Certified Black Belt Handbook Chapter

T C S S B B H S E

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Also available from ASQ Quality Press: The Certified Six Sigma Green Belt Handbook Roderick A. Munro, Matthew J. Maio, Mohamed B. Nawaz, Govindarajan Ramu, and Daniel J. Zrymiak Six Sigma for the New Millennium: A CSSBB Guidebook, Second Edition Kim H. Pries 5S for Service Organizations and Offices: A Lean Look at Improvements Debashis Sarkar The Executive Guide to Understanding and Implementing Lean Six Sigma: The Financial Impact Robert M. Meisel, Steven J. Babb, Steven F. Marsh, and James P. Schlichting Applied Statistics for the Six Sigma Green Belt Bhisham C. Gupta and H. Fred Walker Statistical Quality Control for the Six Sigma Green Belt Bhisham C. Gupta and H. Fred Walker Six Sigma for the Office: A Pocket Guide Roderick A. Munro Lean-Six Sigma for Healthcare: A Senior Leader Guide to Improving Cost and Throughput, Second Edition Chip Caldwell , Greg Butler, and Nancy Poston. Defining and Analyzing a Business Process: A Six Sigma Pocket Guide Jeffrey N. Lowenthal Six Sigma for the Shop Floor: A Pocket Guide Roderick A. Munro Six Sigma Project Management: A Pocket Guide Jeffrey N. Lowenthal Transactional Six Sigma for Green Belts: Maximizing Service and Manufacturing Processes Samuel E. Windsor Lean Kaizen: A Simplified Approach to Process Improvements George Alukal and Anthony Manos A Lean Guide to Transforming Healthcare: How to Implement Lean Principles in Hospitals, Medical Offices, Clinics, and Other Healthcare Organizations Thomas G. Zidel To request a complimentary catalog of ASQ Quality Press publications, call 800-248-1946, or visit our Web site at http://www.asq.org/quality-press.

H1325_Kubiak_BOOK.indb ii

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T C S S B B H S E

T. M. Kubiak Donald W. Benbow

ASQ Quality Press Milwaukee, Wisconsin

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American Society for Quality, Quality Press, Milwaukee 53203 © 2009 by American Society for Quality All rights reserved. Published 2009 Printed in the United States of America 14 13 12 11 10 09 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data Kubiak, T.M. The certified six sigma black belt handbook / T.M. Kubiak and Donald W. Benbow.—2nd ed. p. cm. ISBN 978-0-87389-732-7 (alk. paper) 1. Quality control—Statistical methods—Handbooks, manuals, etc. I. Benbow, Donald W., 1936– II. Title. TS156.B4653 2008 658.4’013--dc22 2008042611 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 www.asq.org/quality-press. Portions of the input and output contained in this publication/book are printed with permission of Minitab Inc. All material remains the exclusive property and copyright of Minitab Inc. All rights reserved. Printed on acid-free paper

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For Jaycob, my grandson: This world is changing with each passing day—sometimes for the better, sometimes not. I will strive to carry your burdens until you are able to do so for yourself. May you always be blessed with the best that life has to offer and always strive to improve not just your life but the lives of others. On life’s journey you will confront challenges that may seem impossible, but always know my strength and support will forever be with you. There will be many twists and turns, but always be faithful to your own values and convictions. Know that if you live life fully, you will surely achieve your dreams. I will always be there to help you find your way, but only you have the strength to spread your wings, soar high, and find your yellow brick road. When you follow your own path, there will be no limits to what you can accomplish. —T. M. Kubiak

For my grandchildren Sarah, Emily, Dana, Josiah, Regan, Alec, Marah, and Liam. —Donald W. Benbow

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Table of Contents

List of Figures and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preface to the Second Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preface to the First Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Part I

Enterprise-Wide Deployment . . . . . . . . . . . . . . . . . . . . . . . . .

xv xxiii xxv xxvii

1

Chapter 1 Enterprise-Wide View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . History of Continuous Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Value and Foundations of Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Value and Foundations of Lean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integration of Lean and Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Business Processes and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Six Sigma and Lean Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 2 6 7 8 9 10

Chapter 2 Leadership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enterprise Leadership Responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Organizational Roadblocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Change Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Six Sigma Projects and Kaizen Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Six Sigma Roles and Responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14 14 14 15 16 17

Part II

21

Organizational Process Management and Measures . . . .

Chapter 3 Impact on Stakeholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impact on Stakeholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22 22

Chapter 4 Critical to x (CTx) Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Critical to x (CTx) Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24 24

Chapter 5 Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26 26

Chapter 6 Business Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Business Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28 28

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Chapter 7 Financial Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common Financial Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32 32

Part III

37

Team Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 8 Team Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Team Types and Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Team Roles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Team Member Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Launching Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38 38 39 40 41

Chapter 9 Team Facilitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Team Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Team Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Team Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42 42 43 44

Chapter 10 Team Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Team Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46 46

Chapter 11 Time Management for Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time Management for Teams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49 49

Chapter 12 Team Decision-Making Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Team Decision-Making Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50 50

Chapter 13 Management and Planning Tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . Management and Planning Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52 52

Chapter 14 Team Performance Evaluation and Reward . . . . . . . . . . . . . . . . . . . Team Performance Evaluation and Reward . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58 58

Part IV

61

Define . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 15 Voice of the Customer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Customer Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Customer Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Customer Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62 62 63 64

Chapter 16 Project Charter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Project Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Goals and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Project Performance Measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71 71 72 73 74

Chapter 17 Project Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Project Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75 75

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Part V

Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

79

Chapter 18 Process Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input and Output Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Flow Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Analysis Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80 80 81 83

Chapter 19 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Types of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sampling Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Collecting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90 90 91 92 93

Chapter 20 Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement Systems Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement Systems in the Enterprise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95 95 97 118 119

Chapter 21 Basic Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graphical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Valid Statistical Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

122 122 123 126 129 137

Chapter 22 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commonly Used Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

138 138 148 158

Chapter 23 Process Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Capability Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Performance Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short-Term and Long-Term Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Capability for Non-Normal Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Capability for Attributes Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Capability Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Performance vs. Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

167 167 171 173 174 175 176 178

Part VI

Analyze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 24 Measuring and Modeling Relationships between Variables . . . . Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multivariate Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multi-Vari Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Attributes Data Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 25 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statistical vs. Practical Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sample Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Point and Interval Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tests for Means, Variances, and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Variance (ANOVA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Goodness-of-Fit (Chi Square) Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Non-Parametric Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

230 230 231 231 234 244 255 259 261 264

Chapter 26 Failure Mode and Effects Analysis (FMEA). . . . . . . . . . . . . . . . . . . Failure Mode and Effects Analysis (FMEA) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

278 278

Chapter 27 Additional Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gap Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Root Cause Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Waste Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

283 283 284 290

Part VII

293

Improve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 28 Design of Experiments (DOE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Planning Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . One-Factor Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Level Fractional Factorial Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . Full Factorial Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

294 294 297 309 311 319 325

Chapter 29 Waste Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Waste Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

332 332

Chapter 30 Cycle-Time Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cycle-Time Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

337 337

Chapter 31 Kaizen and Kaizen Blitz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kaizen and Kaizen Blitz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

342 342

Chapter 32 Theory of Constraints (TOC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory of Constraints (TOC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

344 344

Chapter 33 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

347 347

Chapter 34 Risk Analysis and Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Risk Analysis and Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

351 351

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Part VIII

Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

357

Chapter 35 Statistical Process Control (SPC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selection of Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rational Subgrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Chart Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Chart Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

358 358 360 360 361 389

Chapter 36 Other Control Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total Productive Maintenance (TPM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Visual Factory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

400 400 401

Chapter 37 Maintain Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement System Re-analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

403 403 406

Chapter 38 Sustain Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lessons Learned. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Training Plan Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Documentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ongoing Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

408 408 409 410 411

Part IX Design for Six Sigma (DFSS) Frameworks and Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

413

Chapter 39 Common DFSS Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DMADV (Define, Measure, Analyze, Design, and Validate) . . . . . . . . . . . . . . DMADOV (Define, Measure, Analyze, Design, Optimize, and Validate) . . .

414 414 415

Chapter 40 Design for X (DFX) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design for X (DFX) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

416 416

Chapter 41 Robust Design and Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robust Design and Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

418 418

Chapter 42 Special Design Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Strategic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tactical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

424 424 426

Part X

431

Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix 1

ASQ Code of Ethics (May 2005) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

433

Appendix 2A ASQ Six Sigma Black Belt Certification Body of Knowledge (2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

434

Appendix 2B ASQ Six Sigma Black Belt Certification Body of Knowledge (2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

447

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Table of Contents

Appendix 3

Control Chart Combinations for Measurement Data . . . . . . . . . .

460

Appendix 4

Control Chart Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

462

Appendix 5

Constants for A7, B7, and B8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

465

Appendix 6

Factors for Estimating σX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

470

Appendix 7

Control Charts Count Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

471

Appendix 8

Binomial Distribution Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

472

Appendix 9

Cumulative Binomial Distribution Table . . . . . . . . . . . . . . . . . . . .

476

Appendix 10

Poisson Distribution Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

481

Appendix 11

Cumulative Poisson Distribution Table . . . . . . . . . . . . . . . . . . . .

489

Appendix 12

Standard Normal Distribution Table . . . . . . . . . . . . . . . . . . . . . . .

496

Appendix 13

Cumulative Standard Normal Distribution Table . . . . . . . . . . .

499

Appendix 14 t Distribution Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

502

Appendix 15

Chi-Square Distribution Table . . . . . . . . . . . . . . . . . . . . . . . . . . . .

504

Appendix 16 F(0.99) Distribution Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

507

Appendix 17 F(0.975) Distribution Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

511


515


519


523


527

Appendix 22 F(0.025) Distribution Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

531


535

Appendix 24

Median Ranks Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

539

Appendix 25

Normal Scores Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

543

Appendix 26

Factors for One-Sided Tolerance Limits . . . . . . . . . . . . . . . . . . . .

546

Appendix 27

Factors for Two-Sided Tolerance Limits . . . . . . . . . . . . . . . . . . . .

550

Appendix 28

Equivalent Sigma Levels, Percent Defective, and PPM . . . . . . .

554

Appendix 29 Critical Values for the Mann-Whitney Test Table (One-Tail, Alpha = 0.05) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

556

Appendix 30 Critical Values for the Mann-Whitney Test Table (One-Tail, Alpha = 0.01) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

557

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xiii

Appendix 31 Critical Values for the Mann-Whitney Test Table (Two-Tail, Alpha = 0.025) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

558

Appendix 32 Critical Values for the Mann-Whitney Test Table (Two-Tail, Alpha = 0.005) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

559

Appendix 33

Critical Values for the Wilcoxon Signed-Rank Test . . . . . . . . . .

560

Appendix 34

Glossary of Six Sigma and Related Terms . . . . . . . . . . . . . . . . . .

561

Appendix 35

Glossary of Japanese Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

600

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

603 609

CD-ROM Contents Sample Examination Questions for Parts I–IX Certified Six Sigma Black Belt—Simulated Exam

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List of Figures and Tables

Part I Table 1.1

Some approaches to quality over the years. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

Figure 1.1

Example of a process flowchart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

Figure 1.2

Relationship among systems, processes, subprocesses, and steps.. . . . . . . . .

11

Figure 4.1

Example of a CTQ tree diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

Figure 7.1

Traditional quality cost curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

Figure 7.2

Modern quality cost curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

Figure 9.1

Team stages.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

Figure 10.1

Team obstacles and solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

Figure 12.1

Example of a force field analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Figure 13.1

Example of an affinity diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

Figure 13.2

Example of an interrelationship digraph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

Figure 13.3

Example of a tree diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

Figure 13.4

Example of a prioritization matrix—first step. . . . . . . . . . . . . . . . . . . . . . . . . .

55

Figure 13.5

Example of a prioritization matrix—second step. . . . . . . . . . . . . . . . . . . . . . . .

55

Figure 13.6

Example of a matrix diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

Figure 13.7

Example of a PDPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

Figure 13.8

Example of an AND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

Figure 15.1

CTQ flow-down. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

Figure 15.2

Example of a CTQ flow-down. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

Figure 15.3

Example of a QFD matrix for an animal trap. . . . . . . . . . . . . . . . . . . . . . . . . . .

67

Figure 15.4

Map of the entries for the QFD matrix illustrated in Figure 15.3. . . . . . . . . . .

68

Figure 15.5

Kano model for customer satisfaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

Figure 17.1

Project network diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

Figure 17.2

Example of a Gantt chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

Part II

Part III

Part IV

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Part V Figure 18.1

Process diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

Figure 18.2

Example of a SIPOC form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

Figure 18.3

Generic process flowchart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

Figure 18.4

Process flowchart and process map example. . . . . . . . . . . . . . . . . . . . . . . . . . .

84

Figure 18.5

Example of written procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

Figure 18.6

Example of work instructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

Figure 18.7

Example of the symbology used to develop a value stream map. . . . . . . . . .

87

Figure 18.8

Example of a value stream map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

Figure 18.9

Example of a spaghetti diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

Figure 18.10 Example of a circle diagram.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

Figure 20.1

Accuracy versus precision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

Figure 20.2

Blank GR&R data collection sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

101

Figure 20.3

GR&R data collection sheet with data entered and calculations completed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

103

Figure 20.4

Blank GR&R report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

105

Figure 20.5

GR&R report with calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

106

Figure 20.6

Gage R&R Study—ANOVA method: source tables. . . . . . . . . . . . . . . . . . . . . .

108

Figure 20.7

Gage R&R study—ANOVA method: components of variation. . . . . . . . . . . . – Minitab session window output of the R&R study—X/R method: source tables for Example 20.3.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – – Graphical results of the GR&R study—X/R method: X and R control charts by operators (appraisers) for Example 20.3. . . . . . . . . . . . . . . .

109

Figure 20.8 Figure 20.9 Table 20.1

110 110

Attribute agreement analysis—data for Example 20.4. . . . . . . . . . . . . . . . . . .

111

Figure 20.10 Minitab session window output for Example 20.4. . . . . . . . . . . . . . . . . . . . . . .

113

Figure 20.11 Graphical results of the attribute agreement analysis for Example 20.4. . . . .

115

Table 20.2

117

Attribute gage study—data for Example 20.5. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 20.12 Graphical results of the attribute gage analysis for Example 20.5. . . . . . . . . .

117

Table 21.1

122

Commonly used symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 21.1

Dot plot for a simple population of three numbers. . . . . . . . . . . . . . . . . . . . . .

123

Table 21.2

Sampling distribution of the mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123

Figure 21.2

Dot plot of the sample means from Table 21.2. . . . . . . . . . . . . . . . . . . . . . . . . .

124

Figure 21.3

Example of a histogram from a large non-normal looking population.. . . . .

124

Figure 21.4

Examples of the impact of the CLT when sampling from various populations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

125

Figure 21.5

Example of a data set as illustrated by a frequency distribution, a dot plot, and a histogram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

126

Table 21.3

Summary of descriptive measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

128

Figure 21.6

Example of a cumulative frequency distribution in table and graph form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

128

Table 21.4

A comparison of various graphical methods. . . . . . . . . . . . . . . . . . . . . . . . . . .

129

Figure 21.7

Stem-and-leaf diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

130

Figure 21.8

Box plot with key points labeled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131

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Figure 21.9

Examples of box plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131

Figure 21.10 Example of a multiple box plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

132

Figure 21.11 Example of a run chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

133

Table 21.5

Data for scatter diagrams shown in Figure 21.12. . . . . . . . . . . . . . . . . . . . . . . .

134

Figure 21.12 Examples of scatter diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

134

Figure 21.13 Example of the use of normal probability graph paper. . . . . . . . . . . . . . . . . . .

136

Figure 21.14 Example of a normal probability plot.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

136

Figure 22.1

Venn diagram illustrating the probability of event A. . . . . . . . . . . . . . . . . . . .

139

Figure 22.2

Venn diagram illustrating the complementary rule of probability. . . . . . . . .

139

Figure 22.3

Venn diagram illustrating the addition rule of probability with independent events A and B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

140

Figure 22.4

Venn diagram illustrating the general version of the addition rule of probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

141

Table 22.1

Example of a contingency table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

141

Table 22.2

Contingency table for Examples 22.4–22.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

142

Table 22.3

Summary of the rules of probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

147

Table 22.4

Summary of formulas, means, and variances of commonly used distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

149

Figure 22.5

Standard normal distribution for Example 22.14. . . . . . . . . . . . . . . . . . . . . . . .

150

Figure 22.6

Standard normal distribution for Example 22.15. . . . . . . . . . . . . . . . . . . . . . . .

151

Figure 22.7

Poisson distribution with mean λ = 4.2 for Example 22.16. . . . . . . . . . . . . . . .

153

Figure 22.8

Binomial distribution with n = 6 and p = 0.1428 for Example 22.17.. . . . . . .

155

Figure 22.9

Example of a chi-square distribution with various degrees of freedom. . . . .

156

Figure 22.10 Example of a t distribution with various degrees of freedom. . . . . . . . . . . . .

157

Figure 22.11 Example of an F distribution with various degrees of freedom. . . . . . . . . . . .

158

Table 22.5

Summary of formulas, means, and variances of other distributions. . . . . . . .

159

Figure 22.12 Hypergeometric distribution for Example 22.18. . . . . . . . . . . . . . . . . . . . . . . .

161

Figure 22.13 Exponential distribution for Example 22.19. . . . . . . . . . . . . . . . . . . . . . . . . . . .

163

Figure 22.14 Lognormal distribution for Example 22.20. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

164

Figure 22.15 Example of a Weibull function for various values of the shape parameter β. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

166

Table 23.1

Cable diameter data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

170

Figure 23.1

Example of a process capability analysis using the data given in Table 23.1.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

171

Methods of determining the standard deviation for use in process capability indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

174

Binomial probabilities for Example 23.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

176

Table 23.2 Table 23.3

Part VI Figure 24.1

Examples of different types of correlations. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

185

Table 24.1

Data for Example 24.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

185

Figure 24.2

Graphical depiction of regression concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

190

Figure 24.3

Scatter diagram developed from the data given in Table 24.1. . . . . . . . . . . . .

191

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xviii List of Figures and Tables

Figure 24.4

Scatter diagram from Figure 24.3 with two proposed lines. . . . . . . . . . . . . . .

191

Table 24.2

Computed values for the proposed lines in Figure 24.4. . . . . . . . . . . . . . . . . .

192

Table 24.3

Computed values for the proposed lines given in Figure 24.4 with residual values added. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

192

Residual values for the least squares regression line from Example 24.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

194

Table 24.5

Census data for Examples 24.10 and 24.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

198

Figure 24.5

Example of a principal components analysis using the data given in Table 24.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

199

Figure 24.6

Scree plot for Examples 24.10 and 24.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

199

Figure 24.7

Example of a factor analysis using the data given in Table 24.5.. . . . . . . . . . .

200

Table 24.6

Salmon data for Example 24.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

201

Figure 24.8

Example of a discriminant analysis using the data given in Table 24.6.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

203

Table 24.7

Plastic film data for Example 24.13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

205

Figure 24.9

Table 24.4

Example of MANOVA using the data given in Table 24.7. . . . . . . . . . . . . . . .

205

Figure 24.10 Stainless steel casting with critical ID.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

209

Figure 24.11 Data collection sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

210

Table 24.8

Casting data for Example 24.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

211

Figure 24.12 Multi-vari chart of data from Table 24.8.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

212

Figure 24.13 Multi-vari chart of data from Table 24.8 with the means of each factor connected by lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

212

Table 24.9

Casting data for Example 24.14 with precision parts. . . . . . . . . . . . . . . . . . . .

213

Figure 24.14 Multi-vari chart of data from Table 24.9 with the means of each factor connected by lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

214

Figure 24.15 Multi-vari chart of data from Table 24.9.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

215

Table 24.10

Casting data for Example 24.14 after pressure wash. . . . . . . . . . . . . . . . . . . . .

216

Figure 24.16 Multi-vari chart of data from Table 24.10.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

217

Table 24.11

Resting pulse data for Example 24.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

219

Figure 24.17 Minitab session window output for the binary logistic regression based on data given in Table 24.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

221

Figure 24.18 Delta chi-square versus probability analysis for Example 24.15. . . . . . . . . . .

222

Figure 24.19 Delta chi-square versus leverage analysis for Example 24.15. . . . . . . . . . . . . .

223

Table 24.12

Favorite subject data for Example 24.16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

224

Figure 24.20 Minitab session window output for the nominal logistic regression based on data given in Table 24.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

225

Table 24.13

Toxicity data for Example 24.17.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

227

Figure 24.21 Minitab session window output for the ordinal logistic regression based on data given in Table 24.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

228

Figure 25.1

Four outcomes associated with statistical hypotheses. . . . . . . . . . . . . . . . . . . .

231

Table 25.1

Sample size formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

232

Table 25.2

Confidence intervals for means. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

238

Table 25.3

Confidence intervals for variances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

240

Table 25.4

Confidence intervals for proportions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

242

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xix

Table 25.5

Hypothesis tests for means. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

245

Table 25.6

Hypothesis tests for variances or ratios of variances. . . . . . . . . . . . . . . . . . . . .

249

Table 25.7

Hypothesis tests for proportions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

251

Figure 25.2

Hypothesis test flowchart (part 1).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

253

Figure 25.3


254

Figure 25.4


255

Table 25.8

Example of a one-way ANOVA source table. . . . . . . . . . . . . . . . . . . . . . . . . . . .

257

Table 25.9

Moisture content data for Example 25.12.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

257

Table 25.10

Completed one-way ANOVA source table for the data given in Table 25.9.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

258

Table 25.11

Example of a two-way ANOVA source table. . . . . . . . . . . . . . . . . . . . . . . . . . .

259

Table 25.12

Historical data of defect types along with current data from a randomly selected week for Example 25.13. . . . . . . . . . . . . . . . . . . . . . . . . . . .

260

Table 25.13

Goodness-of-fit table for Example 25.13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

261

Table 25.14

The general form of a two-way contingency table. . . . . . . . . . . . . . . . . . . . . . .

262

Table 25.15

Observed frequencies of defectives for Example 25.14. . . . . . . . . . . . . . . . . . .

262

Table 25.16

Computation of the expected frequencies for Example 25.14. . . . . . . . . . . . . .

263

Table 25.17

Comparison of parametric and non-parametric hypothesis tests. . . . . . . . . .

264

Table 25.18

Common non-parametric hypothesis tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

265

Table 25.19

Data for Mood’s Median test in Example 25.15. . . . . . . . . . . . . . . . . . . . . . . . .

268

Table 25.20

Computation of the expected frequencies for Example 25.15. . . . . . . . . . . . . .

268

Table 25.21

Data for Levene’s test for Example 25.16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

270

Table 25.22

Levene’s test for Example 25.16.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

271

Table 25.23

Levene’s test for Example 25.16 (continued). . . . . . . . . . . . . . . . . . . . . . . . . . . .

271

Table 25.24


272

Table 25.25


272

Table 25.26

Data for Kruskal-Wallis test for Example 25.17.. . . . . . . . . . . . . . . . . . . . . . . . .

273

Table 25.27

Determining ranks for Example 25.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

274

Table 25.28

Kruskal-Wallis test for Example 25.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

275

Table 25.29

Data for Mann-Whitney test for Example 25.18. . . . . . . . . . . . . . . . . . . . . . . . .

276

Table 25.30

Determining ranks for Example 25.18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

277

Table 25.31

Mann-Whitney test for Example 25.18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

277

Figure 26.1

Example of a PFMEA form.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

279

Figure 26.2

Example of a DFMEA form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

280

Figure 27.1

Example of a blank cause-and-effect diagram. . . . . . . . . . . . . . . . . . . . . . . . . .

285

Figure 27.2

Example of a cause-and-effect diagram after a few brainstorming steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

286

Figure 27.3

Example of a Pareto chart for defects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

286

Table 27.1

Cost to correct each defect type. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

287

Figure 27.4

Example of a Pareto chart for defects weighted by the cost to correct. . . . . .

288

Figure 27.5

Basic FTA symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

289

Figure 27.6

Example of stoppage of agitation in a tank. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

290

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xx


Part VII Table 28.1 Table 28.2

A 23 full factorial data collection sheet for Example 28.1. . . . . . . . . . . . . . . . . .

296

3

A 2 full factorial data collection sheet with data entered for Example 28.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

296

Table 28.3

A 2 full factorial data collection sheet with run averages. . . . . . . . . . . . . . . .

300

Figure 28.1

Graph of the main effects for the data given in Table 28.3. . . . . . . . . . . . . . . .

302

Table 28.4

A 2 full factorial design using the + and – format. . . . . . . . . . . . . . . . . . . . . .

303

Table 28.5

A 23 full factorial design showing interaction columns. . . . . . . . . . . . . . . . . . .

304

3

Figure 28.2

Graph of the interaction effects for the data given in Table 28.3. . . . . . . . . . .

305

Table 28.6

Half fraction of 23 (also called a 23–1 design). . . . . . . . . . . . . . . . . . . . . . . . . . . .

305

Table 28.7

Half fraction of 23 with completed interaction columns. . . . . . . . . . . . . . . . . .

306

Table 28.8

A 24 full factorial design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

308

Table 28.9

A 24–1 fractional factorial design with interactions. . . . . . . . . . . . . . . . . . . . . . .

308

Table 28.10

Statistical models for common experimental designs. . . . . . . . . . . . . . . . . . . .

312

Table 28.11

Examples of source tables for the models given in Table 28.10. . . . . . . . . . . .

314

Table 28.12

Sums of squares for the models given in Table 28.10. . . . . . . . . . . . . . . . . . . . .

315

Table 28.13

Examples of Latin squares from each main class up to order 5. . . . . . . . . . . .

316

Table 28.14

Latin square analysis for Example 28.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

317

Table 28.15

Completed Latin square source table for Example 28.8.. . . . . . . . . . . . . . . . . .

319

Table 28.16

A 24–1 fractional factorial for Example 28.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

320

Table 28.17

Session window from Minitab for the data given in Table 28.16. . . . . . . . . . .

321

Table 28.18

Minitab main effects plot for the analysis given in Table 28.17. . . . . . . . . . . .

323

Table 28.19

Minitab interaction effects plot for the analysis given in Table 28.17. . . . . . .

324

Table 28.20

Minitab analysis of residuals for the data given in Table 28.16. . . . . . . . . . . .

325

Table 28.21

Relevant tables for two-way full factorial design. . . . . . . . . . . . . . . . . . . . . . . .

326

Table 28.22

Data for a 22 full factorial experiment with three replicates. . . . . . . . . . . . . . .

329

Table 28.23

Session window results for the data given in Table 28.22. . . . . . . . . . . . . . . . .

329

Table 28.24

Main effects plot for the data given in Table 28.22. . . . . . . . . . . . . . . . . . . . . . .

330

Table 28.25

Interaction plot for the data given in Table 28.22. . . . . . . . . . . . . . . . . . . . . . . .

330

Table 28.26

Residual plots for the data given in Table 28.22. . . . . . . . . . . . . . . . . . . . . . . . .

331

Figure 32.1

The Drum-Buffer-Rope subordinate step analogy—no rope. . . . . . . . . . . . . .

345

Figure 32.2

The Drum-Buffer-Rope subordinate step analogy—with rope. . . . . . . . . . . .

345

Figure 32.3

The interdependence of throughput, inventory, and operating expense measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

346

Figure 33.1

Example of a ranking matrix with criteria weights shown. . . . . . . . . . . . . . . .

347

Table 34.1

Data for Example 34.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

352

Table 34.2

Data for Example 34.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

352

Figure 34.1

SWOT analysis for Example 34.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

353

Figure 34.2

PEST analysis for Example 34.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

354

Figure 35.1

Function of SPC tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

359

Figure 35.2

Conveyor belt in chocolate-making process. . . . . . . . . . . . . . . . . . . . . . . . . . . .

361

Part VIII

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Figure 35.3

Figure 35.5

Conveyor belt in chocolate-making process with rational subgroup choice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – – Data for Examples 35.1 and 35.2—X – R and X – s charts, respectively. . . . . – X – R chart for data given in Table 35.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – X – s chart for data given in Table 35.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 35.2

Data for Example 35.3—individual and moving range chart. . . . . . . . . . . . . .

Table 35.1 Figure 35.4

xxi

361 363 364 365 367

Figure 35.6

Individual and moving range chart for data given in Table 35.2. . . . . . . . . . .

367

Table 35.3

Data for Example 35.4—p chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

369

Figure 35.7

p chart for data given in Table 35.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

370

Table 35.4

Data for Example 35.5—np chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

371

Figure 35.8

np chart for data given in Table 35.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

372

Table 35.5

Data for Example 35.6—c chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

373

Figure 35.9

c chart for data given in Table 35.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

374

Table 35.6

Data for Example 35.7—u chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

375

Figure 35.10 u chart for data given in Table 35.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

376

Figure 35.11 Short-run SPC decision flowchart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

377

Table 35.7

Summary of formulas for short-run SPC charts. . . . . . . . . . . . . . . . . . . . . . . . .

378

Table 35.8

Short-run chart data for Example 35.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

382

Table 35.9

MAMR data for Example 35.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

386

Figure 35.12 Moving average chart of length three from Example 35.9. . . . . . . . . . . . . . . .

388

Figure 35.13 Moving average range chart of length three from Example 35.9. . . . . . . . . . .

388

Table 35.10

Interpreting control chart out-of-control conditions used by Minitab. . . . . .

391

Figure 35.14 Example of out-of-control condition #1 from Minitab. . . . . . . . . . . . . . . . . . . .

392


392


393


393


394


394


395


395

Figure 35.22 Example of out-of-control condition #1 from AIAG.. . . . . . . . . . . . . . . . . . . . .

396


396


397


397


398


398

Figure 37.1

Example of an acceptable level of variation due to the measurement system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

404

Figure 37.2

Example of an unacceptable level of variation due to the measurement system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

405

Figure 37.3

Example of two different formats for control plans. . . . . . . . . . . . . . . . . . . . . .

406

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xxii List of Figures and Tables

Part IX Figure 41.1

Nonlinear response curve with input noise. . . . . . . . . . . . . . . . . . . . . . . . . . . .

419

Figure 41.2

Nonlinear response curve showing the impact on Q of input noise at P1.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

419

Figure 41.3

Nonlinear response curve showing the impact on Q of input noise at P1, P2, and P3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

420

Figure 41.4

Using a response curve to determine tolerance. . . . . . . . . . . . . . . . . . . . . . . . .

421

Figure 41.5

Conventional stack tolerance dimensioning. . . . . . . . . . . . . . . . . . . . . . . . . . . .

421

Figure 42.1

Example of a product family matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

426

Figure 42.2

First step in forming a Pugh matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

429

Figure 42.3

Second step in forming a Pugh matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

429

Figure 42.4

Third step in forming a Pugh matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

430

Figure 42.5

Final step in forming a Pugh matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

430

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Preface to the Second Edition

I

n the spirit of customer-supplier relationships, we are pleased to provide our readers with the second edition of The Certified Six Sigma Black Belt Handbook. The handbook has been updated to reflect the most recent Six Sigma Black Belt Body of Knowledge, released in 2007. As with all ASQ certification–based handbooks, the primary audience for this work is the individual who plans to prepare to sit for the Six Sigma Black Belt certification examination. Therefore, the book assumes the individual has the necessary background and experience in quality and Six Sigma. Concepts are dealt with briefly but facilitated with practical examples. We have intentionally avoided theoretical discussion unless such a discussion was necessary to communicate a concept. As always, readers are encouraged to use additional sources when seeking much deeper levels of discussion. Most of the citations provided in the references will be helpful in this regard. A secondary audience for the handbook is the quality and Six Sigma professional who would like a relevant Six Sigma reference book. With this audience in mind, we have greatly expanded the appendices section: • Although the Body of Knowledge was updated in 2007, we have elected to keep the 2001 Body of Knowledge so that readers can compare changes and perhaps offer recommendations for future Bodies of Knowledge. • All tables were developed using a combination of Microsoft Excel and Minitab 15. Thus, the reader may find some differences between our tables and those published in other sources. Appendices 29–33 are examples of where such differences might occur. Note that years ago many statistical tables were produced either by hand or by using rudimentary calculators. These tables have been handed down from author to author and have remained largely unchanged. Our approach was to revert to the formulas and algorithms that produced the tables and then redevelop them using statistical software. • The table for control constants has been expanded to now include virtually all control constants. To the best of our knowledge, this handbook is probably the only reference source that includes this information.

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xxiv Preface to the Second Edition

• Tables for both cumulative and noncumulative forms of the most useful distributions are now present—for example, binomial, Poisson, and normal. • Additional alpha values in tables have been included. For example, large alpha values for the left side of the F distribution now exist. Thus, it will no longer be necessary to use the well-known conversion property of the distribution to obtain critical F values associated with higher alpha values. Though the conversion formula is straightforward, everyone seems to get it wrong. We expect our readers will appreciate this. • The glossary has grown significantly. Most notable is the inclusion of more terms relating to Lean. • A second glossary has been added as well. This short glossary is limited to the most common Japanese terms used by quality and Six Sigma professionals. We are confident that readers will find the above additions useful. As you might expect, chapter and section numbering follows the same method used in the Six Sigma Black Belt Body of Knowledge. This has made for some awkward placement of discussions (for example, the normal distribution is referred to several times before it is defined), and in some cases, redundancy of discussion exists. However, where possible, we have tried to reference the main content in the handbook and refer the reader there for the primary discussion. After the first edition was published, we received several comments from readers who stated that their answers did not completely agree with those given in the examples. In many instances, we found that discrepancies could be attributed to the following: use of computers with different bits, the number of significant digits accounted for by the software used, the sequence in which the arithmetic was performed, and the propagation of errors due to rounding or truncation. Therefore, we urge the reader to carefully consider the above points as the examples are worked. However, we do recognize that errors occasionally occur and thus have established a SharePoint site that will permit readers to recommend suggestions, additions, corrections, or deletions, as well as to seek out any corrections that may have been found and published. The SharePoint site address is http://asqgroups. asq.org/cssbbhandbook/. Finally, the enclosed CD contains supplementary problems covering each chapter and a simulated exam that has problems distributed among chapters according to the scheme published in the Body of Knowledge. It is suggested that the reader study a particular chapter, repeating any calculations independently, and then do the supplementary problems for that chapter. After attaining success with all chapters, the reader may complete the simulated exam to confirm mastery of the entire Six Sigma Black Belt Body of Knowledge. —The Authors

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Preface to the First Edition

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e decided to number chapters and sections by the same method used in the Body of Knowledge (BOK) specified for the Certified Six Sigma Black Belt examination. This made for some awkward placement (the normal distribution is referred to several times before it is defined), and in some cases, redundancy. We thought the ease of access for readers, who might be struggling with some particular point in the BOK, would more than balance these disadvantages. The enclosed CD contains supplementary problems covering each chapter and a simulated exam that has problems distributed among chapters according to the scheme published in the Body of Knowledge. It is suggested that the reader study a particular chapter, repeating any calculations independently, and then do the supplementary problems for that chapter. After attaining success with all chapters, the reader may complete the simulated exam to confirm mastery of the entire Six Sigma Black Belt Body of Knowledge. —The Authors

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Acknowledgments

W

e would like to express our deepest appreciation to Minitab Inc., for providing us with the use of Minitab 15 and Quality Companion 2 software and for permission to use several examples from Minitab 15 and forms from Quality Companion 2. This software was instrumental in creating and verifying examples used throughout the book. In addition we would like to thank the ASQ management and Quality Press staffs for their outstanding support and exceptional patience while we prepared this second edition. Finally, we would like to thank the staff of Kinetic Publishing Services, LLC, for applying their finely tuned project management, copyediting, and typesetting skills to this project. Their support has allowed us to produce a final product suitable for the ASQ Quality Press family of publications. —The Authors

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Part I Chapter 1 Chapter 2

Enterprise-Wide View Leadership

Part I

Enterprise-Wide Deployment

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Chapter 1 Part I.A.1

Enterprise-Wide View

HISTORY OF CONTINUOUS IMPROVEMENT Describe the origins of continuous improvement and its impact on other improvement models. (Remember) Body of Knowledge I.A.1

Most of the techniques found in the Six Sigma toolbox have been available for some time, thanks to the groundbreaking work of many professionals in the quality sciences. Walter A. Shewhart worked at the Hawthorne plant of Western Electric, where he developed and used control charts. He is sometimes referred to as the father of statistical quality control (SQC) because he brought together the disciplines of statistics, engineering, and economics. He describes the basic principles of SQC in his book Economic Control of Quality of Manufactured Product (1931). He was the first honorary member of the American Society for Quality (ASQ). W. Edwards Deming developed a list of 14 points in which he emphasized the need for change in management structure and attitudes. As stated in his book Out of the Crisis (1986), these 14 points are as follows: 1. Create constancy of purpose for improvement of product and service. 2. Adopt a new philosophy. 3. Cease dependence on inspection to achieve quality. 4. End the practice of awarding business on the basis of price tag alone. Instead, minimize total cost by working with a single supplier. 5. Improve constantly and forever every process for planning, production, and service. 6. Institute training on the job. 7. Adopt and institute leadership. 8. Drive out fear. 9. Break down barriers between staff areas. 2


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10. Eliminate slogans, exhortations, and targets for the workforce. 11. Eliminate numerical quotas for the workforce and numerical goals for management.

13. Institute a vigorous program of education and self-improvement for everyone.

Part I.A.1

12. Remove barriers that rob people of pride of workmanship. Eliminate the annual rating or merit system.

14. Put everybody in the company to work to accomplish the transformation. Joseph M. Juran pursued a varied career in management beginning in 1924 as an engineer, executive, government administrator, university professor, labor arbitrator, corporate director, and consultant. He developed the Juran trilogy, three managerial processes—quality planning, quality control, and quality improvement—for use in managing for quality. Juran wrote hundreds of papers and 12 books, including Juran’s Quality Control Handbook (1999), Juran’s Quality Planning & Analysis for Enterprise Quality (with F. M. Gryna; 2007), and Juran on Leadership for Quality (2003). His approach to quality improvement includes the following points: • Create awareness of the need and opportunity for improvement • Mandate quality improvement; make it a part of every job description • Create the infrastructure: Establish a quality council; select projects for improvement; appoint teams; provide facilitators • Provide training in how to improve quality • Review progress regularly • Give recognition to the winning teams • Propagandize the results • Revise the reward system to enforce the rate of improvement • Maintain momentum by enlarging the business plan to include goals for quality improvement Deming and Juran worked in both the United States and Japan to help businesses understand the importance of continuous process improvement. Philip B. Crosby, who originated the zero defects concept, was an ASQ honorary member and past president. He wrote many books, including Quality Is Free (1979), Quality without Tears (1984), Let’s Talk Quality (1990), and Leading: The Art of Becoming an Executive (1990). Crosby’s 14 steps to quality improvement are as follows: 1. Make it clear that management is committed to quality 2. Form quality improvement teams with representatives from each department 3. Determine how to measure where current and potential quality problems lie


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4

Part I: Enterprise-Wide Deployment

4. Evaluate the cost of quality and explain its use as a management tool 5. Raise the quality awareness and personal concern of all employees

Part I.A.1

6. Take formal actions to correct problems identified through previous steps 7. Establish a committee for the zero defects program 8. Train all employees to actively carry out their part of the quality improvement program 9. Hold a “zero defects day” to let all employees realize that there has been a change 10. Encourage individuals to establish improvement goals for themselves and their groups 11. Encourage employees to communicate to management the obstacles they face in attaining their improvement goals 12. Recognize and appreciate those who participate 13. Establish quality councils to communicate on a regular basis 14. Do it all over again to emphasize that the quality improvement program never ends Armand V. Feigenbaum originated the concept of total quality control in his book Total Quality Control (1991), first published in 1951. The book has been translated into many languages, including Japanese, Chinese, French, and Spanish. Feigenbaum is an ASQ honorary member and served as ASQ president for two consecutive terms. He lists three steps to quality: 1. Quality leadership 2. Modern quality technology 3. Organizational commitment Kaoru Ishikawa (1985) developed the cause-and-effect diagram. He worked with Deming through the Union of Japanese Scientists and Engineers (JUSE). The following points summarize Ishikawa’s philosophy: • Quality first—not short-term profit first. • Consumer orientation—not producer orientation. Think from the standpoint of the other party. • The next process is your customer—breaking down the barrier of sectionalism. • Using facts and data to make presentations—utilization of statistical methods. • Respect for humanity as a management philosophy—full participatory management. • Cross-function management.


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Table 1.1

Some approaches to quality over the years.

Quality approach

Approximate time frame

Short description

Quality circles

1979–1981

Quality improvement or self-improvement study groups composed of a small number of employees (10 or fewer) and their supervisor. Quality circles originated in Japan, where they are called quality control circles.

Statistical process control (SPC)

Mid-1980s

The application of statistical techniques to control a process. Also called “statistical quality control.”

ISO 9000

1987–present

A set of international standards on quality management and quality assurance developed to help companies effectively document the quality system elements to be implemented to maintain an efficient quality system. The standards, initially published in 1987, are not specific to any particular industry, product, or service. The standards were developed by the International Organization for Standardization (ISO), a specialized international agency for standardization composed of the national standards bodies of 91 countries. The standards underwent major revision in 2000 and now include ISO 9000:2005 (definitions), ISO 9001:2008 (requirements), and ISO 9004:2000 (continuous improvement).

Reengineering

1996–1997

A breakthrough approach involving the restructuring of an entire organization and its processes.

Benchmarking

1988–1996

An improvement process in which a company measures its performance against that of best-in-class companies, determines how those companies achieved their performance levels, and uses the information to improve its own performance. The subjects that can be benchmarked include strategies, operations, processes, and procedures.

1990s–present

A management concept that helps managers at all levels monitor their results in their key areas.

Balanced Scorecard

Part I.A.1

Genichi Taguchi taught that any departure from the nominal or target value for a characteristic represents a loss to society. He also popularized the use of fractional factorial experiments and stressed the concept of robustness. In addition to these noted individuals, Toyota Motor Company has been recognized as the leader in developing the concept of lean manufacturing systems. Various approaches to quality have been in vogue over the years, as shown in Table 1.1.

Continued


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6


Part I.A.2

Table 1.1

Some approaches to quality over the years. Continued

Quality approach

Approximate time frame

Baldrige Award Criteria

1987–present

An award established by the U.S. Congress in 1987 to raise awareness of quality management and recognize U.S. companies that have implemented successful quality management systems. Two awards may be given annually in each of six categories: manufacturing company, service company, small business, education, health care, and nonprofit. The award is named after the late secretary of commerce Malcolm Baldrige, a proponent of quality management. The U.S. Commerce Department’s National Institute of Standards and Technology manages the award, and ASQ administers it.

Six Sigma

1995–present

As described in Chapter 1.

Lean manufacturing

2000–present

As described in Chapter 1.

Lean-Six Sigma

2002–present

This approach combines the individual concepts of Lean and Six Sigma and recognizes that both are necessary to effectively drive sustained improvement.

Short description

VALUE AND FOUNDATIONS OF SIX SIGMA Describe the value of Six Sigma, its philosophy, history, and goals. (Understand) Body of Knowledge I.A.2

A wide range of companies have found that when the Six Sigma philosophy is fully embraced, the enterprise thrives. What is this Six Sigma philosophy? Several definitions have been proposed, with the following common threads: • Use of teams that are assigned well-defined projects that have direct impact on the organization’s bottom line. • Training in statistical thinking at all levels and providing key people with extensive training in advanced statistics and project management. These key people are designated “Black Belts.” • Emphasis on the DMAIC approach to problem solving: define, measure, analyze, improve, and control. • A management environment that supports these initiatives as a business strategy. The literature is replete with examples of projects that have returned high dollar amounts to the organizations involved. Black Belts are often required to manage


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four projects per year for a total of $500,000–$5,000,000 in contributions to the company’s bottom line. Opinions on the definition of Six Sigma differ:

Part I.A.3

• Philosophy—The philosophical perspective views all work as processes that can be defined, measured, analyzed, improved, and controlled (DMAIC). Processes require inputs and produce outputs. If you control the inputs, you will control the outputs. This is generally expressed as the y = f(x) concept. • Set of tools—Six Sigma as a set of tools includes all the qualitative and quantitative techniques used by the Six Sigma expert to drive process improvement. A few such tools include statistical process control (SPC), control charts, failure mode and effects analysis, and process mapping. Six Sigma professionals do not totally agree as to exactly which tools constitute the set. • Methodology—The methodological view of Six Sigma recognizes the underlying and rigorous approach known as DMAIC. DMAIC defines the steps a Six Sigma practitioner is expected to follow, starting with identifying the problem and ending with implementing long-lasting solutions. While DMAIC is not the only Six Sigma methodology in use, it is certainly the most widely adopted and recognized. • Metrics—In simple terms, Six Sigma quality performance means 3.4 defects per million opportunities (accounting for a 1.5-sigma shift in the mean). In the first edition of this book, we used the following to define Six Sigma: Six Sigma is a fact-based, data-driven philosophy of improvement that values defect prevention over defect detection. It drives customer satisfaction and bottom-line results by reducing variation and waste, thereby promoting a competitive advantage. It applies anywhere variation and waste exist, and every employee should be involved. However, going forward, we combined the definitions of Lean and Six Sigma and proffer a definition for Lean-Six Sigma. This is discussed in detail in Section I.A.4.

VALUE AND FOUNDATIONS OF LEAN Describe the value of Lean, its philosophy, history, and goals. (Understand) Body of Knowledge I.A.3

The term “lean thinking” refers to the use of ideas originally employed in lean manufacturing to improve functions in all departments of an enterprise. The National Institute of Standards and Technology (NIST), through its Manufacturing Extension Partnership, defines Lean as follows:


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8


Part I.A.4

A systematic approach to identifying and eliminating waste (non-value-added activities) through continuous improvement by flowing the product at the pull of the customer in pursuit of perfection. ASQ defines the phrase “non-value-added” as follows: A term that describes a process step or function that is not required for the direct achievement of process output. This step or function is identified and examined for potential elimination. This represents a shift in focus for manufacturing engineering, which has traditionally studied ways to improve value-added functions and activities (for example, how can this process run faster and more precisely). Lean thinking doesn’t ignore the valued-added activities, but it does shine the spotlight on waste. A discussion of various categories of wastes is provided in the waste analysis section of Chapter 27. Lean manufacturing seeks to eliminate or reduce these wastes by use of the following: • Teamwork with well-informed cross-trained employees who participate in the decisions that impact their function • Clean, organized, and well-marked work spaces • Flow systems instead of batch and queue (that is, reduce batch size toward its ultimate ideal, one) • Pull systems instead of push systems (that is, replenish what the customer has consumed) • Reduced lead times through more efficient processing, setups, and scheduling The history of lean thinking may be traced to Eli Whitney, who is credited with spreading the concept of part interchangeability. Henry Ford, who went to great lengths to reduce cycle times, furthered the idea of lean thinking, and later, the Toyota Production System (TPS) packaged most of the tools and concepts now known as lean manufacturing.

INTEGRATION OF LEAN AND SIX SIGMA Describe the relationship between Lean and Six Sigma. (Understand) Body of Knowledge I.A.4

After reading the description in the last few paragraphs of Section I.A.2, Six Sigma purists will be quick to say, “You’re not just talking about Six Sigma; you’re talking about Lean too.” The demarcation between Six Sigma and Lean has blurred. We are hearing about terms such as “Lean-Six Sigma” with greater frequency because process improvement requires aspects of both approaches to attain positive results.


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Part I.A.5

Six Sigma focuses on reducing process variation and enhancing process control, whereas Lean—also known as lean manufacturing—drives out waste (non-value-added) and promotes work standardization and flow. Six Sigma practitioners should be well versed in both. More details of what is sometimes referred to as lean thinking are given in Chapters 29–33. Lean and Six Sigma have the same general purpose of providing the customer with the best possible quality, cost, delivery, and a newer attribute, nimbleness. There is a great deal of overlap, and disciples of both disagree as to which techniques belong where. Six Sigma Black Belts need to know a lot about Lean (witness the appearance of lean topics in the Body of Knowledge for Black Belt certification). The two initiatives approach their common purpose from slightly different angles: • Lean focuses on waste reduction, whereas Six Sigma emphasizes variation reduction • Lean achieves its goals by using less technical tools such as kaizen, workplace organization, and visual controls, whereas Six Sigma tends to use statistical data analysis, design of experiments, and hypothesis tests The most successful users of implementations have begun with the lean approach, making the workplace as efficient and effective as possible, reducing the (now) eight wastes, and using value stream maps to improve understanding and throughput. When process problems remain, the more technical Six Sigma statistical tools may be applied. One thing they have in common is that both require strong management support to make them the standard way of doing business. Some organizations have responded to this dichotomy of approaches by forming a Lean-Six Sigma problem-solving team with specialists in the various aspects of each discipline but with each member cognizant of others’ fields. Task forces from this team are formed and reshaped depending on the problem at hand. Given the earlier discussion, we believe a combined definition is required and proffer the following: Lean-Six Sigma is a fact-based, data-driven philosophy of improvement that values defect prevention over defect detection. It drives customer satisfaction and bottom-line results by reducing variation, waste, and cycle time, while promoting the use of work standardization and flow, thereby creating a competitive advantage. It applies anywhere variation and waste exist, and every employee should be involved.

BUSINESS PROCESSES AND SYSTEMS Describe the relationship among various business processes (design, production, purchasing, accounting, sales, etc.) and the impact these relationships can have on business systems. (Understand) Body of Knowledge I.A.5


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10


Part I.A.6

Number of hours

Calculate gross pay

Over $100?

Yes

Deduct tax No

Hourly rate

Deduct Social Security

Print check

Figure 1.1

Example of a process flowchart.

Processes A process is a series of steps designed to produce products and/or services. A process is often diagrammed with a flowchart depicting inputs, the path that material or information follows, and outputs. An example of a process flowchart is shown in Figure 1.1. Understanding and improving processes is a key part of every Six Sigma project. The basic strategy of Six Sigma is contained in DMAIC. These steps constitute the cycle Six Sigma practitioners use to manage problem-solving projects. The individual parts of the DMAIC cycle are explained in Chapters 15–38.

Business Systems A business system is designed to implement a process or, more commonly, a set of processes. Business systems make certain that process inputs are in the right place at the right time so that each step of the process has the resources it needs. Perhaps most importantly, a business system must have as its goal the continual improvement of its processes, products, and services. To this end, the business system is responsible for collecting and analyzing data from the process and other sources that will help in the continual incremental improvement of process outputs. Figure 1.2 illustrates relationships among systems, processes, subprocesses, and steps. Note that each part of a system can be broken into a series of processes, each of which may have subprocesses. The subprocesses may be further broken into steps.

SIX SIGMA AND LEAN APPLICATIONS Describe how these tools are applied to processes in all types of enterprises: manufacturing, service, transactional, product and process design, innovation, etc. (Understand) Body of Knowledge I.A.6


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Systems

Part I.A.6

Processes

Subprocesses

Steps

Figure 1.2

Relationship among systems, processes, subprocesses, and steps.

The most successful implementations of Lean and Six Sigma have an oversight group with top management representation and support. This group defines and prioritizes problems and establishes teams to solve them. The oversight group is responsible for maintaining a systemic approach. It also provides the training, support, recognition, and rewards for teams. The following are examples of problems that would be assigned to teams: • A number of customers of an accounting firm have complained about the amount of time the firm takes to perform an audit. The oversight group forms a team consisting of three auditors (one of them a lead auditor), two cost accountants, and two representatives from the firm’s top customers. The oversight group asks the team to determine if the lead time is indeed inordinate and to propose measures that will reduce it. The team begins by benchmarking (see Chapter 5) a customer’s internal audit process. After allowing for differences between internal and external audits, the team concludes that the lead time should be shortened. The team next uses the material discussed in Chapter 18 to construct a value stream map, which displays work in progress, cycle times, and communication channels. A careful study of the map data shows several areas where lead time can be decreased. • A team has been formed to reduce cycle times on an appliance assembly line. The team consists of the 12 workers on the line (six from each of the two shifts) as well as the 2 shift coaches and the line supervisor. Although this makes a large team, it helps ensure that everyone’s creative energy is tapped. The team decides to start a job rotation process in which each assembler will work one station for a month and then move on to the next station. After three months the workers universally dislike this procedure, but they agree to continue through at


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12


Part I.A.6

least one complete rotation. At the end of nine months, or one and a half rotations, the team acknowledges that the rotation system has helped improve standard work (see Chapter 29) because each person better understands what the next person needs. They are also better equipped to accommodate absences and the training of new people. The resulting reduction in cycle times surprises everyone. • A team has been charged with improving the operation of a shuttle brazer. Automotive radiators are loaded on this machine and shuttled through a series of gas-fired torches to braze the connections. The operator can adjust the shuttle speed, wait time, gas pressure, torch angle, and torch height. There is a tendency to adjust one or more of these settings to produce leak-free joints, but no one seems to know the best settings. The team decides to conduct a full factorial 25 designed experiment with four replications (see Chapter 28) during a planned plant shutdown. • A company is plagued with failure to meet deadlines for software projects. A team is formed to study and improve the design/code/test process. The team splits into three subteams, one for each phase. The design subteam discovers that this crucial phase endures excess variation in the form of customer needs. This occurs because customers change the requirements and because sometimes the software package is designed to serve multiple customers whose needs aren’t known until late in the design phase. The subteam helps the designers develop a generic Gantt chart (see Chapter 17) for the design phase itself. It also establishes a better process for determining potential customer needs (see Chapter 15). The design group decides to develop configurable software packages that permit the user to specify the functions needed. The coding subteam finds that those responsible for writing the actual code are often involved with multiple projects, leading to tension between project managers. This results in spurts of activity and concentration being spent on several projects with the resulting inefficiencies. The subteam collaborates with the project manager to establish a format for prioritization matrices (see Chapter 13), which provide better guidance for coders. The testing subteam determines that there is poor communication between designers and testers regarding critical functions, especially those that appeared late in the design phase. After discussions with those involved, it is decided that for each project a representative of the testing group should be an ex officio member of the design group.

References Crosby, P. B. 1979. Quality Is Free. New York: McGraw-Hill. ———. 1984. Quality without Tears: The Art of Hassle-Free Management. New York: New American Library. ———. 1990. Leading: The Art of Becoming an Executive. New York: McGraw-Hill.


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Part I.A.6

Deming, W. Edwards. 1986. Out of the Crisis. Cambridge, MA: MIT Press. Feigenbaum, A. V. 1991. Total Quality Control. 3rd ed. New York: McGraw-Hill. Gryna, Frank M., Richard C. H. Chua, and Joseph A. DeFeo. 2007. Juran’s Quality Planning & Analysis for Enterprise Quality. 5th ed. New York: McGraw-Hill. Ishikawa, K. 1985. What Is Total Quality Control? Englewood Cliffs, NJ: Prentice Hall. Juran, Joseph M., and A. Blanton Godfrey. 1999. Juran’s Quality Control Handbook. 5th ed. New York: McGraw-Hill.

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Index

attribute charts, 368 c chart, 372–374 np chart, 370–375 p chart, 368–370 u chart, 374–376 attribute gage study—analytic method, 116–118 attributes data, 95 process capability for, 175–176 attributes data analysis, 217 binary logistic regression, 218–223 nominal logistic regression, 218, 224–226 ordinal logistic regression, 218, 226–229 attributes method, of measurement systems analysis, 111–118 attribute agreement analysis, 111–116 attribute gage study—analytic method, 116–118 authorizing entity, duties of, 39 Automotive Industry Action Group (AIAG), out-of-control rules of, 390 Automotive Industry Action Group (AIAG) method, 100–107 AV (appraiser variation), 98 average variation between systems, 99 axiomatic design, 428

Page numbers followed by f or t refer to figures or tables, respectively.

A absolute zero, 91 accuracy components of, 97 defined, 97 precision vs., 98f activity network diagrams (ANDs), 57, 57f addition rule of probability, 139–141 adjusted coefficient of determination, 186 affinity diagrams, 52, 53f, 72 agenda committees, 49 air gages, 96 aliasing, 298 Altshuller, Genrich, 427 American Society for Quality (ASQ), 2 Code of Ethics, 433 Six Sigma Black Belt Certification Body of Knowledge (2001), 447–459 Six Sigma Black Belt Certification Body of Knowledge (2007), 434–446 analysis of variance (ANOVA) method, 107–109, 255 one-way, 256–258 two-way, 258–259 ANDs (activity network diagrams), 57, 57f ANOVA (analysis of variance) method. See analysis of variance (ANOVA) method appraisal costs, 34 appraiser variation (AV), 98 ASQ. See American Society for Quality (ASQ) assembly, design for, 417 attractive requirements, 70 attribute agreement analysis, 111–116

B balanced design, 297, 306 balanced scorecards, 5t KPIs in, 29–30 perspectives of, 28–29 Baldrige Award Criteria, 6t benchmarking, 5t, 26–27 collaborative, 27 competitive, 27 functional, 27 internal, 27 steps in, 27

609


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610 Index

between-conditions variation, 99 bias, defined, 97 binomial distributions, 149t cumulative table, 476–479 table, 472–475 bivariate distributions, 159t bivariate normal distributions, 159t, 162 Black Belts (BBs), 6–7, 17–18 black box engineering, 418 Blazey, Mark, 88 blocking, 297, 299–300 planning experiments and, 310 Bloom’s Taxonomy, 445–446, 458–459 boundaries, project, 72 box-and-whisker charts, 129t, 130 box plots, 130, 131f multiple, 131–132, 132f Brinnell method, 97 business processes, 10 business systems, 10

C calipers, 96 called yield, 179, 180 capability, tolerance and, 423 capability indices assumptions for, 174 long-term, 173–174 short-term, 173–174 causality, correlations vs., 186–187 cause-and-effect diagrams, 4, 72, 285, 286f, 385f causes common, 359 special, 359 c chart, 372–374 central limit theorem (CLT), 123–125 central tendency, measures of, 128 CFM (continuous flow manufacturing), 339 Champions, 15 change management, 15–16 changeover time, 83, 340 reducing, 340–341 check sheets, 93–94 chi square (goodness-of-fit) tests, 259–261 chi-square distributions, 149t, 155–156 table, 504–505 circle diagrams, 88–89, 89f CLT (central limit theorem), 123–125 CMMs (coordinate measuring machines), 96–97 coaches, duties of, 40


Code of Ethics, ASQ, 433 coefficient of determination, 186 adjusted, 186 cognition, levels of, based on Bloom’s Taxonomy, 445–446, 458–459 collaborative benchmarking, 27 common causes, 359 competitive benchmarking, 27 complementary rule of probability, 139 completeness of the system, law of, 427 conditional probability, 143–144 confidence intervals, 125 for correlations coefficient, 187–188 for means, 237–240, 238–239t point estimates and, 237 for proportions, 241–243, 242t for regression line, 194–195 for variances, 240–241 confounding, 297, 298 planning experiments and, 310 constraints. See theory of constraints (TOC) contingency tables, 141–143, 261–264 continuous data, 90, 95 continuous flow manufacturing (CFM), 339 control chart method, 109–111 control charts analyzing, 389–399 attribute charts, 368–376 c chart, 372–374 combinations for measurements, 460–461 constants, 462–464 constants for A7, B7, and B8, 465–469 control limits for, 362 count data, 471 individual and moving range chart, 366–367 moving average and moving range (MAMR), 383–389 np chart, 370–375 p chart, 368–370 purpose of, 359 short-run, 376–382 triggers for updating, 407 u chart, 374–376 variables, 361–362 variables selection for, 360 Xbar – R chart, 362–364 Xbar – s chart, 364–365 control limits, 362 formulas for, 389 control plans, 406–407 conversion/diversion, 51

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I 611

coordinate measuring machines (CMMs), 96–97 correlation coefficient, 184–188 confidence interval for, 187–188 hypothesis test for, 187 correlations, causality vs., 186–187 cost curves, 35 modern quality, 35f traditional quality, 34f cost of quality, 34–35 costs appraisal, 34 defined, 33 external failure, 34 internal failure, 34 prevention, 34 quality, 34–35 CPM (Critical Path Method), 76 crashing projects, 76 critical parameter management, 428–429 critical path, defined, 76 Critical Path Method (CPM), 76 critical path time, defined, 76 critical-to-cost (CTC), 24 critical-to-delivery (CTD), 25 critical-to-process (CTP), 25 critical-to-quality (CTQ) flow-down tool, 64–65, 65f, 66f critical-to-quality (CTQs), 24 critical-to-safety (CTS), 25 critical to x (CTx) requirements, 24–25 Crosby, Philip B., 3–4 CTC (critical-to-cost), 25 CTD (critical-to-delivery), 25 CTQ (critical-to-quality) flow-down tool, 64–65, 65f, 66f customer loyalty, 31 customer perspective, 28 customers determining and meeting needs of, 64–70 external, 22 feedback from, 63 internal, 22 loyal, 31 profitable, 31 tolerant, 31 unprofitable, 31 customer segmentation, 31, 62 cycle time, 82–83 defined, 337 cycle-time reduction, 337–341 continuous flow manufacturing, 339 reducing changeover time, 340–341 cycle variation, 208


D data attribute, 95 collecting, 93–94 continuous, 95 discrete, 95 errors, 92–93 process capability for non-normal data, 174–175 quantitative, 90–91 variables, 95 decision-making tools, for teams conversion/diversion, 51 force field analysis, 50–51, 50f multivoting, 51 nominal group technique, 50 decision matrix, 429–430 defects per million opportunities (DPMO), 179, 180 defects per unit (DPU), 179, 180 define, measure, analyze, design, and validate (DMADV), 414–415 define, measure, analyze, design, optimize, and validate (DMADOV), 415 define, measure, analyze, improve, and control (DMAIC), 7, 10 Deming, W. Edwards, 2–3 dependent events, 144–145 descriptive statistics, 126–128 descriptive studies, 137 design FMEA (DFMEA), 278 design for assembly, 417 design for maintainability, 417 design for manufacturing, 417 design for producibility, 417 design for robustness, 417 functional requirements for, 418 noise factors for, 418–420 statistical tolerances for, 420–423 tolerance design and, 420 design for test, 417 design for X (DFX), 416–417 design of experiments (DOE) guidelines for conducting, 310–311 planning, 309–311 principles, 297–308 terminology for, 294–297 design space, defined, 295 Design-to-Cost (DTC), 416 DFX (Design for X), 416–417 discrete data, 90–91, 95 discriminant analysis, 198, 201–204

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612 Index

discrimination, 99 distributions binomial, 153–155 bivariate, 159t bivariate normal, 159t, 162 chi-square, 155–156 exponential, 160t, 162-163 F, 157–158 frequency, 129t hypergeometric, 158–162, 159t lognormal, 160t, 164–165 normal, 148–151 Poisson, 152–153, 159t summary of, 149t t (Student’s t), 156–157 Weibull, 160t, 165–166 diversion/conversion, 51 dividing heads, 96 DMADOV (define, measure, analyze, design, optimize, and validate), 415 DMADV (define, measure, analyze, design, and validate), 414–415 DMAIC (define, measure, analyze, improve, and control), 7, 10 documentation, 410–411 DOE. See design of experiments (DOE) dot plots, 123, 123f, 124f DPMO (defects per million opportunities), 179, 180 DPU (defects per unit), 179, 180 driver, 54 Drum-Buffer-Rope subordinate step analogy, 344f, 345–346

E effect, defined, 294 effects interaction, 297, 303–305 main, 297, 300–303 efficient estimators, 235 energy transfer in the system, law of, 427 equipment variation (EV), 98 equivalent sigma levels, 554–555t errors in data, 92 experimental, 295 minimizing, 92–93 EV (equipment variation), 98 evaluation, ongoing, 411–412 events dependent, 144–145 independent, 144–145 mutually exclusive, 145


executives, 18 experimental errors, 188–189, 295 experimental plan, 310 experimental run, defined, 295 experiments. See also design of experiments (DOE) full factorial, 325–331 one-factor, 311–319 two-level fractional factorial, 319–325 exponential distributions, 160t, 162–163 external activities, 340 external customers, 22 external failure costs, 34 external suppliers, 22

F facilitators, duties of, 39 factor, defined, 294 factor analysis, 197, 200–201 factorial designs, defined, 319 failure mode and effects analyses (FMEAs), 278–282 design, 278 process, 278 fault tree analysis (FTA), 288–290 basic symbols, 289f fault trees, 54 F distribution, 149t, 157–158 F(0.01) distribution table, 535–537 F(0.025) distribution table, 531–533 F(0.05) distribution table, 527–529 F(0.10) distribution table, 523–525 F(0.90) distribution table, 519–521 F(0.95) distribution table, 515–517 F(0.975) distribution table, 511–513 F(0.99) distribution table, 507–509 feasibility studies, 351 feedback, from customers, 63 focus groups for, 63 in-person interviews for, 63 interviews for, 63 Feigenbaum, Armand V., 4 financial measures margin, 32 market share, 32 net present value, 33–34 return on investment (ROI), 32–33 revenue growth, 32 financial perspective, 28 fishbone diagrams, 285, 285f, 286f Fisher transformation, 235 five forces, Porter’s, 425 5S system, 333–334

11/20/08 6:19:32 PM

I 613

5 whys technique, 285–286 flowcharts, 10, 10f, 84, 84f generic, 82f flows, metrics for evaluating process, 81–83, 82f focus groups, for customer feedback, 63 force field analysis, 50–51, 50f Ford, Henry, 8 forecasts, 339 formal, 38 formal teams, 38 Fourteen Points, Deming’s, 2–3 4:1 ratio (25%) rule, 404 fractional factorial experiments, 5 frequency distributions, 129t full factorial experiments, 325–331 source table for, 237t statistical model for, 326t sums of squares for, 328t functional benchmarking, 27 functional gages, 96 functional requirements, 418

G gage blocks, 95–96 gage repeatability and reproducibility (GR&R) study, 99, 403–404 example, 100–107 Gantt charts, 76, 77f for time management of teams, 49 gap analysis, 283 general stakeholders, 22–23 goals SMART statements for, 73 statement of, for teams, 44 goodness-of-fit (chi square) tests, 259–261 graphical methods, 129 gray box design, 418 Green Belts (GBs), 18 growth and learning perspective, 29 GR&R (gage repeatability and reproducibility) study, 99 example, 100–107

H harmonization, law, 427 height gages, 96 histograms, 124, 124f, 358–359 hoshin planning, 16, 425–426 hypergeometric distributions, 158–162, 159t


hypothesis tests contingency tables, 261–264 for correlation coefficient, 187 goodness-of-fit (chi square) tests, 259–261 for means, 244–248, 245–247t non-parametric tests, 264–277 process for conducting, 244 for proportions, 250–255, 251t for regression coefficient, 196 for variances, 248–250, 249t

I ideality, law of increasing, 427 Imai, Masaaki, 342 implementation, 347–350 framework for, 349–350 income, defined, 33 independent events, 144–145 individual and moving range chart, 366–367 inferential studies, 137 informal teams, 38 in-person interviews, for customer feedback, 63 interaction effects, 297, 303–305 internal activities, 340 internal benchmarking, 27 internal customers, 22 internal failure costs, 34 internal perspective, 29 internal suppliers, 22 interrelationship digraphs, 52–54, 53f interval scales, 91 interviews, for customer feedback, 63 Ishikawa, Kaoru, 4 Ishikawa diagrams, 285, 285f, 286f ISO 9000, 5t

J Juran, Joseph M., 3 Juran trilogy, 3

K kaizen, 336, 337, 338 defined, 342–343 kaizen blitz, 337 defined, 342–343 kanban systems, 332–333 Kano model, 69–70, 69f Kaplan, Robert S., 28

11/20/08 6:19:32 PM

614 Index

key performance indicators (KPIs) in balanced scorecards, 29–30 defined, 29 KPIs. See key performance indicators (KPIs) Kruskal-Wallis test, 266t, 272–275 kurtosis, 127

L Latin square designs, 313t, 315–319 source tables for, 314t sums of squares for, 315t leadership, 14–19 change management and, 15–16 organizational roadblocks to, 14–15 Lean, defined, 7–8 lean manufacturing, 6t, 8 Lean-Six Sigma, 6t, 8 defined, 9 implementations of, 11–12 lean thinking, 7–8, 340 integrating Six Sigma and, 8–9 learning and growth perspective, 29 level, defined, 295 Levene’s test, 265t, 269–272 limits natural process, 178 specification, 178–179 linearity, defined, 97 linear regression multiple, 196–197 simple, 189–192 linear regression coefficients, 189 linear regression equation, 189 link functions, 218 lognormal distributions, 160t, 164–165 long-term capability, 173–174 loyal customers, 31

M main effects, 297, 300–303 maintainability, design for, 417 MAMR (moving average and moving range) control charts, 383–389 considerations when using, 383–384 constructing, 384–385 Mann-Whitney test, 266t, 275–277 one-tail critical values for, 556–557 two-tail critical values, 558–559 MANOVA (multiple analysis of variance), 198, 204–208 manufacturing, design for, 417


margin, 32 market share, 32 Master Black Belts (MBBs), 18 matrix diagram, 56, 56f mean(s), 127–128, 128t, 358–359 commonly used symbol for, 122t confidence intervals for, 237–240, 238–239t hypothesis tests for, 244–248, 245–247t measurement error, causes of, 120–121 measurement scales, 91 interval, 91 nominal, 91 ordinal, 91 ratio, 91 measurement systems components of, 99 in enterprises, 118–119 re-analysis of, 403–405 measurement systems analysis, 97–99 attributes, 111–118 variables, 99–111 measurement tools, 95–97 examples of, 96–97 measures of central tendency, 128 median, 127–128, 128t median ranks table, 539–541 method of least squares, 188–189 metrology, 119–121 micrometers, 96 Minitab, 107–109 rules for out-of-control conditions, 390 mode, 127–128, 128t models, 348 Mood’s median test, 264–268, 265t moving average and moving range (MAMR) control charts, 383–389 considerations when using, 383–384 constructing, 384–385 moving range charts. See individual and moving range chart multiple analysis of variance (MANOVA), 198, 204–208 multiple linear regression, 196–197 multivariate analysis, 197 discriminant analysis, 198, 201–204 factor analysis, 197, 200–201 multiple analysis of variance (MANOVA), 198, 204–208 principal components analysis, 197, 198–200 multi-vari studies, 208–217 multivoting, 51, 55

11/20/08 6:19:32 PM

I 615

must-be requirements, 70 mutually exclusive events, 145

N n, defined, 295 natural process limits, 178 net present value (NPV), 33–34 neutral characteristics, 70 NGT (nominal group technique), 50 Nippondenso, 400 noise factors defined, 295 planning experiments and, 310 for robust design, 418–420 nominal group technique (NGT), 50 nominal logistics regression, 218, 224–226 nominal scales, 91 non-normal data, process capability for, 174–175 non-parametric tests, 264, 265–266t Kruskal-Wallis test, 266t, 272–275 Levene’s test, 269–272 Mann-Whitney test, 266t, 275–277 Mood’s Median test, 264–268 non-value-added, defined, 8 normal distributions, 148–151, 149t cumulative standard table, 499–501 standard table, 496–498 normal probability plots, 135–137, 136 normal scores table, 543–545 norms, team, 44–45 Norton, David P., 28 np chart, 370–375 NPV. See net present value (NPV)

O objectives, statement of, for teams, 44 observed value, defined, 294 Ohno, Taiichi, 332 one-dimensional requirements, 70 one-factor experiments, 311–319 completely randomized, 311 Latin square designs, 315–319 randomized complete block design (RCBD), 311 one-sided tolerance limits, factors for, 546–549 one-way ANOVA designs, 256–258, 311, 312t source tables for, 314t sums of squares for, 315t ongoing evaluation, 411–412


optical comparators, 96 order, 297, 298 run, 299 standard, 298 ordinal logistic regression, 218, 226–229 ordinal scales, 91 organizational memory, 408–409 out-of-control rules, 389 of Automotive Industry Action Group (AIAG), 390, 396–399 Minitab, 390, 391–396

P Pareto charts, 72, 285–288, 286f Pareto principle, 131–132 parts per million (PPM), 179, 180–181 payback period, 33 p chart, 368–370 PDPC (process decision program chart), 56–57 percent agreement, 99 percent defective, equivalent sigma levels and, 554–555 perspectives customer, 28 financial, 28 internal, 29 learning and growth, 29 PERT (Project Evaluation and Review Technique), 76 PEST (political, economic, social, and technological) analysis, 354 phone interviews, for customer feedback, 63 pilot runs, 348 Plackett-Burman designs, 310 planning, strategic, 424–426 tactical, 426–430 point estimates, 237 Poisson distributions, 149t, 152–153 cumulative table, 489–495 table, 481–487 poka-yoke, 335–336 population, 122 population parameters, 122 Porter, Michael, 425 Porter’s five forces, 425 portfolio architecting, 425 positional variation, 208 power defined, 230 power, sample size and, 297–298 PPM (parts per million), 179, 180–181

11/20/08 6:19:32 PM

616 Index

practical significance, statistical significance vs., 231 precision components of, 98–99 defined, 98 precision protractors, 96 precision-to-tolerance ratio (PTR), 99 prediction intervals, 195, 235–236 prevention costs, 34 principal components analysis, 197, 198–200 prioritization matrix, 54–56, 55f probability addition rule of, 139–141 classic definition, 138 complementary rule of, 139 conditional, 143–144 multiplication rule of, 145–147 relative-frequency definition, 138 rules of, 147t problem statements, 71 procedures, written, 84–85, 85f, 86 process analysis tools, 83–89 flowcharts, 84, 84f process maps, 84, 84f spaghetti diagrams, 88, 88f value stream maps, 85–88, 87f written procedures, 84–85, 85f, 86f process capability for attributes data, 175–176 defined, 167 for non-normal data, 174–175 process capability indices, 167–171 process capability studies, 176–177 conducting, 177 process decision program chart (PDPC), 56–57 processes defined, 80 metrics for evaluating flow in, 81–83, 82f SIPOC tool for, 80–81, 81f processes, business, 10 process flowcharts, 10, 10f process flow metrics, 81–83 process FMEA (PFMEA), 278 process improvement teams, 38 process logs, 389 process maps, 72, 84, 84f process owners, 18–19 process performance defined, 171 specification vs., 178–181 process performance indices, 171–173


process performance metrics, 179–181 defects per million opportunities (DPMO), 179, 180 defects per unit (DPU), 179, 180 parts per million (PPM), 179, 180–181 rolled throughput yield (RTY), 179, 181 throughput yield, 179, 180 process-related training plans, developing, 410 process stakeholders, 22–23 process variation, sources of, 359 producibility, design for, 417 profitable customers, 31 project charters defined, 71 goals and objectives for, 73 performance measures for, 74 problem statements, 71 project scope, 72–73 Project Evaluation and Review Technique (PERT), 76 project tracking, 73–77 proportions confidence intervals for, 241–243, 242t hypothesis tests for, 250–255, 251t prototypes, 348 PTR (precision-to-tolerance ratio), 99 Pugh analysis, 429–430 pull systems, 333–334 push systems, 339 p-value defined, 230

Q quality circles, 5t quality costs, 34 quality function deployment (QFD), 66–69, 67f, 68f quality improvement, history of, 2–6 quartiles, 130

R randomization, 297, 299 planning experiments and, 310 randomized complete block design (RCBD), 311, 312t source tables for, 314t sums of squares for, 315t random sampling, 93 range, 127, 128t rapid continuous improvement (RCI), 337

11/20/08 6:19:32 PM

I 617

rapid exchange of tooling and dies (RETAD), 340 rational subgroups, choosing, 360–361 ratio scales, 91 RCBD (randomized complete block design), 340 RCI (rapid continuous improvement), 337 re-analysis, of measurement systems, 403–405 recognition, as team motivation technique, 42 recorders duties of, 40 reengineering, 5t regression binary logistic, 218–223 nominal logistic, 218, 224–226 ordinal logistic, 218, 226–229 regression analysis, 188–197 confidence intervals for, 194–195 hypothesis tests for, 196 method of least squares, 192–194 multiple linear regression, 196–197 prediction intervals for, 195 simple linear regression, 189–192 relationships within teams, as motivation technique, 43 repeatability, 98 repeated measures, 297, 298 repetition, 298 replication, 297, 298 reproducibility, 98–99 requirements attractive, 70 must-be, 70 one-dimensional, 70 residuals, 188–189 resolution, 99, 297, 307–308 planning experiments and, 310 response variable, defined, 294 RETAD (rapid exchange of tooling and dies), 340 return on investment (ROI), 32–33 revenue growth, 32 reversal characteristics, 70 rewards, as team motivation technique, 42 ring gages, 96 risk analysis, 351–352 roadblocks, organizational, 14–15 robustness, 5 design for, 417 Rockwell method, 97 ROI (return on investment), 32–33


rolled throughput yield (RTY), 179, 180 root cause analysis, 284 cause-and-effect diagrams, 285, 285f, 286f fault tree analysis, 288–290, 289f 5 whys technique, 284–285 Pareto charts, 285–288, 286f RTY (rolled throughput yield), 179, 180 run charts, 130t, 132–133, 133f run order, 299

S sample homogeneity, 93 sample size, 231–234 commonly used symbol for, 122t formulas for, 232t power and, 297–298 sample standard deviation, 127, 128t sampling methods, 92–93 scales interval, 91 nominal, 91 ordinal, 91 ratio, 91 scatter diagrams, 130t, 133–135, 134t scope, defining, 72–73 screening designs, 310 scribes duties of, 40 self-directed teams, 38 setup time, 83 6Ms, 120 7Ms, 120–121 Shewhart, Walter A., 2 Shingo, Shigeo, 340 Shingo methodology, 340 short-run control charts, 376–382, 377f constructing, 380–381 rules for, 380 summary of formulas for, 378–379t short-term capability, 173–174 sigma levels, equivalent, 554–555 significance statistical vs. practical, 231 simple linear regression, 189–192 simulations, 348 sine bars, 96 single minute exchange of dies (SMED), 340 SIPOC (suppliers, inputs, process, outputs, customers) tool, 80–81, 81f Six Sigma, 6t defined, 6–7 integrating Lean and, 8–9

11/20/08 6:19:32 PM

618 Index

projects, 16–17 responsibilities, 17–19 roles, 17–19 Six Sigma Black Belt Certification Body of Knowledge (2001), 447–459 Six Sigma Black Belt Certification Body of Knowledge (2007), 434–446 Six Sigma projects effective, 23 impact on stakeholders and, 23 storyboards for, 77 teams and, 23 skewness, 127 SMART (specific, measurable, achievable, relevant, timely) goal statements, 73 SMED (single minute exchange of dies), 340 source tables for full factorial experiments, 327t spaghetti diagrams, 88, 88f SPC (statistical process control), 5t objectives of tools for, 358–359 special causes, 359 specification limits, 178–179 process performance vs., 178–181 sponsor entity duties of, 39 SQC (statistical quality control), 2 stability, of measurement system, defined, 97 stakeholders, 22–23 general, 22 impact of Six Sigma projects on, 23 process, 22–23 standard deviation, 358–359 commonly used symbol for, 122t sample, 127, 128t standard error of the estimate, 194 standard operating procedures (SOPs), documenting, 411 standard order, 298 standard work, 334 statement of goals and objectives, for teams, 44 statistical conclusions descriptive, 137 inferential, 137 statistical control, state of, 167 statistical process control (SPC), 5t objectives of tools for, 358–359 statistical quality control (SQC), 2 statistical significance, practical significance vs., 231


statistics, 122 commonly used symbols, 122t stem-and-leaf diagrams, 129t, 130 storyboards, 77 for Six Sigma projects, 77 strategic planning, 424 hoshin planning, 425–426 Porter’s five forces model, 425 portfolio architecting model, 425 stratified sampling, 93 Student’s t distribution, 149t, 156–157 subgroups, choosing rational, 360–361 substance-field involvement, law of, 428 sums of squares for full factorial experiments, 328t for Latin square designs, 315t one-way ANOVA designs, 315t for randomized complete block design, 315t suppliers external, 22 internal, 22 surveys for customer feedback, 63 SWOT (strengths, weaknesses, opportunities, and threats) analysis, 353 symbols, statistical, commonly used, 122t systematic design, 428 systems, business, 10

T tactical planning, 426–430 axiomatic design, 428 critical parameter management, 428–429 Pugh analysis, 429–430 systematic design, 428 TRIZ, 427–428 Taguchi, Genichi, 5 takt time, 82, 83 defined, 338 tallies, 129t t distribution (Student’s t distribution), 149t, 156–157 table, 502–503 team leaders, duties of, 39 team members duties of, 40 selecting, 40 team motivation, techniques for, 42–43 team roles, 39–40

11/20/08 6:19:32 PM

I 619

teams, 44f common obstacles and solutions for, 47–48f communication and, 44–45 decision-making tools for, 50–51 dynamics of, 46 growth stages of, 43 informal, 38 launching, 41 norms for, 44–45 performance criteria for, 58 process improvement, 38 rewards for, 58–59 selecting members for, 40 self-directed, 38 statement of objectives for, 44 time management for, 49 virtual, 38 work group, 38 temporal variation, 208 10:1 ratio rule, 404 test, design for, 417 theory of constraints (TOC), 344–346 impact of, 346 thread snap gages, 96 throughput, 83 throughput yield, 179 time management, for teams, 49 TOC. See theory of constraints (TOC) tolerance design, 420 tolerance intervals, 236–237 tolerance limits one-sided, factors for, 546–549 two-sided, factors for, 550–553 tolerances, statistical capability and, 423 conventional, 420, 421–422 statistical, 420, 422–423 tolerant customers, 31 total productive maintenance (TPM), 400–401 total quality control, 4 touch time, 82 Toyota Production System (TPS), 8 TPM (total productive maintenance), 400–401 tracking, project, 73–77 training initial, 409 recurring, 409 training plans considerations, 410 developing process-related, 410


transfer devices, 96 transition from macro to micro, law of, 428 transition to super system, law of, 428 treatment, defined, 295 tree diagrams, 54, 54f CTQ, 25f TRIZ (Teorija Rezbenija Izobretaltelshih Zadach), 427–428 Tukey, John, 130 two-level fractional factorial experiments, 319–325 two-sided tolerance limits, factors for, 550–553 two-way ANOVA, 258–259 Type I error, 231 defined, 230 Type II error, 231 defined, 230

U u chart, 374–376 unbiased estimators, 234–235 uneven development of parts, law of, 427 unprofitable customers, 31

V value-added, 332 value-added time, 83 value stream maps, 85–88, 87f variables control charts, 361–362, 389 variables data, 95 variables method, of measurement systems analysis, 99–111 ANOVA method, 107–109 control chart method, 109–111 GR&R study, 100–107 variables selection, for control charts, 360 variances confidence intervals for, 240–241 hypothesis tests for, 248–250 virtual teams, 38 visual controls, 402 visual factory, 401–402 voice of customer (VOC), 62, 66–67

W waste analysis, sources of, 290–291 waste elimination, 332–336 5S system for, 333–334 kaizen for, 336

11/20/08 6:19:32 PM

620 Index

kanban systems for, 332–333 poka-yoke for, 335–336 pull systems for, 333–334 standard work for, 334 Weibull distributions, 160t, 165–166 Whitney, Eli, 8 Wilcoxon signed-rank test, critical values for, 560 within-system variation, 98 work group teams, 38 work in progress (WIP), 82


work in queue (WIQ), 82 written procedures, 84–85, 85f, 86f

X Xbar – R chart, 362–364 Xbar – s chart, 364–365

Z zero defects concept, 3

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Certified Black Belt Handbook Chapter

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