1、Designation: E2782 111E2782 17 An American National StandardStandard Guide forMeasurement Systems Analysis (MSA)1This standard is issued under the fixed designation E2782; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of
2、 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 NOTEEditorial corrections were made throughout in May 2014.1. Scope1.1 This guide presents terminology, concepts, and selected
3、methods and formulas useful for measurement systems analysis(MSA). Measurement systems analysis may be broadly described as a body of theory and methodology that applies to thenon-destructive measurement of the physical properties of manufactured objects.1.2 UnitsThe system of units for this guide i
4、s not specified. Dimensional quantities in the guide are presented only asillustrations of calculation methods and are not binding on products or test methods treated.1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof
5、 the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E177 Practice for Use of the Terms Precision and Bias in ASTM Test MethodsE456 Terminology Relating to Qual
6、ity and StatisticsE2586 Practice for Calculating and Using Basic StatisticsE2587 Practice for Use of Control Charts in Statistical Process Control3. Terminology3.1 Definitions:3.1.1 Unless otherwise noted, terms relating to quality and statistics are defined in Terminology E456.3.1.2 accepted refere
7、nce value, na value that serves as an agreed-upon reference for comparison, and which is derived as: (1)a theoretical or established value, based on scientific principles, (2) an assigned or certified value, based on experimental work ofsome national or international organization, or (3) a consensus
8、 or certified value, based on collaborative experimental work underthe auspices of a scientific or engineering group. E1773.1.3 calibration, nprocess of establishing a relationship between a measurement device and a known standard value(s).3.1.4 gage, ndevice used as part of the measurement process
9、to obtain a measurement result.3.1.5 measurement process, nprocess used to assign a number to a property of an object or other physical entity.3.1.5.1 DiscussionThe term “measurement system” is sometimes used in place of measurement process. (See 3.1.7.)3.1.6 measurement result, nnumber assigned to
10、a property of an object or other physical entity being measured.3.1.6.1 Discussion1 This guide is under the jurisdiction ofASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.20 on Test Method Evaluationand Quality Control.Current edition approved Nov. 1
11、5, 2011Jan. 1, 2017. Published February 2012February 2017. Originally approved in 2011. Last previous edition approved in 2011 asE2782 111. DOI: 10.1520/E2782-11E01.10.1520/E2782-17.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.or
12、g. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard 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
13、may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Ha
14、rbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1The word “measurement” is used in the same sense as measurement result.3.1.7 measurement system, nthe collection of hardware, software, procedures and methods, human effort, environmentalconditions, associated devices, and the
15、objects that are measured for the purpose of producing a measurement.3.1.8 measurement systems analysis (MSA), nany of a number of specialized methods useful for studying a measurementsystem and its properties.3.2 Definitions of Terms Specific to This Standard:3.2.1 appraiser, nthe person who uses a
16、 gage or measurement system.3.2.2 discrimination ratio, nstatistical ratio calculated from the statistics from a gage R control chart methodologies are as described in Practice E2587.5. Characteristics of a Measurement System (Process)5.1 Measurement has been defined as “the assignment of numbers to
17、 material objects to represent the relations existing amongthem with respect to particular properties. The number assigned to some particular property serves to represent the relative amountof this property associated with the object concerned.” (1)35.2 A measurement system may be described as a col
18、lection of hardware, software, procedures and methods, human effort,environmental conditions, associated devices, and the objects that are measured for the purpose of producing a measurement. Inthe practical working of the measurement system, these factors combine to cause variation among measuremen
19、ts of the same objectthat would not be present if the system were perfect. A measurement system can have varying degrees of each of these factors,and in some cases, one or more factors may be the dominant contributor to this variation.5.2.1 A measurement system is like a manufacturing process for wh
20、ich the product is a supply of numbers called measurementresults. The measurement system uses input factors and a sequence of steps to produce a result. The inputs are just varying degreesof the several factors described in 5.2 including the objects being measured. The sequence of process steps are
21、that which wouldbe described in a method or procedure for producing the measurement. Taken as a whole, the various factors and the process stepswork collectively to form the measurement system/process.5.3 An important consideration in analyzing any measurement process is its interaction with time. T
22、his gives rise to theproperties of stability and consistency. A system that is stable and consistent is one that is predictable, within limits, over a periodof time. Such a system has properties that do not deteriorate with time (at least within some set time period) and is said to be ina state of s
23、tatistical control. Statistical control, stability and consistency, and predictability have the same meaning in this sense.Measurement system instability and inconsistency will cause further added overall variation over a period of time.5.3.1 In general, instability is a common problem in measuremen
24、t systems. Mechanical and electrical components may wearor degrade with time, human effort may exhibit increasing fatigue with time, software and procedures may change with time,environmental variables will vary with time, and so forth. Thus, measurement system stability is of primary concern in any
25、 ongoingmeasurement effort.5.4 There are several basic properties of measurement systems that are widely recognized among practitioners. These arerepeatability, reproducibility, linearity, bias, stability, consistency, and resolution. In studying one or more of these properties, thefinal result of a
26、ny such study is some assessment of the capability of the measurement system with respect to the property underinvestigation. Capability may be cast in several ways, and this may also be application dependent. One of the primary objectivesin any MSAeffort is to assess variation attributable to the v
27、arious factors of the system.All of the basic properties assess variationin some form.5.4.1 Repeatability is the variation that results when a single object is repeatedly measured in the same way, by the sameappraiser, under the same conditions (see Fig. 1). The term “precision” also denotes the sam
28、e concept, but “repeatability” is foundmore often in measurement applications. The term “conditions” is sometimes combined with repeatability to denote “repeatabilityconditions” (see Terminology E456).5.4.1.1 The phrase “intermediate precision” is also used (for example, see Practice E177). The user
29、 of a measurement systemshall decide what constitutes “repeatability conditions” or “intermediate precision conditions” for the given application. Typically,repeatability conditions for MSA will be as described above.in 5.4.1.5.4.2 Reproducibility is defined as the variation among average values as
30、determined by several appraisers when measuring thesame group of objects using identical measurement systems under the same conditions (see Fig. 2). In a broader sense, this may3 The boldface numbers in parentheses refer to the list of references at the end of this standard.E2782 173be taken as vari
31、ation in average values of samples, either identical or selected at random from one homogeneous population, amongseveral laboratories or as measured using several systems.5.4.2.1 Reproducibility may include different equipment and measurement conditions. This broader interpretation has attached“repr
32、oducibility conditions” and shall be defined and interpreted by the user of a measurement system. (In Practice E177,reproducibility includes interlaboratory variation.)5.4.3 Bias is the difference between a standard or accepted reference value for an object, often called a “master,” and the averagev
33、alue of a sample of measurements of the object(s) under a fixed set of conditions.conditions (see Fig. 1).5.4.4 Linearity is the change in bias over the operational range of the measurement system. If the bias is changing as a functionof the object being measured, we would say that the system is not
34、 linear. Linearity can also be interpreted to mean that aninstrument response is linearly related to the characteristic being measured.5.4.5 Stability is variation in bias with time, usually a drift or trend, or erratic behavior.5.4.6 Consistency is the change in repeatability with time. A system is
35、 consistent with time when the standard deviation of therepeatability error remains constant. When a measurement system is stable and consistent, we say that it is a state of statisticalcontrol.5.4.7 The resolution of a measurement system has to do with its ability to discriminate between different
36、objects.Asystem withhigh resolution is one that is sensitive to small changes from object to object. Inadequate resolution may result in identicalmeasurements when the same object is measured several times under identical conditions. In this scenario, the measurement deviceis not capable of picking
37、up variation as a result of repeatability (under the conditions defined). Poor resolution may also resultin identical measurements when differing objects are measured. In this scenario, the objects themselves are too close in truemagnitude for the system to distinguish among.5.4.7.1 Resolution plays
38、 an important role in measurement in general.We can imagine the output of a process that is in statisticalcontrol and follows a normal distribution with mean, , and standard deviation, . Based on the normal distribution, the naturalspread of the process is 6. Suppose we measure objects from this pro
39、cess with a perfect gage except for its finite resolutionproperty. Suppose further that the gage we are using is “graduated” as some fraction, 1/k, of the 6 natural process spread (integerk). For example, if k = 4, then the natural process tolerance would span four graduations on the gage; if k = 6,
40、 then the naturalprocess spread would span six graduations on the gage. It is clear that, as k increases, we would have an increasingly betterresolution and would be more likely to distinguish between distinct objects, however close their magnitudes; at the oppositeextreme, for small k, fewer and fe
41、wer distinct objects from the process would be distinguishable. In the limit, for large k, everyobject from this process would be distinguishable.5.4.7.2 In using this perfect gage, the finite resolution property plays a role in repeatability. For very large k, the resultingstandard deviation of man
42、y objects from the process would be nearly the magnitude of the true object standard deviation, . Ask diminishes, the standard deviation of the measurements would increase as a result of the finite resolution property. Fig. 3illustrates this concept for a process centered at 0 and having = 1 for k =
43、 4.FIG. 1 Repeatability and Bias ConceptsFIG. 2 Reproducibility ConceptE2782 1745.4.7.3 The illustration from Fig. 3 is a system capable of discriminating objects into groups no smaller than 1.5 in width sothat a frequency distribution of measured objects from this system will generally have four bi
44、ns. This means four distinct productvalues can be detected. Using Fig. 3 and the theoretical probabilities from the normal distribution, it is possible to calculate thevariance of the measured values for various values of k. In this case, the variance of the measured values is approximately 1.119or
45、11.9 % larger than the true variance. The standard deviation is, therefore, 1.058 or 5.8 % larger.5.4.7.4 This illustrates the important role that resolution plays in measurement in general and an MSAstudy in particular. Thereis a subtle interaction between the degree of resolution and more general
46、repeatability and other measurement effects. In extremecases of poor resolution, an MSAstudy may not be able to pick up a repeatability effect (all objects measured yield the same value).For an ideal system, for varying degrees of finite resolution as described in 5.4.7, there will be a component of
47、 variance as a resultof resolution alone. For positive integer value, k, when the smallest measurement unit for a device is 1/kth of the 6 true naturalprocess range, the standard deviation as a result of the resolution effect may be determined theoretically (assuming a normaldistribution). Table 1 s
48、hows the effect for selected values of k.5.4.7.5 A common rule of thumb is for a measurement device to have a resolution no greater than 0.6, where is the truenatural process standard deviation. This would give us k = 10 graduation divisions within the true 6 natural process limits. In thatparticula
49、r case, the resulting variance of all measurements would have increased by approximately 1.9 % (Table 1, k = 10).5.5 MSA is a broad class of activities that studies the several properties of measurement systems, either individually, or somerelevant subset of properties taken collectively. Much of this activity uses well known methods of classical statistics, most notablyexperimental design techniques. In classical statistics, the term variance is used to denote variation in a set of numbers. It is thesquare of the standard deviation. One of the prima
