule.It describes the relationship between the conformance zone (locating conforming characteristics)and the acceptance zone (locating acceptable measurement results). This Technical Reportaddresses the problem
21、of determining the gauging limits (or test limits) that define the boundariesof the acceptance zone. The limits are chosen to balance the risks of the two types of decisionerrors, whose relative magnitudes depend upon product-specific economic factors that are outsidethe scope of this Report.ivASME
22、STANDARDS COMMITTEE B89Dimensional Metrology(The following is the roster of the Committee at the time of approval of this Technical Report.)OFFICERSB. Parry, ChairD. E. Beutel, Vice ChairM. Lo, SecretaryCOMMITTEE PERSONNELD. E. Beutel, CaterpillarJ. B. Bryan, Bryan AssociatesT. E. Carpenter, U.S. Ai
23、r Force Metrology LabsT. Charlton, Jr., Charlton AssociatesG. A. Hetland, International Institute of Geometric Dimensioningand TolerancingR. J. Hocken, University of North Carolina, CharlotteM. Liebers, Professional Instruments Co.SUBCOMMITTEE 7 MEASUREMENT UNCERTAINTYG. A. Hetland, Chair, Internati
24、onal Institute of GeometricDimensioning and TolerancingD. A. Swyt, Vice Chair, National Institute of Standards andTechnologyW. Beckwith, Brown 7, para. B.2.9.measured value: value obtained by measurement.NOTE: The measured value is the result of the measurement 2,para. 3.1 and is the value attribute
25、d to the measurand after per-forming a measurement.ASME B89.7.4.1-2005 MEASUREMENT UNCERTAINTY AND CONFORMANCE TESTING:RISK ANALYSISmeasurement capability index, Cm: in the case of measuringa characteristic for conformance to a two-sided tolerancezone of width T, Cmp T/4um, where umis the standardun
26、certainty associated with the estimate of the charac-teristic; for a one-sided tolerance zone of width T, CmpT/2um; and in the case of calibration or verification ofa measuring instrument with specified maximum per-missible error MPE, Cmp MPE/2ue, where ueis thestandard uncertainty associated with t
27、he estimate of theinstrument error.nonacceptance: decision that the measured value of a char-acteristic does not satisfy the acceptance criteria.nonconforming: a characteristic is nonconforming if itstrue value lies outside the boundary of the tolerancezone.NOTE: In ASME B89.7.2-1999, nonconforming
28、is defined as havinga measured value lying outside the boundary of the allowabletolerance band. This definition would be correct if measured werechanged to true.pass error: acceptance, as a result of measurement error,of a characteristic whose value is outside specified toler-ances (also known as a
29、Type II error) 4.process distribution: probability distribution characteriz-ing reasonable belief in values of a characteristicresulting from a manufacturing process.NOTE: The form of this distribution can be inferred from a fre-quency distribution (usually displayed in a histogram) of measuredchara
30、cteristics from a large sample of items.producers risk: probability of a fail (or Type I) error. (Thecost of such an error is generally borne by the producer.)rejection: see nonacceptance.rejection zone: set of values of a characteristic, for a speci-fied measurement process and decision rule, that
31、resultsin product rejection when a measurement result is withinthis zone 3.specification limits: see tolerance limits.test limits: see gauging limits.tolerance: total amount by which a specific characteristicis permitted by specifications to vary.NOTE: The tolerance is the difference between the upp
32、er andlower specification limits 5, para. 1.4.4; 8, para. 1.3.3.tolerance interval: region between, and including, the tol-erance limits 5; para. 1.4.5.tolerance limits: specified values of the characteristic, giv-ing upper and/or lower bounds of the permissible value5, para. 1.4.3.lower tolerance l
33、imit (TL): specification limit that definesthe lower conformance boundary for an individual unitof a manufacturing or service operation.upper tolerance limit (TU): specification limit thatdefines the upper conformance boundary for an individ-ual unit of a manufacturing or service operation.2NOTE: Fo
34、r a single-sided conformance test, there is only a singletolerance limit.tolerance zone: see tolerance interval.3 INSPECTION MEASUREMENTS AND PASS/FAILDECISIONSIn a typical inspection measurement or conformancetest, a characteristic or feature is measured1and theresult compared with a specified acce
35、ptance criterion inorder to establish whether there is an acceptable proba-bility that the characteristic conforms to its tolerancerequirements. Such a conformance test consists of thefollowing sequence of three operations:(a) measure a characteristic of interest(b) compare the result of the measure
36、ment with aspecified requirement(c) decide on the subsequent actionIn practice, once the measurement data are in hand,the comparison/decision operations are typically imple-mented by way of a decision rule that depends on themeasurement result and its associated uncertainty, thespecified requirement
37、, and the chances and conse-quences of making an erroneous decision. The produceris generally responsible for choosing the decision ruleto be used when making conformance decisions.Documentary guidance is available regarding the for-mulation of a decision rule. ASME B89.7.3.1-2001 3,for example, pro
38、vides a unified set of guidelines fordocumenting a chosen decision rule, including anexplicit description of the role of the measurementuncertainty in setting the test limits (or guard bands).In an industrial and commercial setting, inspectionmeasurement or conformance test procedures aredesigned to
39、 obtain, at reasonable cost, information thatwill enable rational business decisions to be made.Money spent to reduce uncertainty below the level atwhich a rational business decision can be made willusually lead to lost revenue. An inspection sequencewith its associated decision rule (measure compar
40、e/decide) is thus necessarily very closely tied to matterssuch as costs and risks. As such, the design of an effectiveinspection measurement or conformance test is not apurely technical exercise, but also depends upon eco-nomic factors that are specific to the particular enter-prise. For this reason
41、, generic or default decision rules(such as those proposed in ISO 14253-1) that are basedonly on the measurement uncertainty and with no con-sideration of costs can be inadequate for maximizingreturn on investment.1This Report considers only scalar characteristics that are measur-able on a continuou
42、s scale. An inspection measurement of such acharacteristic is called inspection by variables.MEASUREMENT UNCERTAINTY AND CONFORMANCE TESTING: ASME B89.7.4.1-2005RISK ANALYSISTolerance zonex0TLTUGENERAL NOTE: The tolerance zone 5,8 is equivalent to thespecification zone 3.Fig. 1 Tolerance Zone4 FREQU
43、ENCY DISTRIBUTIONS: VARIABLEPRODUCTION PROCESSES AND NOISYMEASUREMENTS4.1 Specification and ToleranceThe following simple one-dimensional example willserve to illustrate in detail the development of a pass/failconformance test procedure for a manufactured work-piece. A manufacturer produces metal sp
44、acers of nominallength x0. The design specification includes a tolerance Tand calls for x0to lie at the center of a tolerance zone oflength T. An acceptable spacer must therefore have alength X in the range TL X TU, where the lower toler-ance limit TLp x0 T/2 and the upper tolerance limitTUp x0+ T/2
45、. The tolerance is simply related to the toler-ance limits by T p TU TL, as shown in Fig. 1. A spaceris said to be conforming if its length X lies in the specifica-tion zone and nonconforming otherwise.4.2 Process VariationBy design and adjustment, the manufacturing processcan be arranged so that, o
46、n average, it produces a spacerwhose length equals the nominal value x0. Due to unpre-dictable and unavoidable process variations, however,there will be some distribution of actual lengths in anyparticular batch of parts. The nature of this distributioncan be studied by measuring a large sample of s
47、pacersand plotting the results in a histogram. In such a study,any nonrepeatability in the measuring system will besuperimposed on the variability due to the productionprocess. In studying process variation, the measurementdata can be corrected for this effect (see para. 4.5).Figure 2 shows a histog
48、ram for the lengths of a batch ofspacers produced by a hypothetical production process.2Thevertical axisshowsthefraction (orrelativefrequency)of parts whose lengths lie in the various narrow bins dis-tributed along the horizontal (length) axis. The width ofthe histogram isa measure of the variabilit
49、yof the produc-tion process. The data in Fig. 2 show that most of the spac-ers are conforming, but there are clearly somenonconforming ones in the batch. The goal of a confor-mance test plan is to detect and remove these bad parts.2The data in Fig. 2 are taken to be the true lengths of the sample.3Length, xpFrequencyx0TLTUH9268Fig. 2 Frequency Distribution of a Sample ofSpacersDenoting by x1,x2, ., xNthe individual lengthsof a sam-ple ofN spacers,it is commonto summarizethe character-istics of the sample by calculating the sample mean, x, a
