Practical Attribute and Variable

Measurement Systems Analysis (MSA)

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ASQ Quality PressMilwaukee, Wisconsin

Practical Attribute and Variable

Measurement Systems Analysis (MSA)

A Guide for Conducting Gage R&R Studies and Test Method Validations

Mark Allen Durivage

American Society for Quality, Quality Press, Milwaukee 53203 2016 by ASQAll rights reserved. Published 2015Printed in the United States of America21 20 19 18 17 16 15 5 4 3 2 1

Library of Congress Cataloging-in-Publication Data

Durivage, Mark Allen. Practical attribute and variable measurement systems analysis (MSA) : a guide for conducting gage R&R studies and test method validations / Mark Allen Durivage. pages cm Includes bibliographical references and index. ISBN 978-0-87389-915-4 (hard cover : alk. paper) 1. Acceptance sampling. 2. Quality controlStatistical methods. 3. Measurement. I. Title.

TS156.4.D87 2015 658.4'013dc23 2015021647

ISBN: 978-0-87389-915-4

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vList of Figures and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Chapter 2: The Gage R&R Study Life Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 7Chapter 3: How to Address Variation within a Sample . . . . . . . . . . . . . . . . . 13

Case A: Either We Do Not Know What to Expect or It Is Logical to Assume No Significant Variation within the Sample . . . . . . . . . . . . . . . . 13

Case B: We Know There Is Significant Variation within the Sample . . . . . . 16

Chapter 4: Performing a Traditional R&R Study . . . . . . . . . . . . . . . . . . . . . . 174.1 Performing the Traditional Gage R&R Study . . . . . . . . . . . . . . . . . . . . . 184.2 Gage R&R Traditional Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3 The Number of Distinct Categories (NDC) . . . . . . . . . . . . . . . . . . . . . . . . 24

Chapter 5: Performing an ANOVA Gage R&R Study . . . . . . . . . . . . . . . . . . 275.1 Performing the ANOVA Gage R&R Study . . . . . . . . . . . . . . . . . . . . . . . 295.2 Gage R&R ANOVA Example with Interaction . . . . . . . . . . . . . . . . . . . . 33

Results for Appraisers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Results for Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Results for Interactions (Appraisers and Parts) . . . . . . . . . . . . . . . . . . . . 38

5.3 Gage R&R ANOVA Example without Interaction . . . . . . . . . . . . . . . . . . 39Results for Appraisers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Results for Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.4 Gage R&R ANOVA Example without Appraiser . . . . . . . . . . . . . . . . . . . 41Results for Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Chapter 6: Bias, Linearity, and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.1 Bias and Linearity Graphical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.2 Bias and Linearity Analytical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.3 Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.4 Linearity Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.5 Bias Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Table of Contents

vi Table of Contents

6.6 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.7 Control Chart Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.8 X and R Control Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.9 XmR (Moving Range) Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Chapter 7: Measurement Uncertainty and Guard Banding . . . . . . . . . . . . . . 657.1 Type A and Type B Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.2 Guard Banding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.3 Guard Banding Using the Traditional Gage R&R Example . . . . . . . . . . . 677.4 Guard Banding Using the ANOVA Gage R&R Example . . . . . . . . . . . . . 68

Chapter 8: Process and Measurement Capability Indices . . . . . . . . . . . . . . . 718.1 MCI1Measurement Capability Index as a Percentage of

Process Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718.2 MCI2Measurement Capability Index as a Percentage of

Process Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 738.3 Gage R&R and Process Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 758.4 How the Indices Relate to One Another and to CP . . . . . . . . . . . . . . . . . . 768.5 Relationship between Process Capability and Measurement

Capability Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778.6 The Effect of Gage R&R on Process Capability . . . . . . . . . . . . . . . . . . . 79

MCI1 (in Proportions) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79MCI2 (in Proportions) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

8.7 Confidence Levels in Estimating Standard Deviations . . . . . . . . . . . . . . 808.8 Traditional R&R Study Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 818.9 ANOVA Gage R&R Study Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Chapter 9: Performing an Attribute Gage R&R Study . . . . . . . . . . . . . . . . . 839.1 The Short-Form Attribute Gage R&R Study . . . . . . . . . . . . . . . . . . . . . . 83

The Short-Form Attribute R&R Study Process . . . . . . . . . . . . . . . . . . . 849.2 The Short-Form Attribute R&R Study with Standards . . . . . . . . . . . . . . 85

The Short-Form Attribute R&R Study with Standards Process . . . . . . . 869.3 Attribute R&R Study with Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

The Attribute R&R Study with Standards Process . . . . . . . . . . . . . . . . . 899.4 Attribute R&R Study Using Cohens Kappa Statistic . . . . . . . . . . . . . . . . 93

Attribute R&R Study Using Cohens Kappa Statistic Process . . . . . . . . 939.5 Attribute R&R Study Using Fleisss Kappa Statistic . . . . . . . . . . . . . . . . 98

The Attribute R&R Study Using Fleisss Kappa Statistic Process . . . . . 98

Chapter 10: When the Results Are Unacceptable . . . . . . . . . . . . . . . . . . . . . . 105Chapter 11: Special Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

11.1 X-Ray Gage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10711.2 Electronic Width Gage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10811.3 Electronic Temperature Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10811.4 Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Table of Contents vii

11.5 Sheet Flatness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11011.6 Physical (Destructive) Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11111.7 Profilometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11111.8 Micrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11211.9 Scales and Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Case A: Short-Term Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Case B: Long-Term Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

11.10 Bore Gage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11411.11 Nuclear Moisture Gage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Chapter 12: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Appendix A: Control Chart Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Appendix B: C2 Correction Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Appendix C: Selected Percentages of the F-Distribution . . . . . . . . . . . . . . . . 123Appendix D: Critical Values of the Correlation Coefficient . . . . . . . . . . . . . . 127Appendix E: Students t-Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Appendix F: Guard Banding Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Appendix G: Gage R&R Study Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Appendix H: Gage R&R Study Audit Checklist . . . . . . . . . . . . . . . . . . . . . . . 139Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

ix

Figure 1.1 Possible sources of process variation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Repeatability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 1.3 Reproducibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 1.4 Repeatability, reproducibility, and R&R. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Figure 1.5 Measurement system Pythagorean relationship. . . . . . . . . . . . . . . . . . . . . . 5Figure 2.1 Gage R&R study life cycle considerations. . . . . . . . . . . . . . . . . . . . . . . . . . 7Figure 3.1 Actual repeatability, within-sample variation, and observed

repeatability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Table 4.1 Forbidden area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 4.1 Traditional gage R&R template. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 4.2 Completed traditional gage R&R template. . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 4.3 Range chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Table 4.2 Gage acceptability criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 4.4 Relationship between the number of distinct categories and the

corresponding gage R&R values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Table 5.1 Forbidden area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 5.1 Two-Way ANOVA data sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Table 5.2 Two-way ANOVA summary table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Table 5.3 Two-way ANOVA variance table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 5.2 Completed two-way ANOVA data sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 5.3 Range chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 5.4 Decision limit appraisers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Table 5.4 Completed two-way ANOVA summary table. . . . . . . . . . . . . . . . . . . . . . . . 37Table 5.5 Completed two-way ANOVA variance table. . . . . . . . . . . . . . . . . . . . . . . . 37Figure 5.5 Decision limit parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 5.6 Decision limit interaction (appraisers and parts). . . . . . . . . . . . . . . . . . . . . 38Table 5.6 Gage acceptability criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 5.7 Decision limit appraisers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Table 5.7 Completed two-way ANOVA summary table without interaction. . . . . . . . 40Table 5.8 Completed two-way ANOVA variance table without interaction. . . . . . . . . 40

List of Figures and Tables

x List of Figures and Tables

Figure 5.8 Decision limit parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 5.9 Decision limit parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Table 5.9 Completed two-way ANOVA summary table without appraiser. . . . . . . . . 42Table 5.10 Completed two-way ANOVA variance table without appraiser. . . . . . . . . . 42Figure 6.1 Relationship between the target value, accuracy, and precision. . . . . . . . . . 45Figure 6.2 Accuracy versus precision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Figure 6.3 Bias and linearity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Table 6.1 Reference parts versus measured parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 6.4 Linearity plot for the example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Table 6.2 Summary data table for the example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Figure 6.5 Relative degrees of correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 6.6 Decision limit for linearity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Figure 6.7 Decision limit for bias. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 6.8 Bias and linearity plot for the example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 6.9 Stable and unstable variation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 6.10 Control chart interpretation rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Table 6.3 Data for X and R chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 6.11 X-bar and R chart example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Table 6.4 Data for XmR chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 6.12 XmR chart example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 7.1 Type A and B measurement uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 7.2 Guard banding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 7.3 Consumers and producers risk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 7.4 Traditional gage R&R guard banding results. . . . . . . . . . . . . . . . . . . . . . . . 68Figure 7.5 ANOVA gage R&R guard banding results. . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 8.1 Gage R&R as a proportion of process variation. . . . . . . . . . . . . . . . . . . . . . 72Table 8.1 Gage acceptability criteria for the MCI1 index. . . . . . . . . . . . . . . . . . . . . . . 73Figure 8.2 Gage R&R as a proportion of the tolerance. . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 8.3 Errors caused by gage R&R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Table 8.2 Gage acceptability criteria for the MCI2 index. . . . . . . . . . . . . . . . . . . . . . . 75Figure 8.4 Distortion of Cp for MCI1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Figure 8.5 Distortion of Cp for MCI2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Figure 8.6 Relationship of Cp and measurement capability indices. . . . . . . . . . . . . . . . 77Figure 8.7 Cp contours for MCI1 and MCI2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 8.8 Precision in estimating the standard deviation as a function of degrees

of freedom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 9.1 Short-form attribute R&R study template. . . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure 9.2 Sample selection distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

List of Figures and Tables xi

Figure 9.3 Completed short-form attribute R&R study. . . . . . . . . . . . . . . . . . . . . . . . . 86Figure 9.4 Short-form attribute R&R study with standards template. . . . . . . . . . . . . . 87Table 9.1 Gage acceptability criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Figure 9.5 Completed short-form attribute R&R study with standards. . . . . . . . . . . . . 88Table 9.2 Attribute R&R study with standards acceptability table. . . . . . . . . . . . . . . 89Figure 9.6 Attribute R&R study with standards template. . . . . . . . . . . . . . . . . . . . . . . 90Figure 9.7 Attribute R&R study with standards results table. . . . . . . . . . . . . . . . . . . . 92Figure 9.8 Attribute R&R study using Cohens kappa statistic template. . . . . . . . . . . . 94Figure 9.9 Cohens kappa statistic contingency table. . . . . . . . . . . . . . . . . . . . . . . . . . . 95Table 9.3 Gage acceptability criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Figure 9.10 Completed attribute R&R study using Cohens kappa statistic

template. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Figure 9.11 Attribute R&R study using Fleisss kappa statistic template. . . . . . . . . . . . 98Table 9.4 Interpreting the Fleisss kappa statistic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Figure 9.12 Completed attribute R&R study using Fleisss kappa statistic. . . . . . . . . . . 101Table G.1 Gage R&R acceptance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Table G.2 Gage acceptability criteria (short form). . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Table G.3 Gage acceptability criteria with standard. . . . . . . . . . . . . . . . . . . . . . . . . . . 136Table G.4 Gage acceptability criteria (Cohens kappa statistic). . . . . . . . . . . . . . . . . . 136Table G.5 Gage acceptability criteria (Fleisss kappa statistic). . . . . . . . . . . . . . . . . . . 137

xiii

This booka result of 30 years of quality-related work experiencewas written to aid quality technicians and engineers. To that end, the intent of this book is to provide the quality professional working in virtually any industry a quick, con-venient, and comprehensive guide to properly conducting measurement systems analy-sis (MSA).

The purpose of this book is to provide background and examples on the application of gage R&R methodology (test method validation) for variable and attribute data, help for those who work with devices that dont fit the usual approach, and ideas for measure-ment devices that require innovation to assess their performance under off-line, static conditions. The ultimate objective is to ensure the measurement system is suitable for its intended purpose and capable of consistently providing valid measurements so that one may effectively control and ultimately improve the performance of a process. The reader is assumed to be familiar with basic control charting methodology since assessment of statistical control of the measurement process is important.

One may wonder why performing a gage R&R is so important; the simple answers are profit, public health, and safety. Companies that are shipping product that is out of specification can be subjected to expensive litigation, especially in the aviation, pharma-ceutical, and medical device industries.

It is the authors contention that decision making on and evaluation of measurement systems should be done in the context of a systems approach. The particular criterion used for measurement capability is less important than the full context of measurement and process variation.

This book will be a useful reference when preparing for and taking many of the ASQ quality certification examinations, including the Certified Quality Technician (CQT), Certified Calibration Technician (CCT), Certified Quality Inspector (CQI), Certified Six Sigma Green Belt (CSSGB), Certified Quality Engineer (CQE), Certified Six Sigma Black Belt (CSSBB), and Certified Reliability Engineer (CRE).

Preface

xv

I would like to acknowledge the previous work of Larry B. Barrentine in Concepts for R&R Studies. This book is an expansion of his efforts and an attempt to continue his style of presenting R&R studies in a simple, easy-to-follow style. I would like to thank those who have inspired, taught, and trained me throughout my academic and pro-fessional career. I also wish to recognize my friend, colleague, author of Implementing ISO/IEC 17024:2005, and fellow ASQ Fellow Bhavan Bob Mehta, principal consul-tant at GMP & ISO Expert Services, for lending his expertise in reviewing this book for accuracy and content. ASQs reviewers T. Gourishankar and Autumn Farrell also pro-vided invaluable insight and detailed feedback. A special thanks to my friend and col-league Joshua Ball for lending his expertise and experience in developing the sample study procedure and sample audit checklist included in the appendixes. Additionally, I would like to thank ASQ Quality Press, especially Matt Meinholz, Acquisitions Editor, and Paul OMara, Managing Editor, for their expertise and technical competence, which made this project a reality. Lastly, I would like to acknowledge the patience of my wife Dawn and my sons Jack and Sam, who allowed me time to research and write Practical Attribute and Variable Measurement Systems Analysis (MSA): A Guide for Conducting Gage R&R Studies and Test Method Evaluations.

LiMiT oF LiAbiLiTy/DiSCLAiMer oF WArrAnTy

The author has put forth his best efforts in compiling the content of this book; however, no warranty with respect to the materials accuracy or completeness is made. Addition-ally, no warranty is made in regard to applying the recommendations made in this book to any business structure or environments. Businesses should consult regulatory, quality, and/or legal professionals prior to deciding on the appropriateness of advice and recom-mendations made within this book. The author shall not be held liable for loss of profit or other commercial damages resulting from the employment of recommendations made within this book, including special, incidental, consequential, or other damages.

Acknowledgments

1Gage R&Rrepeatability and reproducibilitystudies analyze the variation of measurements of a gage (repeatability) and the variation of measurements by operators (reproducibility). Gage R&R studies are also referred to as test method validation (TMV) in the Food and Drug Administration (FDA)regulated industries. To understand why this is so important, recall that the goal of process control is reduction of variation in the process and, ultimately, the product. To address actual process variabil-ity, the variation due to the measurement system must be identified and separated from that of the process. Studies of measurement variation are a waste of time and money unless they lead to action to reduce process variation and improve process control. Since you can not address something that can not be measured precisely, the assessment of the gage becomes an early priority during the design and development and transfer phases prior to commercial production.

Before we can continue discussing gage R&R, we have to define gage. The term gage actually refers to any device used for making measurements. In this book, the terms gage and device are used interchangeably and refer to any device or equipment for making a measurement.

Every observation of a process contains both actual process variation and measure-ment variation (Figure 1.1). In the case of measurement systems, the sources are: 1. The gage/device.

a. Calibrationis the gage accurate?

b. Stabilitydoes the gage change over time?

2. The operatordoes the operator have the necessary skill and training?

3. Within-sample variationvariation within a sample is a part of process variation that is often mixed with measurement variation.

4. Repeatabilitythe variation observed when an operator measures the same sample using the same gage several times.

5. Reproducibilitythe additional variation observed when several operators use the same gage to measure the same sample.

6. Linearityis the gage more accurate at low values than at high values, or vice versa?

1Introduction

2 Chapter One

7. Biasis there a shift of the average measurements from the reference value?

8. Discriminationis the gage sensitive enough to measure the part?

Gage R&R studies assess reproducibility (operator variation) and repeatability (gage variation). Repeatability is the variation observed when an operator measures the same sample using the same gage several times (see Figure 1.2).

Figure 1.1 Possible sources of process variation.

Observed process variation

Measurement variation

BiasLinearityStabilityCalibrationRepeatability

Actual process variation

Short-termprocessvariation

Variationwithin asample

Variationdue to

operators(Reproducibility)

Variationdue togage

Long-termprocessvariation

Figure 1.2 Repeatability.

Measurements

Repeatability

Introduction 3

Reproducibility is the additional variation observed when several operators use the same gage to measure the same sample (see Figure 1.3). The combination of both sources of variation is referred to as gage R&R (see Figure 1.4). Note that gage R&R does not address the total measurement system but is narrowly defined and is gage specific.

Figure 1.3 Reproducibility.

Appraiser averages

Appraiser A

Appraiser CAppraiser B

Figure 1.4 Repeatability, reproducibility, and R&R.

Distribution of repeated measurements on the same part by one operator with the same gage

Repeatability

Distribution of theaverages of manyoperators using thesame gage

Reproducibility

The combined effect ofgage variation amongoperators

R&R

+

=

4 Chapter One

The exclusion of the other potential sources of measurement variation does not imply that calibration, stability, or linearity are unimportant; it is just that those sources are ordinarily less significant in their impact. For that reason, gage R&R are often studied and quantified first. In order to improve them, you must address the key measurement process variables via procedures, standards, training, and appropriate studies. We plan and execute gage R&R studies in a fashion designed to avoid confusion with sources of variation other than repeatability (gage) and reproducibility (operator). While this man-ual describes how to perform gage R&R studies, you can not ignore the other sources of variation for long. In particular, the actual process variation is the ultimate subject to be addressed. Customers require both gage R&R studies and process capability. Process capability includes both process variation and measurement variation. Consequently, gage R&R studies should be accompanied or quickly followed by evaluations of calibra-tion, variation within the sample, and any other relevant source of variability.

Variation within the sample being measured is often difficult to exclude from the gage R&R study. While not attributable to measurement, this source is extremely important and should always be pursued with diligence. It not only has relevance to understanding gage R&Rs but also provides vital information on how to gain process capability improvements.

A specific example of variation within the sample is apparent in measurements of surface texture by a profilometer. The test piece itself is sufficiently variable that if the measurement is made at a random position, the variation within the sample will inflate the estimate of repeatability. It is necessary to identify and measure this vari-ability within the sample; but this alone is not identified by a gage R&R study. The key point is to make certain that process variability within the sample does not intrude on the gage R&R study if it can, or must, be avoided. Determination of an unsatisfactory gage R&R should always lead to an evaluation of whether variation within the sample is part of the problem.

The impact of any environmental conditions also needs to be evaluated. This is more appropriately addressed by designed experiments. Prior to conducting gage R&R studies, an effort is made to block out such sources of variation during the devel-opment phase.

It is necessary to introduce the mathematical version of Figure 1.4 since this relationship is used repeatedly. To add distributions, one must add the variances, or 2s, of the distributions being added. If the distributions, or spread, due to repeatabil-ity and reproducibility can be characterized by their respective sigmas (Repeatability and Reproducibility), then combining these distributions as in Figure 1.2 results in the following distribution for gage R&R:

= + R&R2

Repeatability2

Reproducibility2

The sigma for gage R&R is the square root of this expression. This same Pythagorean relationship will be used to relate the process variation to the measurement system vari-ation and the part variation (see Figure 1.5).

Introduction 5

Throughout this book there are several examples that are fully worked out using a simple scientific calculator. If the examples are worked using a spreadsheet or a com-mercially available software package, the results can and will vary. The differences are attributed to rounding errors. Although there are differences, essentially the same results and conclusions will be obtained.

Figure 1.5 Measurement system Pythagorean relationship.

2Process = 2Part = 2GRR

where 2Process = Process variation 2Part = Part variation 2GRR = Measurement system variation

2Process

2Part

2GRR

149

Aaccuracy, versus precision, 45ANOVA gage R&R study, 2743

example with interaction, 3339example without appraiser, 4143example without interaction, 3941guard banding using, 68MCI in, example, 82steps in performing, 2933

appraiser variation (AV), 17appraisers

in gage R&R study, 8, 17results for, in ANOVA gage R&R

with interaction, 36without interaction, 39

attribute gage R&R study, performing, 83103short-form, 8385short-form with standards, 8589

attribute measurements, in gage R&R study, 78

attribute R&R study using Cohens kappa statistic, 9397

attribute R&R study using Fleisss kappa statistic, 98103

attribute R&R study with standards, 8993

Bbalances, and scales, 11314bias, 2

definition, 45and linearity, 46

analytical method, 4749graphical method, 47

relationships with linearity and stability, 4561

bias test, 54bore gage, 11415

Ccalibration, in gage R&R study, 8, 109, 11314chemical analysis, 10910Cohens kappa statistic, attribute R&R study

using, 9397common cause variation, 56confidence levels, in estimating standard

deviations, 8081consumers risk, 67control chart constants (Appendix A), 119control charts, interpretation, 5657correlation analysis, 4952correlation coefficient, 4952

critical values of (Appendix D), 127C2 correction factors (Appendix B), 121

Ddestructive tests, 111device. See gagediscrimination, measurement, 2

in gage R&R study, 10distributions, in gage R&R, 4

Eelectronic temperature equipment, 1089electronic width gage, 108environmental conditions, in gage R&R study, 9equipment variation (EV), 1718

Ffalse alarms, 8993F-distribution, selected percentages of (Appendix

C), 12325

Index

150 Index

Fleisss kappa statistic, attribute R&R study using, 98103

Food and Drug Administration (FDA), 1

Ggage

definition, 1number of, in gage R&R study, 11as source of variation, 1

gage R&R (repeatability and reproducibility), 14definition, 1, 19effect on process capability, 7980and process capability, 75

gage R&R studyattribute, performing, 83103attribute with standards, 8993audit checklist, example (Appendix H), 139frequency of, 11importance of performing, xiiilife cycle, 711performing ANOVA, 2743performing traditional, 1725procedure, example (Appendix G), 13337short-form attribute, 8385short-form attribute with standards, 8589special considerations in, 10716within-sample variation in, addressing, 1316

guard banding, 6567and measurement uncertainty, 6568table (Appendix F), 13132using ANOVA gage R&R example, 68using traditional gage R&R example, 67

Iinteractions (appraisers and parts), results for, in

ANOVA gage R&R, 3839

Lleak rate, 8993linearity, 1

and bias, 46analytical method, 4749graphical method, 47

definition, 45relationships with bias and stability, 4561

linearity test, 5253lower limit of detection (LLD), 110lower limit of quantification (LLOQ), 110

MMcCune, Duncan C., 80MCI1 (percentage of process variation), 10, 7173

effect on process capability, 79MCI2 (percentage of process specifications), 10,

7375effect on process capability, 7980

measurement, considerations in gage R&R study, 10

measurement capability indices, 7182relationship between, and with Cp, 7677,

7778measurement discrimination, in gage R&R study,

10measurement systems, sources of variation in, 12measurement systems analysis (MSA),

introduction to, 15measurement uncertainty, and guard banding,

6568micrometers, 11213moisture gage, nuclear, 11516MR (moving range) chart, 61

Nnuclear moisture gage, 11516number of distinct categories (NDC), 2425

Oone-sided tolerances, in gage R&R study, 10operator

in gage R&R study, 8as source of variation, 1

Pparts, results for, in ANOVA gage R&R

with interaction, 36without appraiser, 41without interaction, 39

physical tests, 111planning, in gage R&R study, 711precision, versus accuracy, 45process capability (Cp)

effect of gage R&R on, 7980and gage R&R, 75, 106relationship to measurement capability

indices, 7677, 7778process capability indices, 7182

Index 151

producers risk, 67profilometers, 11112

RR chart, 27range method, of gage R&R study, 17, 27reference parts, 47repeatability, 1, 2, 38, 105reproducibility, 1, 2, 3, 105results

in gage R&R study, analyzing, 10unacceptable, understanding, 1056

root cause analysis (RCA), 28

Ssample selection strategy, in gage R&R study, 9samples, in gage R&R study, 8scales, and balances, 11314sheet flatness, 11011short-form attribute R&R study, 8385short-form attribute R&R study with standards,

8589special cause variation, 56special causes, in gage R&R study, identifying, 11stability, 5556

definition, 45relationships with bias and linearity, 4561

standard deviations, confidence levels in estimating, 8081

Students t-distribution (Appendix E), 12930Students t-test, 5254

Ttest method validation (TMV), 1tolerances, one-sided, in gage R&R study, 10traditional gage R&R, guard banding using, 67

traditional variables R&R study, 1725example, 2124MCI in, example, 8182steps in performing, 1821

trials, in gage R&R study, 9, 17two-way ANOVA, in gage R&R study, 28

Uuncertainty

in measurement, and guard banding, 6568type A, 65type B, 65

upper limit of detection (ULOD), 110upper limit of quantification (ULOQ), 110

Vvariable data, in gage R&R study, 78variation

in measurement systems, sources of, 12in process, 1See also within-sample variation

Wwithin-sample variation, 1, 4

addressing, in gage R&R study, 1316case A: no significant variation, 1316case B: significant variation present, 16

minimizing, in gage R&R study, 9

XX chart, 61X-bar and R charts, 5760XmR (moving range) charts, 61X-ray gage, 1078

Title pageCIP dataTable of ContentsList of Figures and TablesPrefaceAcknowledgmentsChapter 1: IntroductionIndex