Statistical Quality Control for the Six Sigma Green Belt

H. Fred Walker, Bhisham C. Gupta

Description

This book is a desk reference and instructional aid for those individuals currently involved with, or preparing for involvement with, Six Sigma project teams. As Six Sigma team members, Green Belts help select, collect data for, and assist with the interpretation of a variety of statistical or quantitative tools within the context of the Six Sigma methodology. The second in a four-book series geared specifically for these Green Belt activities, this book provides a thorough discussion of statistical quality control (SQC) tools. These tools are introduced and discussed from the perspective of application rather than theoretical development. From this perspective, readers are taught to consider the SQC tools as statistical “alarm bells” that send signals when there are one or more problems with a particular process. Guidance is also given on the use of Minitab and JMP in doing these various SQC applications. In addition, examples and sample problems from all industries appear throughout the book to aid a Green Belt's comprehension of the material.

Sujets

• Business
• Qualité, hygiène, sécurité, environnement
• Sciences & Techniques
• Statistiques
• Statistiques
• Total Quality Management
• Gestion et management
• Seis Sigma
• Economics
• Minitab
• Six Sigma

Informations

• Publié par: ASQ Quality Press
• Date de parution: 30 juin 2007
• Nombre de lectures: 2
• EAN13: 9780873891622
• Langue: English
• Poids de l'ouvrage: 15 Mo

Extrait

Statistical Quality Control for the Six Sigma Green Belt

Also available from ASQ Quality Press:

Applied Statistics for the Six Sigma Green Belt Bhisham C. Gupta and H. Fred Walker

The Certified Six Sigma Green Belt Handbook Roderick A. Munro, Matthew J. Maio, Mohamed B. Nawaz, Govindarajan Ramu, and Daniel J. Zrymiak

Transactional Six Sigma for Green Belts: Maximizing Service and Manufacturing Processes Samuel E. Windsor

The Executive Guide to Understanding and Implementing Lean Six Sigma: The Financial Impact Robert M. Meisel, Steven J. Babb, Steven F. Marsh, & James P. Schlichting

Applying the Science of Six Sigma to the Art of Sales and Marketing Michael J. Pestorius

Six Sigma Project Management: A Pocket Guide Jeffrey N. Lowenthal

Six Sigma for the Next Millennium: A CSSBB Guidebook Kim H. Pries

The Certified Quality Engineer Handbook, Second Edition Roger W. Berger, Donald W. Benbow, Ahmad K. Elshennawy, and H. Fred Walker, editors

The Certified Quality Technician Handbook Donald W. Benbow, Ahmad K. Elshennawy, and H. Fred Walker

The Certified Manager of Quality/Organizational Excellence Handbook: Third Edition Russell T. Westcott, editor

Business Performance through Lean Six Sigma: Linking the Knowledge Worker, the Twelve Pillars, and Baldrige James T. Schutta

To request a complimentary catalog of ASQ Quality Press publications, call 800-248-1946, or visit our Web site at http://qualitypress.asq.org.

Statistical Quality Control for the Six Sigma Green Belt

Bhisham C. Gupta H. Fred Walker

ASQ Quality Press Milwaukee, Wisconsin

American Society for Quality, Quality Press, Milwaukee 53203 © 2007 by American Society for Quality All rights reserved. Published 2007 Printed in the United States of America 12 11 10 09 08 07 06 5 4 3 2 1

Library of Congress CataloginginPublication Data

Gupta, Bhisham C., 1942–  Statistical quality control for the Six sigma green belt / Bhisham C. Gupta and H. Fred Walker.  p. cm.  Includes index.  ISBN 978-0-87389-686-3 (hard cover : alk. paper)  1. Six sigma (Quality control standard) 2. Quality control—Statistical  methods. I. Walker, H. Fred, 1963– II. Title.

TS156.G8674 2007 658.5′62—dc22

2007000315

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.

Publisher: William A. Tony Acquisitions Editor: Matt Meinholz Project Editor: Paul OMara Production Administrator: Randall Benson

ASQ Mission: The American Society for Quality advances individual, organizational, and community excellence worldwide through 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 on acid-free paper

In loving memory of my parents, Roshan Lal and Sodhan Devi. —Bhisham

In loving memory of my father, Carl Ellsworth Walker. —Fred

Contents

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

Chapter 1 Introduction to Statistical Quality Control . . . . . . . . . . 1.1 Identifying the Tools of SQC. . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Relating SQC to Applied Statistics and to DOE . . . . . . . . . . . . 1.3 Understanding the Role of Statistics in SQC . . . . . . . . . . . . . . 1.4 Making Decisions Based on Quantitative Data . . . . . . . . . . . . . 1.5 Practical versus Theoretical or Statistical Significance. . . . . . . 1.6 Why We Cannot Measure Everything . . . . . . . . . . . . . . . . . . . . 1.7 A Word on the Risks Associated with Making Bad Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 2 Elements of a Sample Survey . . . . . . . . . . . . . . . . . . . . . 2.1 Basic Concepts of Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . Sampling Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Simple Random Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Estimation of a Population Mean and Population Total 2.2.2 Confidence Interval for a Population Mean and Population Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Determination of Sample Size . . . . . . . . . . . . . . . . . . . 2.3 Stratified Random Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Estimation of a Population Mean and Population Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Confidence Interval for a Population Mean and Population Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Determination of Sample Size . . . . . . . . . . . . . . . . . . . 2.4 Systematic Random Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Estimation of a Population Mean and Population Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

1 2 2 4 5 5 7

7

11 11 14 15 16

20 20 21

22

24 26 27

28

viii Contents

2.5

2.4.2 Confidence Interval for a Population Mean and Population Total . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Determination of Sample Size . . . . . . . . . . . . . . . . . . . Cluster Random Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Estimation of a Population Mean and Population Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Confidence Interval for a Population Mean and Population Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Determination of Sample Size . . . . . . . . . . . . . . . . . . .

Chapter 3 Phase I (Detecting Large Shifts)—SPC: Control Charts for Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Basic Definition of Quality and Its Benefits . . . . . . . . . . . . . . . 3.2 SPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Check Sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pareto Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cause-and-Effect (Fishbone or Ishikawa) Diagram . . . . . . . . . Defect Concentration Diagram. . . . . . . . . . . . . . . . . . . . . . . . . Run Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Control Charts for Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Action on Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Action on Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common Causes or Random Causes. . . . . . . . . . . . . . . . . . . . Special Causes or Assignable Causes. . . . . . . . . . . . . . . . . . . . Local Actions and Actions on the System . . . . . . . . . . . . . . . . Preparation for Use of Control Charts. . . . . . . . . . . . . . . . . . . Benefits of Control Charts. . . . . . . . . . . . . . . . . . . . . . . . . . . . Rational Samples for a Control Chart . . . . . . . . . . . . . . . . . . . ARL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OC Curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 3.3.1 ShewhartXandRControl Charts . . . . . . . . . . . . . . . . . – 3.3.2 ShewhartXandRControl Charts When Process Meanµand Process Standard DeviationσAre Known. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Shewhart Control Chart for Individual Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 3.3.4 ShewhartXandSControl Charts. . . . . . . . . . . . . . . . . 3.4 Process Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 4 Phase I (Detecting Large Shifts)—SPC: Control Charts for Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Control Charts for Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 ThepChart: Control Chart for Fraction of Nonconforming Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Limits for thepChart. . . . . . . . . . . . . . . . . . . . . . . . .

30 30 32

33

34 37

39 40 41 43 45 47 48 50 51 51 51 51 52 52 52 53 55 56 57 57 59 60

68

69 72 79

83 83

85 85

4.3

4.4

4.5

4.2.1 ThepChart: Control Chart for Fraction Nonconforming with Variable Samples . . . . . . . . . . . . ThenpChart: Control Chart for Number of Nonconforming Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Limits for thenpControl Chart. . . . . . . . . . . . . . . . . . ThecChart (Nonconformities versus Nonconforming Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TheuChart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

92 92

93 96

Chapter 5 Phase II (Detecting Small Shifts)—SPC: Cumulative Sum, Moving Average, and Exponentially Weighted Moving Average Control Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.1 Basic Concepts of the CUSUM Control Chart . . . . . . . . . . . . . 102 – CUSUM Control Chart versus ShewhartX-RControl Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.2 Designing a CUSUM Control Chart . . . . . . . . . . . . . . . . . . . . . 104 5.2.1 Two-Sided CUSUM Control Chart Using Numerical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.2.2 The Fast Initial Response Feature for the CUSUM Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.2.3 Combined Shewhart-CUSUM Control Chart . . . . . . . . 115 5.2.4 CUSUM Control Chart for Controlling Process Variability116. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 The MA Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.4 The EWMA Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Chapter 6 Process Capability Indices . . . . . . . . . . . . . . . . . . . . . . . 6.1 Development of Process Capability Indices . . . . . . . . . . . . . . . 6.2 PCIC p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 PCIC pk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 PCIC pm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 PCIC pmk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 PCIC pnst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples ComparingCwith PCIsCandC. . . . . . . . . . pnst pk pm 6.6.1 Certain Features of the Capability IndexC . . . . . . . pnst 6.7 PCIsPandP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p pk

Chapter 7 Measurement Systems Analysis . . . . . . . . . . . . . . . . . . . 7.1 Using SQC to Understand Variability . . . . . . . . . . . . . . . . . . . . Variability in the Production or Service Delivery Process . . . . Variability in the Measurement Process . . . . . . . . . . . . . . . . . . 7.2 Evaluating Measurement System Performance . . . . . . . . . . . . . 7.2.1 MSA Based on Range. . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 MSA Based on ANOVA . . . . . . . . . . . . . . . . . . . . . . . . 7.3 MCIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MCI as a Percentage of Process Variation (MCI pv ) . . . . . . . . . MCI as a Percentage of Process Specification (MCI). . . . . . ps

127 127 130 135 136 138 139 141 142 144

147 148 148 148 149 150 156 162 162 163

Contentsix