1、Guidelines for the Evaluationof Dimensional Measurement UncertaintyASME B89.7.3.2-2007(Technical Report)ASME B89.7.3.2-2007(Technical Report)Guidelines forthe Evaluationof DimensionalMeasurementUncertaintyThree Park Avenue New York, NY 10016Date of Issuance: March 2, 2007This Technical Report will b
2、e 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, construction, proprietary device, or activity.ASM
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6、 NY 10016-5990Copyright 2007 byTHE AMERICAN SOCIETY OF MECHANICAL ENGINEERSAll rights reservedPrinted in U.S.A.CONTENTSForeword ivCommittee Roster . vAbstract . 11 Scope 12 Simplifications in the Evaluation of Measurement Uncertainty 13 Basic Concepts and Terminology of Uncertainty . 14 Combining Un
7、certainty Sources 65 Basic Procedure for Uncertainty Evaluation 76 Examples . 7Figure1 Measurement Uncertainty Quantities . 2Table1 Measurement and Validity Conditions 7Nonmandatory AppendicesA Type A Evaluation of Standard Uncertainty 11B Type B Evaluation of Standard Uncertainty . 12C Influence Qu
8、antities . 14D Thermal Effects in Dimensional Measurements . 16E Bibliography . 19iiiFOREWORDThe ISO Guide to the Expression of Uncertainty in Measurement (GUM) is now the internation-ally accepted method of expressing measurement uncertainty 1. The U.S. has adopted the GUMas a national standard 2.
9、The evaluation of measurement uncertainty has been applied for sometime at national measurement institutes but more recently issues such as measurement traceabilityand laboratory accreditation are resulting in its widespread use in calibration laboratories.Given the potential impact to business prac
10、tices, national and international standards commit-tees are working to publish new standards and technical reports that will facilitate the integrationof the GUM approach and the consideration of measurement uncertainty. In support of thiseffort, ASME B89 Committee for Dimensional Metrology has form
11、ed Division 7 MeasurementUncertainty.Measurement uncertainty has important economic consequences for calibration and measure-ment activities. In calibration reports, the magnitude of the uncertainty is often taken as anindication of the quality of the laboratory, and smaller uncertainty values gener
12、ally are of highervalue and of higher cost. ASME B89.7.3.1, Guidelines for Decision Rules in Determining Confor-mance to Specifications 3, addresses the role of measurement uncertainty when accepting orrejecting products based on a measurement result and a product specification. This document,ASME B
13、89.7.3.2, Guidelines for the Evaluation of Dimensional Measurement Uncertainty, providesa simplified approach (relative to the GUM) to the evaluation of dimensional measurementuncertainty. ASME B89.7.3.3, Guidelines for Assessing the Reliability of Dimensional MeasurementUncertainty Statements 4, ex
14、amines how to resolve disagreements over the magnitude of themeasurement uncertainty statement. Finally, ASME B89.7.4, Measurement Uncertainty and Con-formance Testing: Risk Analysis 5, provides guidance on the risks involved in any productacceptance/rejection decision.With the increasing number of
15、laboratories that are accredited, more and more metrologistswill need to develop skills in evaluating measurement uncertainty. This report provides guidancefor both the novice and experienced metrologist in this endeavor. Additionally, this report maybe used to understand the accuracy of measurement
16、s at a more comprehensive level than thevariation captured by “Gage Repeatability and Reproducibility” (GRhowever, most uncertainty evaluations involve uncorre-lated uncertainty sources. Consequently, correlationeffects are omitted in this document, except for someguidelines to identify when they ar
17、e present and hencemore advanced methods (beyond the scope of this docu-ment) are needed.Accordingly, this guideline has the following twoassumptions:(a) Uncertainty sources are not assigned any degreesof freedom (i.e., no attempt is made to evaluate theuncertainty of the uncertainty). Hence, it is
18、assumedthat the expanded (k p 2) uncertainty interval has a95% probability of containing the true value of themeasurand.(b) All uncertainty sources are assumed to be uncorre-lated. Finally, for simplicity, all input quantities of theuncertainty budget are packaged in quantities that havethe unit of
19、the measurand (i.e., length). This avoids theissue of sensitivity coefficients that typically involve par-tial differentiation.3 BASIC CONCEPTS AND TERMINOLOGY OFUNCERTAINTYThe formal definition of the term “uncertainty of mea-surement” in the current International Vocabulary ofBasic and General Ter
20、ms in Metrology (VIM) 7(VIM entry 3.9) is as follows:uncertainty (of measurement): parameter, associated withthe result of a measurement, that characterizes the dis-persion of the values that could reasonably be attributedto the measurand.This can be interpreted as saying that measurementuncertainty
21、 is a number that describes an interval cen-tered about the measurement result where we have rea-sonable confidence that it includes the “true value” ofthe quantity we are measuring.expanded uncertainty (with a coverage factor of 2), U: anumber that defines an interval around the measure-ment result
22、, y, given by y U, that has an approximate95% level of confidence (i.e., probability) of includingASME B89.7.3.2-2007Fig. 1 Measurement Uncertainty QuantitiesUncertainty intervalExpandeduncertaintyUk=2ExpandeduncertaintyUk=2True value Error Measured valueGENERAL NOTE: Figure 1 illustrates the uncert
23、ainty interval of width2U centered about the result of a measurement. There is a probabilityof about 95% that the true value of the measured quantity lies inthis interval. The true value and hence the error are unknown; theerror shown in the figure is among an infinite number of possiblevalues. The
24、subscript k p 2 indicates that U has been calculatedwith a coverage factor of two.the true value of the quantity we are measuring. (Incertain advanced applications of measurement uncer-tainty it may be necessary to have a different level ofconfidence or even an asymmetric uncertainty interval;these
25、topics involve modifying the coverage factor andare beyond the scope of this document; refer to theGUM.) The expanded uncertainty is the end productof an uncertainty evaluation. In this document, unlessotherwise stated, the term “measurement uncertainty”is considered to be the expanded uncertainty w
26、ith acoverage factor of 2. (The issue of the coverage factorwill be discussed later.) Several aspects of measurementuncertainty are described below.(a) Measurement results have uncertainty; measure-ment instruments, gauges, and workpieces are sourcesof uncertainty. For example, measuring the diamete
27、r ofa steel ball using a caliper will generally have smalleruncertainty than when measuring a foam rubber ball,even though it involves the same instrument.(b) The expanded uncertainty, U, is always a positivenumber, and the uncertainty interval around a measure-ment result is of width 2U. (See Fig.
28、1.)(c) The expanded uncertainty (using the GUM proce-dures for evaluating uncertainty) is a statement of beliefabout the accuracy of a measurement result. When addi-tional information becomes available the uncertainty islikely to be re-evaluated yielding a new value. Conse-quently, there is no “true
29、” or “correct” uncertainty value,only a statement of belief that is based on the informa-tion available at the time the uncertainty is evaluated.2(d) The expanded uncertainty is a quantitative state-ment about our ignorance of the true value of the meas-urand.influence quantity: any quantity, other
30、than the quantitybeing measured, that affects the measurement result.Constructing the list of influence quantities is one of thefirst steps of an uncertainty evaluation. This list includesnot only obvious sources of influence such as the uncer-tainty in the value of a reference standard, or the valu
31、eof a force setting on an instrument, but also nuisancequantities such as environmental parameters or gaugecontamination (dirt). (See Nonmandatory Appendix C.)input quantity: a specific “line item” in the uncertaintybudget that represents one or more influence quantitiescombined together into one qu
32、antity. That is, all signifi-cant influence quantities must be included (i.e., “pack-aged”) in some input quantity. Different uncertaintybudgets developed by different metrologists might usedifferent input quantities, but all budgets include (insome input quantity) all the significant influence quan
33、ti-ties. The selection of the input quantities is usually basedon the type of the data available about the influencequantities. For example, if a long-term reproducibilitystudy using a check standard has been conducted(e.g., measuring the same feature on a gauge once aweek, for several years), then
34、the effects of many influ-ence quantities such as temperature, different operators,recalibration of the instrument, and other factors, are allcombined in the observed variation of the check stan-dard results. In this example, a very large number ofinfluence quantities are combined into a single inpu
35、tquantity (i.e., the reproducibility of the check standardresults).1correlation: refers to a relationship between two inputquantities. Correlation between two input quantitiesmeans that these two quantities are not completely inde-pendent. One way in which input quantities can be cor-related is that
36、 the same influence quantity can appearin both input quantities. In this case the same influencequantity has the risk of being “double-counted.” Inadvanced uncertainty budgets this issue is addressed bycalculating correlation coefficients and then the effect ofthe double counting is subtracted. In t
37、his document amore modest approach is suggested, namely that inputquantities should be constructed such that an influencequantity appears in only one input quantity.EXAMPLE: Suppose that gauge blocks are calibrated using a setof master gauge blocks similar to the blocks under calibration.Suppose fur
38、ther that the laboratorys temperature slowly variesby 1C about 20C and that no correction is made for the thermalexpansion of either gauge block. A poor way to model the measure-ment is to employ a separate input quantity for the temperature,1As will be described later, the variation captured by a r
39、eproduc-ibility study can be quantitatively evaluated by a “Type A” evalu-ation.ASME B89.7.3.2-2007Tm, of the master block and for the temperature, Tc, of the custom-ers block under calibration. These two input quantities are stronglycorrelated. This is easily shown by asking the question, “If I kne
40、wfor sure that Tm 20C, would such knowledge tell me anythingabout Tc?” In this case the answer is affirmative (i.e., I would knowthat Tc 20C, because the blocks are similar and share the samethermal environment). Indeed Tm Tcand the two input quantitiesare fully correlated. This correlation can be c
41、ompletely removedby the observation that both blocks will have the same temperature.Thus there is only a single temperature, T, associated with bothblocks, and all that is known is that T p 20C 1C. Hence, thecorrelation is removed by eliminating a redundant uncertaintysource.measurand: the particula
42、r quantity subject to measure-ment. It is defined by a set of specifications (i.e., instruc-tions) that specifies what we intend to measure; it is nota numerical value. It represents the quantity intended tobe measured. It should specify, as generically as possible,exactly the quantity of interest,
43、and avoid specifyingdetails regarding experimental setups that might beused to measure the measurand. For example, measur-ands specified by ASME Y14.5 8, such as the diameterof a feature of size or the concentricity of two bores, donot attempt to describe the measurement procedure indetail.2Ideally
44、the measurand should be completelyindependent of experimental measurement details sothat different measurement technologies can be used tomeasure the same measurand and get the same result.Indeed, the measurand is an idealized concept and itmay be impossible to produce an actual gauge, artifact,or i
45、nstrument exactly to the specifications of the measur-and. Consequently, a well-specified measurand providesenough information, and is generic enough, to allowdifferent techniques to be used to perform the measure-ment. The more completely defined the measurand, theless uncertainty will (potentially
46、) be associated with itsrealization. A completely specified definition of themeasurand has associated with it a unique value, andan incompletely specified measurand may have manyvalues, each conforming to the (incompletely defined)measurand. The ambiguity associated with an incom-pletely defined mea
47、surand results in an uncertainty con-tributor that must be assessed during the measurementuncertainty evaluation.As an example of the significance of the measurand,consider a bore that has a size tolerance specified byASME Y14.5. An inspection of the workpiece involvesa measurand defined as the diam
48、eter of the maximuminscribed cylinder that will just fit in the bore (i.e., thisis the largest diameter cylinder that is constrained bythe workpiece surface, regardless of any translations or2The nominal value that may be attributed to a measurand(e.g., the diameter of a feature of size) is not part
49、 of the measurand;rather, it is the desired result of a measurement of the measurand.Similarly, a tolerance associated with a feature is not part of themeasurand, but rather describes a region within which a measure-ment result is considered to demonstrate the feature to be in confor-mance with the design intent.3rotations that may be applied).3Note the generic natureof this measurand, which avoids specifying any detailsabout potential experimental measurement setups.Unless careful consideration is given to the measurand,different inspection techniques can lea
