MEASUREMENT SYSTEMS ANALYSISReference ManualFourth EditionFirst Edition, October 1990 Second Edition, February 1995; Second Printing, June 1998Third Edition, March 2002; Second Printing, May 2003; Fourth Edition, June 2010Copyright 1990, 1995, 2002, 2010 Chrysler Group LLC, Ford Motor Company, General Motors CorporationISBN#: 978-1-60-534211-5i


FOREWORDThis Reference Manual was developed by a Measurement Systems Analysis (MSA) Work Group,sanctioned by the Chrysler Group LLC, Ford Motor Company, and General Motors Corporation SupplierQuality Requirements Task Force, and under the auspices of the Automotive Industry Action Group(AIAG). The Work Group responsible for this Fourth Edition were Michael Down (General MotorsCorporation), Frederick Czubak (Chrysler Group LLC), Gregory Gruska (Omnex), Steve Stahley(Cummins, Inc.) and David Benham.The manual is an introduction to measurement system analysis. It is not intended to limit evolution ofanalysis methods suited to particular processes or commodities. While these guidelines are intended tocover normally occurring measurement system situations, there will be questions that arise. Thesequestions should be directed to your authorized customer representative.This Manual is copyrighted by Chrysler Group LLC, Ford Motor Company, and General MotorsCorporation, with all rights reserved, 2010. Additional manuals can be ordered from AIAG Permission to reproduce portions of this manual for use within supplier organizations maybe obtained from AIAG at www.aiag.orgUTUTJune 2010iii

MSA 4th Edition Quick GuideType ofMeasurement SystemMSA MethodsChapterBasic VariableRange, Average & Range, ANOVA,Bias, Linearity, Control ChartsIIIBasic AttributeSignal Detection,Hypothesis Test AnalysesIIINon-Replicable(e.g., Destructive Tests)Alternate ApproachesIVComplex VariableRange, Average & Range, ANOVA,Bias Linearity Control ChartsIII, IVMultiple Systems, Gagesor Test StandsControl Charts ANOVA Regression AnalysisIII, IVMiscellaneousAlternate ApproachesIVOtherWhite Papers – available atAIAG website ( Regarding the use of the GRR standard deviationHistorically, by convention, a 99% spread has been used to represent the “full” spread ofmeasurement error, represented by a 5.15 multiplying factor (where GRR is multiplied by 5.15to represent a total spread of 99%).A 99.73% spread is represented by a multiplier of 6.0, which is 3 and represents the fullspread of a “normal” curve.If the reader chooses to increase the coverage level, or spread, of the total measurementvariation to 99.73%, use 6.0 as a multiplier in place of 5.15 in the calculations.Note: The approach used in the 4th Edition is to compare standard deviations. This is equivalentto using the multiplier of 6 in the historical approach.Awareness of which multiplying factor is used is crucial to the integrity of the equations andresultant calculations. This is especially important if a comparison is to be made betweenmeasurement system variability and the tolerance. Consequently, if an approach other than thatdescribed in this manual is used, a statement of such must be stated clearly in any results orsummaries (particularly those provided to the customer).iv

TABLE OF CONTENTSMSA 4th Edition Quick Guide .ivTABLE OF CONTENTS .vList of Tables. viiList of Figures . viiiCHAPTER I General Measurement System Guidelines.1Section A Introduction, Purpose and Terminology .3Introduction .3Purpose .4Terminology .4Section B The Measurement Process P.13Measurement Systems .13The Effects of Measurement System Variability.18Section C Measurement Strategy and Planning.25Section D Measurement Source Development .29Gage Source Selection Process.31Section E Measurement Issues .41Section F Measurement Uncertainty.63Section G Measurement Problem Analysis .65CHAPTER II General Concepts for Assessing Measurement Systems .67Section A Background.69Section B Selecting/Developing Test Procedures.71Section C Preparation for a Measurement System Study .73Section D Analysis of the Results.77CHAPTER III Recommended Practices for Replicable Measurement Systems .81Section A Example Test Procedures.83Section B Variable Measurement System Study Guidelines .85Guidelines for Determining Stability.85Guidelines for Determining Bias PF – Independent Sample Method .87Guidelines for Determining Bias – Control Chart Method.92Guidelines for Determining Linearity P.96Guidelines for Determining Repeatability and Reproducibility P .101Range Method.102Average and Range Method .103Analysis of Variance (ANOVA) Method .123Section C Attribute Measurement Systems Study .131Risk Analysis Methods .131Signal Detection Approach.143Analytic Method P .145CHAPTER IV Other Measurement Concepts and Practices .151Section A Practices for Non-Replicable Measurement Systems .153Destructive measurement systems .153Systems where the part changes on use/test .153Section B Stability Studies .155Section C Variability Studies.161Section D Recognizing the Effect of Excessive Within-Part Variation.167Section E Average and Range Method – Additional Treatment.169Section F Gage Performance Curve P.177Section G Reducing Variation Through Multiple Readings .183Section H Pooled Standard Deviation Approach to GRR P .185APPENDICES.193v

Appendix A.195Analysis of Variance Concepts.195Appendix B.199Impact of GRR on the Capability Index Cp .199Formulas:.199Analysis: .199Graphical Analysis .201Appendix C.203Appendix D.205Gage R Study.205Appendix E.207Alternate PV Calculation Using Error Correction Term.207Appendix F .209P.I.S.M.O.E.A. Error Model.209Glossary .213Reference List .219Sample Forms .223Index .227vi

List of TablesTable I-B1: Control Philosophy and Driving Interest. 18Table II-D 1: GRR Criteria. 78Table III-B 1: Bias Study Data. 90Table III-B 2: Bias Study – Analysis of Bias Study P . 92Table III-B 3: Bias Study – Analysis of Stability Study for Bias. 95Table III-B 4: Linearity Study Data . 99Table III-B 5: Linearity Study – Intermediate Results . 99Table III-B 6: Gage Study (Range Method) . 103Table III-B 6a: Gage Repeatability and Reproducibility Data Collection Sheet .105Table III-B 7: ANOVA Table . 127Table III-B 8: ANOVA Analysis % Variation & Contribution . 127Table III-B 9: Comparison of ANOVA and Average and Range Methods . 129Table III-B 10: GRR ANOVA Method Report . 129Table III-C 1: Attribute Study Data Set. 134Table III-C 2: Cross tabulation Study Results . 136Table III-C 3: Kappa Summary . 137Table III-C 4: Comparisons of Appraisers to Reference . 138Table III-C 5: Study Effectiveness Table. 139Table III-C 6: Example Effectiveness Criteria Guidelines . 140Table III-C 7: Study Effectiveness Summary . 140Table III-C 8: Table III-C 1 sorted by Ref Value. 143Table IV-A 1: Methods Based on Type of Measurement System. 154Table IV-H 1: Pooled Standard Deviation Analysis Data Set . 189Table A 1: Estimate of Variance Components . 195Table A 2: 6 Sigma Spread . 196Table A 3: Analysis of Variance (ANOVA) . 197Table A 4: Tabulated ANOVA Results . 198Table A 5: Tabulated ANOVA Results . 198Table B 1: Comparison of Observed to Actual Cp.201Table C 1:d 2* Table . 203Table F 1: Examples of the PISMOEA Model. 211vii

List of FiguresFigure I-A 1: Example of a Traceability Chain for a Length Measurement . 10Figure I-B 1: Measurement System Variability Cause and Effect Diagram . 17Figure I-E 2: Discrimination .46Figure I-E 3: Impact of Number of Distinct Categories (ndc) of the Process Distribution on Control andAnalysis Activities . 47Figure I-E 4: Process Control Charts . 49Figure I-E 5: Characteristics of the Measurement Process Variation . 50Figure I-E 6: Relationships between Bias and Repeatability . 62Figure III-B 1: Control Chart Analysis for Stability . 86Figure III-B 2: Bias Study – Histogram of Bias Study . 91Figure III-B 3: Linearity Study – Graphical Analysis .100Figure III-B 4: Average Chart – “Stacked”.107Figure III-B 5: Average Chart – “Unstacked”.107Figure III-B 6: Range Chart – “Stacked” .108Figure III-B 7: Range Chart – “Unstacked” .109Figure III-B 8: Run Chart by Part .109Figure III-B 9: Scatter Plot .110Figure III-B 10: Whiskers Chart .111Figure III-B 11: Error Charts .112Figure III-B 12: Normalized Histogram .113Figure III-B 13: X–Y Plot of Averages by Size .114Figure III-B 14: Comparison X–Y Plots .115Figure III-B 15: Completed GR&R Data Collection Sheet . 118Figure III-B 16: Gage Repeatability and Reproducibility Report . 119Figure III-B 18: Residual Plot .126Figure III-C 1: Example Process with Pp Ppk 0.50.132Figure III-C 2: The “Gray” Areas Associated with the Measurement System . 132Figure III-C 3: Example Process with Pp Ppk 1.33.141Figure III-C 4: Attribute Gage Performance Curve Plotted on Normal Probability Paper . 149Figure III-C 5. Attribute Gage Performance Curve UTUTUTUTUTUTFigure IV-E 1: Measurement Evaluation Control Chart ( X& R ) - 1 . 172Figure IV-E 2: Measurement Evaluation Control Chart ( X & R ) - 2 . 173UTUTUTUTFigure IV-E 3: Alternate Computations for Evaluating a Measurement Process (Part 1 of 2). 174Figure IV-E 4: Alternate Computations for Evaluating a Measurement Process (Part 2 of 2). 175Figure IV-F 1: Gage Performance Curve Without Error .180Figure IV-F 2: Gage Performance Curve –Example .181Figure IV-F 3: Gage Performance Curve Plotted on Normal Probability Paper . 182Figure IV-H 1: Pooled Standard Deviation Study Graphical Analysis . 188Figure IV-H 2: Dot diagram of h values.191Figure IV-H 3: Dot diagram of k values. .192Figure B 1: Observed vs. Actual Cp (process based) .201Figure B 2: Observed vs. Actual Cp (tolerance based) .202UTUTUTUTUTUTTTTUUUUTviii

Chapter IGeneral Measurement System GuidelinesCHAPTER IGeneral Measurement SystemGuidelines1

Chapter I – Section AIntroduction, Purpose and Terminology2

Chapter I – Section AIntroduction, Purpose and TerminologySection AIntroduction, Purpose and TerminologyIntroductionMeasurement data are used more often and in more ways than ever before.For instance, the decision to adjust a manufacturing process is nowcommonly based on measurement data. The data, or some statistic calculatedfrom them, are compared with statistical control limits for the process, and ifthe comparison indicates that the process is out of statistical control, then anadjustment of some kind is made. Otherwise, the process is allowed to runwithout adjustment. Another use of measurement data is to determine if asignificant relationship exists between two or more variables. For example, itmay be suspected that a critical dimension on a molded plastic part is relatedto the temperature of the feed material. That possible relationship could bestudied by using a statistical procedure called regression analysis to comparemeasurements of the critical dimension with measurements of thetemperature of the feed material.Studies that explore such relationships are examples of what Dr. W. E.Deming called analytic studies. In general, an analytic study is one thatincreases knowledge about the system of causes that affect the process.Analytic studies are among the most important uses of measurement databecause they lead ultimately to better understanding of processes.The benefit of using a data-based procedure is largely determined by thequality of the measurement data used. If the data quality is low, the benefit ofthe procedure is likely to be low. Similarly, if the quality of the data is high,the benefit is likely to be high also.To ensure that the benefit derived from using measurement data is greatenough to warrant the cost of obtaining it, attention needs to be focused onthe quality of the data.Quality ofMeasurementDataThe quality of measurement data is defined by the statistical properties ofmultiple measurements obtained from a measurement system operating understable conditions. For instance, suppose that a measurement system,operating under stable conditions, is used to obtain several measurements ofa certain characteristic. If the measurements are all “close” to the mastervalue for the characteristic, then the quality of the data is said to be “high”.Similarly, if some, or all, of the measurements are “far away” from themaster value, then the quality of the data is said to be “low”.The statistical properties most commonly used to characterize the quality ofdata are the bias and variance of the measurement system. The propertycalled bias refers to the location of the data relative to a reference (master)value, and the property called variance refers to the spread of the data.One of the most common reasons for low-quality data is too much variation.Much of the variation in a set of measurements may be due to the interactionbetween the measurement system and its environment. For instance, a3

Chapter I – Section AIntroduction, Purpose and Terminologymeasurement system used to measure the volume of liquid in a tank may besensitive to the ambient temperature of the environment in which it is used.In that case, variation in the data may be due either to changes in the volumeor to changes in the ambient temperature. That makes interpreting the datamore difficult and the measurement system, therefore, less desirable.If the interaction generates too much variation, then the quality of the datamay be so low that the data are not useful. For example, a measurementsystem with a large amount of variation may not be appropriate for use inanalyzing a manufacturing process because the measurement system’svariation may mask the variation in the manufacturing process. Much of thework of managing a measurement system is directed at monitoring andcontrolling variation. Among other things, this means that emphasis needs tobe placed on learning how the measurement system interacts with itsenvironment so that only data of acceptable quality are generated.PurposeThe purpose of this document is to present guidelines for assessing thequality of a measurement system. Although the guidelines are generalenough to be used for any measurement system, they are intended primarilyfor the measurement systems used in the industrial world. This document isnot intended to be a compendium of analyses for all measurement systems.Its primary focus is measurement systems where the readings can bereplicated on each part. Many of the analyses are useful with other types ofmeasurement systems and the manual does contain references andsuggestions. It is recommended that competent statistical resources beconsulted for more complex or unusual situations not discussed here.Customer approval is required for measurement systems analysis methodsnot covered in this manual.TerminologyThe discussion of the analysis of measurement system can become confusingand misleading without an established set of terms to refer to the commonstatistical properties and related elements of the measurement system. Thissection provides a summary of such terms which are used in this manual.In this document, the following terms are used: Measurement is defined as “the assignment of numbers [or values]to material things to represent the relations among them with respectto particular properties.” This definition was first given by C.Eisenhart (1963). The process of assigning the numbers is defined asthe measurement process, and the value assigned is defined as themeasurement value.4

Chapter I – Section AIntroduction, Purpose and Terminology Gage is any device used to obtain measurements; frequently used torefer specifically to the devices used on the shop floor; includesgo/no-go devices (also, see Reference List: ASTM E456-96). Measurement System is the collection of instruments or gages,standards, operations, methods, fixtures, software, personnel,environment and assumptions used to quantify a unit of measure orfix assessmen

Alternate Approaches IV Complex Variable Range, Average & Range, ANOVA, Bias Linearity Control Charts III, IV Multiple Systems, Gages or Test Stands Control Charts ANOVA Regression Analysis III, IV Miscellaneous Alternate Approaches IV Othe