00.H1149.FM(i-viii).qxd:00.H1149.FM(i-viii).qxd 5/31/11 10:08 AM Page i Concepts for R&R Studies Second Edition 00.H1149.FM(i-viii).qxd:00.H1149.FM(i-viii).qxd 5/31/11 10:08 AM Page ii Also available from ASQ Quality Press: If Concepts for R&R Studies, Second Edition was of interest to you these publications may also be of value: An Introduction to Design of Experiments: A Simplified Approach Larry B. Barrentine Reliability Methods for Engineers K. S. Krishnamoorthi HALT, HASS & HASA Explained: Accelerated Reliability Techniques Harry W. McLean The Handbook of Applied Acceptance Sampling: Plans, Procedures, and Principles Kenneth S. Stephens Statistical Quality Control Using Excel (book plus software) Steven M. Zimmerman, PhD, and Marjorie L. Icenogle, PhD The Desk Reference of Statistical Quality Methods Mark L. Crossley Statistical Process Control Methods for Long and Short Runs, Second Edition Gary K. Griffith Glossary and Tables for Statistical Quality Control, Third Edition ASQ Statistics Division To request a complimentary catalog of ASQ Quality Press publications, call 800-248-1946, or visit our Web site at http://qualitypress.asq.org . 00.H1149.FM(i-viii).qxd:00.H1149.FM(i-viii).qxd 5/31/11 10:08 AM Page iii Concepts for R&R Studies Second Edition Larry B. Barrentine ASQ Quality Press Milwaukee, Wisconsin 00.H1149.FM(i-viii).qxd:00.H1149.FM(i-viii).qxd 5/31/11 10:08 AM Page iv Concepts for R&R Studies, Second Edition Larry B. Barrentine Library of Congress Cataloging-in-Publication Data Barrentine, Larry B., 1938– Concepts for R&R studies / Larry B. Barrentine.—2nd ed. p. cm. Includes bibliographical references and index. ISBN 0-87389-557-6 (pbk. saddle stitch : alk. paper) 1. Quality control—Statistical methods. 2. Process control—Statistical methods. 3. Mensuration. I. Title: Concepts for R&R studies. II. Title: Concepts for R and R studies. III. Title. TS156 .B43 2002 658.5'62'015195—dc21 2002010554 © 2003 by ASQ All rights reserved. No part of this book may be reproduced in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. 10 9 8 7 6 5 4 3 2 1 ISBN 0-87389-557-6 Publisher: William A. Tony Acquisitions Editor: Annemieke Koudstaal Project Editor: Craig S. Powell Production Administrator: Gretchen Trautman Special Marketing Representative: Denise M. Cawley ASQ Mission: The American Society for Quality advances individual and organizational performance excellence worldwide by providing opportunities for learning, quality improvement, and knowledge exchange. Attention Bookstores, Wholesalers, Schools, and Corporations: ASQ Quality Press books, videotapes, audiotapes, and software are available at quantity discounts with bulk purchases for business, educational, or instructional use. For information, please contact ASQ Quality Press at 800-248-1946, or write to ASQ Quality Press, P.O. Box 3005, Milwaukee, WI 53201-3005. To place orders or to request a free copy of the ASQ Quality Press Publications Catalog, including ASQ membership information, call 800-248-1946. Visit our Web site at www.asq.org or http://qualitypress.asq.org . Printed in the United States of America Printed on acid-free paper Quality Press 600 N. Plankinton Avenue Milwaukee, Wisconsin 53203 Call toll free 800-248-1946 Fax 414-272-1734 www.asq.org http://qualitypress.asq.org http://standardsgroup.asq.org E-mail: [email protected] 00.H1149.FM(i-viii).qxd:00.H1149.FM(i-viii).qxd 5/31/11 10:08 AM Page v Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2 Procedures for Performing an R&R Study . . . . . . . . . . . . . . . . . . 5 Chapter 3 Measurement Capability Indices . . . . . . . . . . . . . . . . . . . . . . . 11 Chapter 4 Planning an R&R Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Chapter 5 What Do We Do If the Results Are Unacceptable? . . . . . . . . . . . . . 23 Chapter 6 How Do I Compare R&R Results to the Device Manufacturer’s Specs? . . 25 Chapter 7 Evaluation by Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . 27 Chapter 8 What Are the Relationships of the Measurement Capability Indices and Process Capability? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Chapter 9 Examples of Problems and Procedures . . . . . . . . . . . . . . . . . . . . 37 X-Ray Gage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Electronic Width Gage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Electronic Temperature Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Sheet Flatness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Physical Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Profilometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Micrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Bore Gage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Nuclear Moisture Gage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Chapter 10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Index to Appendixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Appendix A The Standard Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 52 Appendix B Factors for Varying Sample Sizes . . . . . . . . . . . . . . . . . . . . 53 Appendix C Derivation of Repeatability and K and K Factors . . . . . . . . . . . 54 1 2 Appendix D Derivation of the Calculation of Reproducibility . . . . . . . . . . . . 57 Appendix E How to Address Variation within a Sample . . . . . . . . . . . . . . . 60 v 00.H1149.FM(i-viii).qxd:00.H1149.FM(i-viii).qxd 5/31/11 10:08 AM Page vi vi Contents Appendix F Confidence Levels in Estimating Standard Deviations . . . . . . . . . 64 Appendix G Use of Control Charts . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Appendix H Relationship of Process Capability and Measurement Capability Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Appendix I The Effect of R&R on Process Capability . . . . . . . . . . . . . . . 70 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 00.H1149.FM(i-viii).qxd:00.H1149.FM(i-viii).qxd 5/31/11 10:08 AM Page vii Preface T he intent of this manual is to provide background on the origins of the R&R methodology; help for those who work with devices that don’t fit the usual approach; and ideas for measurement devices that require innovation to assess their performance under off-line, static conditions. The initial utilization of the R&R format is only briefly described; the reader can learn more about how to apply the procedures in 10 minutes of trying them than from several pages of instruction. R&R analysis is not a com- plete measurement assessment. However, it is often easier to start with the limited scope addressed by R&R. Once the R&R is assessed, the need to study further measurement issues can be evaluated. The ultimate objective is to determine how best to improve the control and performance of a process. The reader is assumed to be familiar with basic con- trol charting methodology since assessment of statistical control of the measurement process is important. The material is presented at multiple levels. One reader may concentrate on the “how-to” sections; another may wish to consider the derivations; a third may be interested in the interrelationships of measurement and process capability. Those who are interested in a more rigorous approach should review the appendices and references. Since this manual was first published, several changes and options have evolved in the way R&R studies are analyzed. This revision updates the material in these areas: 1. The original format and procedures were based on a stand-alone form, the “GM long form.” Current availability of computer support makes the use of a prepared form unnecessary. Spreadsheets are faster and easier, providing an easily filed and maintained record. The forms that were originally so useful now simply pro- vide a sample format for spreadsheets. That format is referred to here as the “standard procedure.” vii 00.H1149.FM(i-viii).qxd:00.H1149.FM(i-viii).qxd 5/31/11 10:08 AM Page viii viii Preface 2. The original R&R assessment criterion was made against the product tolerance. Today the assessment is typically calculated against the estimate of process varia- tion. That measure is independent of the specifications and the criteria are more sta- tistically defensible. Since these two assessment techniques answer very different questions, both are presented and the advantages of each are discussed. Preference is given to the assessment against the process variation. 3. The simplest analysis method uses ranges, and that classic approach remains preferred in this manual. Statistical packages are available, however, that can do the equivalent analysis using analysis of variance (ANOVA). Such packages provide a subtle option in the model used, involving the interaction of operator and sample. The application of ANOVA techniques is discussed with an example of typical output. 4. The interrelationship of the two criteria for R&R with process capability, repre- sented by C , is shown to better illustrate the broad view needed to keep R&R p priorities in perspective. It is the author’s contention that decision making on and evaluation of measurement systems should be done in the context of process capability. The particular criterion used for measurement capability is less important than the full context of measurement and process variation. Hopefully some of the points introduced here will help in process improvement efforts. Larry B. Barrentine 8724 Warm Springs Way Knoxville, TN 37923 (865) 692-9950 1 Introduction J ust what is an “R&R” study, anyway? Well, it isn’t a study of “rest and relaxation!” R&R—repeatability and reproducibility—studies analyze the variation of measure- ments of a gage (repeatability) and the variation of measurements by operators (repro- ducibility). 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 variability, 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 con- trol. Since you can’t address something that cannot be measured precisely, the assessment of the gage becomes an early priority. Before we can continue discussing R&R, we have to define “gage.” When asked to name a gage, people typically think of micrometers, pressure gages, temperature gages, and so on. However, the term “gage” actually refers to any device used for making mea- surements. In this manual, 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 2. The operator 3. The variation within the sample Gage variability can be broken into additional components, such as: 1. Calibration (Is the gage accurate?) 2. Stability (Does the gage change over time?) 1 2 Concepts for R&R Studies 3. Repeatability (Is there variation of the gage when used by one operator in a brief time interval?) 4. Linearity (Is the gage more accurate at low values than at high values or vice versa?) Variation within a sample is a part of process variation that is often mixed with mea- surement variation. As noted, R&R studies assess reproducibility (operator variation) and repeatability (gage variation). Repeatability is the variation observed when an operator measures the same sample with the same gage several times. Reproducibility is the additional variation observed when several operators use the same gage to measure the same sample. The com- bination of both sources of variation is referred to as R&R (see Figure 1.2). Note that R&R does not address the total measurement system but is narrowly defined and is gage specific. 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 ordi- narily less significant in their impact. For that reason, R&R are often studied and quanti- fied 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 R&R studies in a fashion designed to avoid confusion with sources of variation other than repeatability (gage) and reproducibility (operator). While this manual describes how to perform R&R studies, you cannot ignore the other sources of variation for long. In partic- ular, the actual process variation is the ultimate subject to be addressed. Customers require both R&R studies and process capability. Process capability includes both process varia- tion and measurement variation. Consequently, R&R studies should be accompanied or quickly followed by evaluations of calibration, variation within the sample, and any other relevant source of variability. Variation within the sample being measured is often difficult to exclude from the R&R study. While not attributable to measurement, this source is extremely important and Observed process variation Actual process variation Measurement variation Long-term Short-term Variation Variation Variation process process within a due to due to variation variation sample operators gage Repeatability Calibration Stability Linearity Figure 1.1 Possible sources of process variation.