# ASTM E2782-17

Designation: E2782 − 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 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 guide presents terminology, concepts, and selectedmethods and formulas useful for measurement systems analy-sis (MSA). Measurement systems analysis may be broadlydescribed as a body of theory and methodology that applies tothe non-destructive measurement of the physical properties ofmanufactured objects.1.2 Units—The system of units for this guide is not speci-fied. Dimensional quantities in the guide are presented only asillustrations of calculation methods and are not binding onproducts or test methods treated.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with 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.2. Referenced Documents2.1 ASTM Standards:2E177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating to Quality and StatisticsE2586 Practice for Calculating and Using Basic StatisticsE2587 Practice for Use of Control Charts in StatisticalProcess Control3. Terminology3.1 Definitions:3.1.1 Unless otherwise noted, terms relating to quality andstatistics are defined in Terminology E456.3.1.2 accepted reference value, n—a value that serves as anagreed-upon reference for comparison, and which is derivedas: (1) a theoretical or established value, based on scientificprinciples, (2) an assigned or certified value, based on experi-mental work of some national or international organization, or(3) a consensus or certified value, based on collaborativeexperimental work under the auspices of a scientific orengineering group. E1773.1.3 calibration, n—process of establishing a relationshipbetween a measurement device and a known standard value(s).3.1.4 gage, n—device used as part of the measurementprocess to obtain a measurement result.3.1.5 measurement process, n—process used to assign anumber to a property of an object or other physical entity.3.1.5.1 Discussion—The term “measurement system” issometimes used in place of measurement process. (See 3.1.7.)3.1.6 measurement result, n—number assigned to a propertyof an object or other physical entity being measured.3.1.6.1 Discussion—The word “measurement” is used in thesame sense as measurement result.3.1.7 measurement system, n—the collection of hardware,software, procedures and methods, human effort, environmen-tal conditions, associated devices, and the objects that aremeasured for the purpose of producing a measurement.3.1.8 measurement systems analysis (MSA), n—any of anumber of specialized methods useful for studying a measure-ment system and its properties.3.2 Definitions of Terms Specific to This Standard:3.2.1 appraiser, n—the person who uses a gage or measure-ment system.3.2.2 discrimination ratio, n—statistical ratio calculatedfrom the statistics from a gage R control chart methodologies are as described in PracticeE2587.5. Characteristics of a Measurement System (Process)5.1 Measurement has been defined as “the assignment ofnumbers to material objects to represent the relations existingamong them with respect to particular properties. The numberassigned to some particular property serves to represent therelative amount of this property associated with the objectconcerned.” (1)35.2 A measurement system may be described as a collectionof hardware, software, procedures and methods, human effort,environmental conditions, associated devices, and the objectsthat are measured for the purpose of producing a measurement.In the practical working of the measurement system, thesefactors combine to cause variation among measurements of thesame object that would not be present if the system wereperfect. A measurement system can have varying degrees ofeach of these factors, and in some cases, one or more factorsmay be the dominant contributor to this variation.5.2.1 A measurement system is like a manufacturing pro-cess for which the product is a supply of numbers calledmeasurement results. The measurement system uses inputfactors and a sequence of steps to produce a result. The inputsare just varying degrees of the several factors described in 5.2including the objects being measured. The sequence of processsteps are that which would be described in a method orprocedure for producing the measurement. Taken as a whole,the various factors and the process steps work collectively toform the measurement system/process.5.3 An important consideration in analyzing any measure-ment process is its interaction with time. This gives rise to theproperties of stability and consistency. A system that is stableand consistent is one that is predictable, within limits, over aperiod of time. Such a system has properties that do notdeteriorate with time (at least within some set time period) andis said to be in a state of statistical control. Statistical control,stability and consistency, and predictability have the samemeaning in this sense. Measurement system instability andinconsistency will cause further added overall variation over aperiod of time.5.3.1 In general, instability is a common problem in mea-surement systems. Mechanical and electrical components maywear or degrade with time, human effort may exhibit increas-ing fatigue with time, software and procedures may change3The boldface numbers in parentheses refer to the list of references at the end ofthis standard.E2782 − 172with time, environmental variables will vary with time, and soforth. Thus, measurement system stability is of primary con-cern in any ongoing measurement effort.5.4 There are several basic properties of measurementsystems that are widely recognized among practitioners. Theseare repeatability, reproducibility, linearity, bias, stability,consistency, and resolution. In studying one or more of theseproperties, the final result of any such study is some assessmentof the capability of the measurement system with respect to theproperty under investigation. Capability may be cast in severalways, and this may also be application dependent. One of theprimary objectives in any MSA effort is to assess variationattributable to the various factors of the system.All of the basicproperties assess variation in some form.5.4.1 Repeatability is the variation that results when a singleobject is repeatedly measured in the same way, by the sameappraiser, under the same conditions (see Fig. 1). The term“precision” also denotes the same concept, but “repeatability”is found more often in measurement applications. The term“conditions” is sometimes combined with repeatability todenote “repeatability conditions” (see Terminology E456).5.4.1.1 The phrase “intermediate precision” is also used (forexample, see Practice E177). The user of a measurementsystem shall decide what constitutes “repeatability conditions”or “intermediate precision conditions” for the given applica-tion. Typically, repeatability conditions for MSA will be asdescribed in 5.4.1.5.4.2 Reproducibility is defined as the variation amongaverage values as determined by several appraisers whenmeasuring the same group of objects using identical measure-ment systems under the same conditions (see Fig. 2). In abroader sense, this may be taken as variation in average valuesof samples, either identical or selected at random from onehomogeneous population, among several laboratories or asmeasured using several systems.5.4.2.1 Reproducibility may include different equipmentand measurement conditions. This broader interpretation hasattached “reproducibility conditions” and shall be defined andinterpreted by the user of a measurement system. (In PracticeE177, reproducibility includes interlaboratory variation.)5.4.3 Bias is the difference between a standard or acceptedreference value for an object, often called a “master,” and theaverage value of a sample of measurements of the object(s)under a fixed set of conditions (see Fig. 1).5.4.4 Linearity is the change in bias over the operationalrange of the measurement system. If the bias is changing as afunction of the object being measured, we would say that thesystem is not linear. Linearity can also be interpreted to meanthat an instrument response is linearly related to the character-istic being measured.5.4.5 Stability is variation in bias with time, usually a driftor trend, or erratic behavior.5.4.6 Consistency is the change in repeatability with time.Asystem is consistent with time when the standard deviation ofthe repeatability error remains constant. When a measurementsystem is stable and consistent, we say that it is a state ofstatistical control.5.4.7 The resolution of a measurement system has to dowith its ability to discriminate between different objects. Asystem with high resolution is one that is sensitive to smallchanges from object to object. Inadequate resolution may resultin identical measurements when the same object is measuredseveral times under identical conditions. In this scenario, themeasurement device is not capable of picking up variation as aresult of repeatability (under the conditions defined). Poorresolution may also result in identical measurements whendiffering objects are measured. In this scenario, the objectsthemselves are too close in true magnitude for the system todistinguish among.5.4.7.1 Resolution plays an important role in measurementin general. We can imagine the output of a process that is instatistical control and follows a normal distribution with mean,µ, and standard deviation, σ. Based on the normal distribution,the natural spread of the process is 6σ. Suppose we measureobjects from this process with a perfect gage except for itsfinite resolution property. Suppose further that the gage we areusing is “graduated” as some fraction, 1/k, of the 6σ naturalprocess spread (integer k). For example, if k = 4, then thenatural process tolerance would span four graduations on thegage; if k = 6, then the natural process spread would span sixgraduations on the gage. It is clear that, as k increases, wewould have an increasingly better resolution and would bemore likely to distinguish between distinct objects, howeverclose their magnitudes; at the opposite extreme, for small k,fewer and fewer distinct objects from the process would bedistinguishable. In the limit, for large k, every object from thisprocess would be distinguishable.5.4.7.2 In using this perfect gage, the finite resolutionproperty plays a role in repeatability. For very large k, theresulting standard deviation of many objects from the processwould be nearly the magnitude of the true object standardFIG. 1 Repeatability and Bias ConceptsFIG. 2 Reproducibility ConceptE2782 − 173deviation, σ.Ask diminishes, the standard deviation of themeasurements would increase as a result of the finite resolutionproperty. Fig. 3 illustrates this concept for a process centered at0 and having σ = 1 for k =4.5.4.7.3 The illustration from Fig. 3 is a system capable ofdiscriminating objects into groups no smaller than 1.5σ inwidth so that a frequency distribution of measured objects fromthis system will generally have four bins. This means fourdistinct product values can be detected. Using Fig. 3 and thetheoretical probabilities from the normal distribution, it ispossible to calculate the variance of the measured values forvarious values of k. In this case, the variance of the measuredvalues is approximately 1.119 or 11.9 % larger than the truevariance. The standard deviation is, therefore, 1.058 or 5.8 %larger.5.4.7.4 This illustrates the important role that resolutionplays in measurement in general and an MSA study inparticular. There is a subtle interaction between the degree ofresolution and more general repeatability and other measure-ment effects. In extreme cases of poor resolution, an MSAstudy may not be able to pick up a repeatability effect (allobjects 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 variance as a result of resolutionalone. For positive integer value, k, when the smallest mea-surement unit for a device is 1/kth of the 6σ true natural processrange, the standard deviation as a result of the resolution effectmay be determined theoretically (assuming a normal distribu-tion). Table 1 shows the effect for selected values of k.5.4.7.5 A common rule of thumb is for a measurementdevice to have a resolution no greater than 0.6σ, where σ is thetrue natural process standard deviation. This would give usk = 10 graduation divisions within the true 6σ natural processlimits. In that particular case, the resulting variance of allmeasurements would have increased by approximately 1.9 %(Table 1, k = 10).5.5 MSAis a broad class of activities that studies the severalproperties of measurement systems, either individually, orsome relevant subset of properties taken collectively. Much ofthis activity uses well known methods of classical statistics,most notably experimental design techniques. In classicalstatistics, the term variance is used to denote variation in a setof numbers. It is the square of the standard deviation. One ofthe primary goals in conducting an MSA study is to assess theseveral variance components that may be at play. Each factorwill have its own variance component that contributes to theoverall variation. Components of variance for independentvariables are additive. For example, suppose y is the result ofa measurement in which three independent factors are at play.Suppose that the three independent factors are x1, x2, and x3.Asimple model for the linear sum of the three components is y =x1+ x2+ x3. The variance of the overall sum, y, given thevariances of the components is:σy25 σ121σ221σ32(1)5.5.1 We say that each variance on the right is a componentof the overall variance on the left. This model is theoretical; inpractice, we do not know the true variances and have toestimate their values from data.5.5.2 Statistical methods allow one to estimate the severalvariance components in MSA. Sometimes the analyst may onlybe interested in one of the components, for example, repeat-ability. In other cases, it may be two or more components thatmay be of interest. Depending on how the MSA study isdesigned, the variance components may be estimable free andclear of each other or combined as a composite measure.Several widely used basic models and associated statisticaltechniques are discussed in Section 6.6. Basic MSA Methods6.1 Simple Repeatability—Simple repeatability