certified black belt handbook chapter

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Also available from ASQ Quality Press:

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

Six Sigma for the New Millennium: A CSSBB Guidebook, Second EditionKim H. Pries

5S for Service Organizations and Offices: A Lean Look at ImprovementsDebashis Sarkar

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

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

Statistical Quality Control for the Six Sigma Green BeltBhisham C. Gupta and H. Fred Walker

Six Sigma for the Office: A Pocket GuideRoderick A. Munro

Lean-Six Sigma for Healthcare: A Senior Leader Guide to Improving Cost and Throughput, Second EditionChip Caldwell , Greg Butler, and Nancy Poston.

Defining and Analyzing a Business Process: A Six Sigma Pocket GuideJeffrey N. Lowenthal

Six Sigma for the Shop Floor: A Pocket GuideRoderick A. Munro

Six Sigma Project Management: A Pocket GuideJeffrey N. Lowenthal

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

Lean Kaizen: A Simplified Approach to Process ImprovementsGeorge Alukal and Anthony Manos

A Lean Guide to Transforming Healthcare: How to Implement Lean Principles in Hospitals, Medical Offices, Clinics, and Other Healthcare OrganizationsThomas 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.

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T�� C�� S� S�� B �� B� � H��

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T. M. Kubiak Donald W. Benbow

ASQ Quality PressMilwaukee, Wisconsin

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American Society for Quality, Quality Press, Milwaukee 53203© 2009 by American Society for QualityAll rights reserved. Published 2009Printed in the United States of America14 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. TonyAcquisitions Editor: Matt MeinholzProject Editor: Paul O’MaraProduction 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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vii

Table of Contents

List of Figures and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvPreface to the Second Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiiPreface to the First Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii

Part I Enterprise-Wide Deployment . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 1 Enterprise-Wide View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2History of Continuous Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Value and Foundations of Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Value and Foundations of Lean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Integration of Lean and Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Business Processes and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Six Sigma and Lean Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Chapter 2 Leadership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Enterprise Leadership Responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Organizational Roadblocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Change Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Six Sigma Projects and Kaizen Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Six Sigma Roles and Responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Part II Organizational Process Management and Measures . . . . 21

Chapter 3 Impact on Stakeholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Impact on Stakeholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Chapter 4 Critical to x (CTx) Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Critical to x (CTx) Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Chapter 5 Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Chapter 6 Business Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Business Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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viii Table of Contents

Chapter 7 Financial Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Common Financial Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Part III Team Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Chapter 8 Team Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Team Types and Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Team Roles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Team Member Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Launching Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Chapter 9 Team Facilitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Team Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Team Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Team Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Chapter 10 Team Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Team Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Chapter 11 Time Management for Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Time Management for Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Chapter 12 Team Decision- Making Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Team Decision- Making Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Chapter 13 Management and Planning Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Management and Planning Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Chapter 14 Team Performance Evaluation and Reward . . . . . . . . . . . . . . . . . . . 58Team Performance Evaluation and Reward . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Part IV Define . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Chapter 15 Voice of the Customer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Customer Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Customer Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Customer Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Chapter 16 Project Charter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Problem Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Project Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Goals and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Project Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Chapter 17 Project Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Project Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

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Part V Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Chapter 18 Process Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Input and Output Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Process Flow Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Process Analysis Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Chapter 19 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Types of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Measurement Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Sampling Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Collecting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Chapter 20 Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Measurement Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Measurement Systems Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Measurement Systems in the Enterprise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Chapter 21 Basic Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Basic Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Graphical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Valid Statistical Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Chapter 22 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Commonly Used Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Other Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Chapter 23 Process Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Process Capability Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Process Performance Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Short- Term and Long- Term Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Process Capability for Non- Normal Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174Process Capability for Attributes Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Process Capability Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176Process Performance vs. Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Part VI Analyze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Chapter 24 Measuring and Modeling Relationships between Variables . . . . 184Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188Multivariate Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Multi- Vari Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208Attributes Data Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

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Chapter 25 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230Statistical vs. Practical Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Sample Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Point and Interval Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234Tests for Means, Variances, and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244Analysis of Variance (ANOVA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Goodness- of-Fit (Chi Square) Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Non- Parametric Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

Chapter 26 Failure Mode and Effects Analysis (FMEA) . . . . . . . . . . . . . . . . . . . 278Failure Mode and Effects Analysis (FMEA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

Chapter 27 Additional Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283Gap Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283Root Cause Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284Waste Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

Part VII Improve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

Chapter 28 Design of Experiments (DOE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297Planning Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 One- Factor Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311Two-Level Fractional Factorial Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319Full Factorial Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

Chapter 29 Waste Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332Waste Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

Chapter 30 Cycle-Time Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Cycle- Time Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

Chapter 31 Kaizen and Kaizen Blitz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342Kaizen and Kaizen Blitz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

Chapter 32 Theory of Constraints (TOC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344Theory of Constraints (TOC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344

Chapter 33 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Chapter 34 Risk Analysis and Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351Risk Analysis and Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

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Part VIII Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

Chapter 35 Statistical Process Control (SPC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358Selection of Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360Rational Subgrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360Control Chart Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361Control Chart Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

Chapter 36 Other Control Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400Total Productive Maintenance (TPM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400Visual Factory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

Chapter 37 Maintain Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403Measurement System Re- analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403Control Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406

Chapter 38 Sustain Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408Lessons Learned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408Training Plan Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410Ongoing Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

Part IX Design for Six Sigma (DFSS) Frameworks and Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

Chapter 39 Common DFSS Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414DMADV (Define, Measure, Analyze, Design, and Validate) . . . . . . . . . . . . . . 414DMADOV (Define, Measure, Analyze, Design, Optimize, and Validate) . . . 415

Chapter 40 Design for X (DFX) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416Design for X (DFX) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416

Chapter 41 Robust Design and Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418Robust Design and Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

Chapter 42 Special Design Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424Strategic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424Tactical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426

Part X Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

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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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





Appendix 22 F(0.025) Distribution Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531


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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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

CD-ROM Contents

Sample Examination Questions for Parts I–IX

Certified Six Sigma Black Belt—Simulated Exam

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xv

List of Figures and Tables

Part ITable 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

Part IIFigure 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

Part IIIFigure 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

Part IVFigure 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

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Part VFigure 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. . . . . . . . . . . . 109

Figure 20.8 Minitab session window output of the R&R study—X–/R method:

source tables for Example 20.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Figure 20.9 Graphical results of the GR&R study—–X/R method:

–X and R

control charts by operators (appraisers) for Example 20.3. . . . . . . . . . . . . . . . 110

Table 20.1 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 Attribute gage study—data for Example 20.5. . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Figure 20.12 Graphical results of the attribute gage analysis for Example 20.5. . . . . . . . . . 117

Table 21.1 Commonly used symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

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

Table 23.2 Methods of determining the standard deviation for use in process capability indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Table 23.3 Binomial probabilities for Example 23.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Part VIFigure 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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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

Table 24.4 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 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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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



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 25.26 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 List of Figures and Tables

Part VIITable 28.1 A 23 full factorial data collection sheet for Example 28.1. . . . . . . . . . . . . . . . . . 296

Table 28.2 A 23 full factorial data collection sheet with data entered for Example 28.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

Table 28.3 A 23 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 23 full factorial design using the + and – format. . . . . . . . . . . . . . . . . . . . . . 303

Table 28.5 A 23 full factorial design showing interaction columns. . . . . . . . . . . . . . . . . . . 304

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



Figure 34.1 SWOT analysis for Example 34.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

Figure 34.2 PEST analysis for Example 34.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

Part VIIIFigure 35.1 Function of SPC tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

Figure 35.2 Conveyor belt in chocolate- making process. . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

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Figure 35.3 Conveyor belt in chocolate- making process with rational subgroup choice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

Table 35.1 Data for Examples 35.1 and 35.2—X– – R and X

– – s charts, respectively. . . . . 363

Figure 35.4 X– – R chart for data given in Table 35.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

Figure 35.5 X– – s chart for data given in Table 35.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

Table 35.2 Data for Example 35.3—individual and moving range chart. . . . . . . . . . . . . . 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








Figure 35.22 Example of out- of-control condition #1 from AIAG.. . . . . . . . . . . . . . . . . . . . . 396






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 IXFigure 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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xxiii

Preface to the Second Edition

In 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 nec-essary 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 seek-ing much deeper levels of discussion. Most of the citations provided in the refer-ences will be helpful in this regard.

A secondary audience for the handbook is the quality and Six Sigma profes-sional 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 awk-ward 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 read-ers 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 dig-its accounted for by the software used, the sequence in which the arithmetic was performed, and the propagation of errors due to rounding or truncation. There-fore, 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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xxv

We 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 strug-gling 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

Preface to the First Edition

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xxvii

We would like to express our deepest appreciation to Minitab Inc., for pro-viding 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 verify-ing 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 suit-able for the ASQ Quality Press family of publications.

—The Authors

Acknowledgments

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1

Part I

Part IEnterprise-Wide Deployment

Chapter 1 Enterprise-Wide ViewChapter 2 Leadership

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I.A

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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 qual-ity 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.

Chapter 1Enterprise-Wide View


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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.

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

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

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 arbitra-tor, corporate director, and consultant. He developed the Juran trilogy, three mana-gerial processes—quality planning, quality control, and quality improvement—for use in managing for quality. Juran wrote hundreds of papers and 12 books, includ-ing 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


4 Part I: Enterprise-Wide DeploymentPa

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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

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. Feigen-baum is an ASQ honorary member and served as ASQ president for two consecu-tive 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 fol-lowing 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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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 rec-ognized 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.

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.

Balanced Scorecard

1990s–present A management concept that helps managers at all levels monitor their results in their key areas.

Continued



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.A.2

VALUE AND FOUNDATIONS OF SIX SIGMA

Describe the value of Six Sigma, its philosophy, history, and goals. (Understand)


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

Table 1.1 Some approaches to quality over the years. Continued

Quality approach

Approximate time frame Short description

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.


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four projects per year for a total of $500,000–$5,000,000 in contributions to the com-pany’s bottom line.

Opinions on the definition of Six Sigma differ:

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 advan-tage. 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)


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 Manu-facturing Extension Partnership, defines Lean as follows:



rt I

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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 tradition-ally 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 discus-sion 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)


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 pro-cess improvement requires aspects of both approaches to attain positive results.


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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 prac-titioners 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 manage-ment support to make them the standard way of doing business.

Some organizations have responded to this dichotomy of approaches by form-ing 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 val-ues 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 advan-tage. 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)




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Processes

A process is a series of steps designed to produce products and/or services. A pro-cess 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 consti-tute 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 improve-ment 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. Fig-ure 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, inno-vation, etc. (Understand)


Yes

No

Number ofhours

Hourly rate

Calculategross pay

Over$100?

Deduct tax

Deduct Social Security

Print check

Figure 1.1 Example of a process flowchart.


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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

Systems

Processes

Subprocesses

Steps

Figure 1.2 Relationship among systems, processes, subprocesses, and steps.



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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.

ReferencesCrosby, 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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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.


609

Index

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

Aabsolute zero, 91accuracy

components of, 97defined, 97precision vs., 98f

activity network diagrams (ANDs), 57, 57faddition rule of probability, 139–141adjusted coefficient of determination, 186affinity diagrams, 52, 53f, 72agenda committees, 49air gages, 96aliasing, 298Altshuller, Genrich, 427American Society for Quality (ASQ), 2

Code of Ethics, 433Six Sigma Black Belt Certification Body of

Knowledge (2001), 447–459Six Sigma Black Belt Certification Body of

Knowledge (2007), 434–446analysis of variance (ANOVA) method,

107–109, 255one-way, 256–258two-way, 258–259

ANDs (activity network diagrams), 57, 57fANOVA (analysis of variance) method.

See analysis of variance (ANOVA) method

appraisal costs, 34appraiser variation (AV), 98ASQ. See American Society for Quality

(ASQ)assembly, design for, 417attractive requirements, 70attribute agreement analysis, 111–116

attribute charts, 368c chart, 372–374np chart, 370–375p chart, 368–370u chart, 374–376

attribute gage study—analytic method, 116–118attributes data, 95

process capability for, 175–176attributes data analysis, 217

binary logistic regression, 218–223nominal logistic regression, 218, 224–226ordinal logistic regression, 218, 226–229

attributes method, of measurement systems analysis, 111–118

attribute agreement analysis, 111–116attribute gage study—analytic method,

116–118authorizing entity, duties of, 39Automotive Industry Action Group (AIAG),

out-of-control rules of, 390Automotive Industry Action Group (AIAG)

method, 100–107AV (appraiser variation), 98average variation between systems, 99axiomatic design, 428

Bbalanced design, 297, 306balanced scorecards, 5t

KPIs in, 29–30perspectives of, 28–29

Baldrige Award Criteria, 6tbenchmarking, 5t, 26–27

collaborative, 27competitive, 27functional, 27internal, 27steps in, 27


610 Index

between-conditions variation, 99bias, defined, 97binomial distributions, 149t

cumulative table, 476–479table, 472–475

bivariate distributions, 159tbivariate normal distributions, 159t, 162Black Belts (BBs), 6–7, 17–18black box engineering, 418Blazey, Mark, 88blocking, 297, 299–300

planning experiments and, 310Bloom’s Taxonomy, 445–446, 458–459boundaries, project, 72box-and-whisker charts, 129t, 130box plots, 130, 131f

multiple, 131–132, 132fBrinnell method, 97business processes, 10business systems, 10

Ccalipers, 96called yield, 179, 180capability, tolerance and, 423capability indices

assumptions for, 174long-term, 173–174short-term, 173–174

causality, correlations vs., 186–187cause-and-effect diagrams, 4, 72, 285, 286f,

385fcauses

common, 359special, 359

c chart, 372–374central limit theorem (CLT), 123–125central tendency, measures of, 128CFM (continuous flow manufacturing), 339Champions, 15change management, 15–16changeover time, 83, 340

reducing, 340–341check sheets, 93–94chi square (goodness-of-fit) tests, 259–261chi-square distributions, 149t, 155–156

table, 504–505circle diagrams, 88–89, 89fCLT (central limit theorem), 123–125CMMs (coordinate measuring machines),

96–97coaches, duties of, 40

Code of Ethics, ASQ, 433coefficient of determination, 186

adjusted, 186cognition, levels of, based on Bloom’s

Taxonomy, 445–446, 458–459collaborative benchmarking, 27common causes, 359competitive benchmarking, 27complementary rule of probability, 139completeness of the system, law of, 427conditional probability, 143–144confidence intervals, 125

for correlations coefficient, 187–188for means, 237–240, 238–239tpoint estimates and, 237for proportions, 241–243, 242tfor regression line, 194–195for variances, 240–241

confounding, 297, 298planning experiments and, 310

constraints. See theory of constraints (TOC)contingency tables, 141–143, 261–264continuous data, 90, 95continuous flow manufacturing (CFM), 339control chart method, 109–111control charts

analyzing, 389–399attribute charts, 368–376c chart, 372–374combinations for measurements,

460–461constants, 462–464constants for A7, B7, and B8, 465–469control limits for, 362count data, 471individual and moving range chart,

366–367moving average and moving range

(MAMR), 383–389np chart, 370–375p chart, 368–370purpose of, 359short-run, 376–382triggers for updating, 407u chart, 374–376variables, 361–362variables selection for, 360Xbar – R chart, 362–364Xbar – s chart, 364–365

control limits, 362formulas for, 389

control plans, 406–407conversion/diversion, 51


I�� 611

coordinate measuring machines (CMMs), 96–97correlation coefficient, 184–188

confidence interval for, 187–188hypothesis test for, 187

correlations, causality vs., 186–187cost curves, 35

modern quality, 35ftraditional quality, 34f

cost of quality, 34–35costs

appraisal, 34defined, 33external failure, 34internal failure, 34prevention, 34quality, 34–35

CPM (Critical Path Method), 76crashing projects, 76critical parameter management, 428–429critical path, defined, 76Critical Path Method (CPM), 76critical path time, defined, 76critical-to-cost (CTC), 24critical-to-delivery (CTD), 25critical-to-process (CTP), 25critical-to-quality (CTQ) flow-down tool,

64–65, 65f, 66fcritical-to-quality (CTQs), 24critical-to-safety (CTS), 25critical to x (CTx) requirements, 24–25Crosby, Philip B., 3–4CTC (critical-to-cost), 25CTD (critical-to-delivery), 25CTQ (critical-to-quality) flow-down tool,

64–65, 65f, 66fcustomer loyalty, 31customer perspective, 28customers

determining and meeting needs of, 64–70external, 22feedback from, 63internal, 22loyal, 31profitable, 31tolerant, 31unprofitable, 31

customer segmentation, 31, 62cycle time, 82–83

defined, 337cycle-time reduction, 337–341

continuous flow manufacturing, 339reducing changeover time, 340–341

cycle variation, 208

Ddata

attribute, 95collecting, 93–94continuous, 95discrete, 95errors, 92–93process capability for non-normal data,

174–175quantitative, 90–91variables, 95

decision-making tools, for teamsconversion/diversion, 51force field analysis, 50–51, 50fmultivoting, 51nominal group technique, 50

decision matrix, 429–430defects per million opportunities (DPMO),

179, 180defects per unit (DPU), 179, 180define, measure, analyze, design, and

validate (DMADV), 414–415define, measure, analyze, design, optimize,

and validate (DMADOV), 415define, measure, analyze, improve, and

control (DMAIC), 7, 10Deming, W. Edwards, 2–3dependent events, 144–145descriptive statistics, 126–128descriptive studies, 137design FMEA (DFMEA), 278design for assembly, 417design for maintainability, 417design for manufacturing, 417design for producibility, 417design for robustness, 417

functional requirements for, 418noise factors for, 418–420statistical tolerances for, 420–423tolerance design and, 420

design for test, 417design for X (DFX), 416–417design of experiments (DOE)

guidelines for conducting, 310–311planning, 309–311principles, 297–308terminology for, 294–297

design space, defined, 295Design-to-Cost (DTC), 416DFX (Design for X), 416–417discrete data, 90–91, 95discriminant analysis, 198, 201–204


612 Index

discrimination, 99distributions

binomial, 153–155bivariate, 159tbivariate normal, 159t, 162chi-square, 155–156exponential, 160t, 162-163F, 157–158frequency, 129thypergeometric, 158–162, 159tlognormal, 160t, 164–165normal, 148–151Poisson, 152–153, 159tsummary of, 149tt (Student’s t), 156–157Weibull, 160t, 165–166

diversion/conversion, 51dividing heads, 96DMADOV (define, measure, analyze, design,

optimize, and validate), 415DMADV (define, measure, analyze, design,

and validate), 414–415DMAIC (define, measure, analyze, improve,

and control), 7, 10documentation, 410–411DOE. See design of experiments (DOE)dot plots, 123, 123f, 124fDPMO (defects per million opportunities),

179, 180DPU (defects per unit), 179, 180driver, 54Drum-Buffer-Rope subordinate step analogy,

344f, 345–346

Eeffect, defined, 294effects

interaction, 297, 303–305main, 297, 300–303

efficient estimators, 235energy transfer in the system, law of, 427equipment variation (EV), 98equivalent sigma levels, 554–555terrors

in data, 92experimental, 295minimizing, 92–93

EV (equipment variation), 98evaluation, ongoing, 411–412events

dependent, 144–145independent, 144–145mutually exclusive, 145

executives, 18experimental errors, 188–189, 295experimental plan, 310experimental run, defined, 295experiments. See also design of experiments

(DOE)full factorial, 325–331one-factor, 311–319two-level fractional factorial, 319–325

exponential distributions, 160t, 162–163external activities, 340external customers, 22external failure costs, 34external suppliers, 22

Ffacilitators, duties of, 39factor, defined, 294factor analysis, 197, 200–201factorial designs, defined, 319failure mode and effects analyses (FMEAs),

278–282design, 278process, 278

fault tree analysis (FTA), 288–290basic symbols, 289f

fault trees, 54F distribution, 149t, 157–158F(0.01) distribution table, 535–537F(0.025) distribution table, 531–533F(0.05) distribution table, 527–529F(0.10) distribution table, 523–525F(0.90) distribution table, 519–521F(0.95) distribution table, 515–517F(0.975) distribution table, 511–513F(0.99) distribution table, 507–509feasibility studies, 351feedback, from customers, 63

focus groups for, 63in-person interviews for, 63interviews for, 63

Feigenbaum, Armand V., 4financial measures

margin, 32market share, 32net present value, 33–34return on investment (ROI), 32–33revenue growth, 32

financial perspective, 28fishbone diagrams, 285, 285f, 286fFisher transformation, 235five forces, Porter’s, 4255S system, 333–334


I�� 613

5 whys technique, 285–286flowcharts, 10, 10f, 84, 84f

generic, 82fflows, metrics for evaluating process,

81–83, 82ffocus groups, for customer feedback, 63force field analysis, 50–51, 50fFord, Henry, 8forecasts, 339formal, 38formal teams, 38Fourteen Points, Deming’s, 2–34:1 ratio (25%) rule, 404fractional factorial experiments, 5frequency distributions, 129tfull factorial experiments, 325–331

source table for, 237tstatistical model for, 326tsums of squares for, 328t

functional benchmarking, 27functional gages, 96functional requirements, 418

Ggage blocks, 95–96gage repeatability and reproducibility

(GR&R) study, 99, 403–404example, 100–107

Gantt charts, 76, 77ffor time management of teams, 49

gap analysis, 283general stakeholders, 22–23goals

SMART statements for, 73statement of, for teams, 44

goodness-of-fit (chi square) tests, 259–261

graphical methods, 129gray box design, 418Green Belts (GBs), 18growth and learning perspective, 29GR&R (gage repeatability and

reproducibility) study, 99example, 100–107

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

159t

hypothesis testscontingency tables, 261–264for correlation coefficient, 187goodness-of-fit (chi square) tests,

259–261for means, 244–248, 245–247tnon-parametric tests, 264–277process for conducting, 244for proportions, 250–255, 251tfor regression coefficient, 196for variances, 248–250, 249t

Iideality, law of increasing, 427Imai, Masaaki, 342implementation, 347–350

framework for, 349–350income, defined, 33independent events, 144–145individual and moving range chart,

366–367inferential studies, 137informal teams, 38in-person interviews, for customer feedback,

63interaction effects, 297, 303–305internal activities, 340internal benchmarking, 27internal customers, 22internal failure costs, 34internal perspective, 29internal suppliers, 22interrelationship digraphs, 52–54, 53finterval scales, 91interviews, for customer feedback, 63Ishikawa, Kaoru, 4Ishikawa diagrams, 285, 285f, 286fISO 9000, 5t

JJuran, Joseph M., 3Juran trilogy, 3

Kkaizen, 336, 337, 338

defined, 342–343kaizen blitz, 337

defined, 342–343kanban systems, 332–333Kano model, 69–70, 69fKaplan, Robert S., 28


614 Index

key performance indicators (KPIs)in balanced scorecards, 29–30defined, 29

KPIs. See key performance indicators (KPIs)Kruskal-Wallis test, 266t, 272–275kurtosis, 127

LLatin square designs, 313t, 315–319

source tables for, 314tsums of squares for, 315t

leadership, 14–19change management and, 15–16organizational roadblocks to, 14–15

Lean, defined, 7–8lean manufacturing, 6t, 8Lean-Six Sigma, 6t, 8

defined, 9implementations of, 11–12

lean thinking, 7–8, 340integrating Six Sigma and, 8–9

learning and growth perspective, 29level, defined, 295Levene’s test, 265t, 269–272limits

natural process, 178specification, 178–179

linearity, defined, 97linear regression

multiple, 196–197simple, 189–192

linear regression coefficients, 189linear regression equation, 189link functions, 218lognormal distributions, 160t, 164–165long-term capability, 173–174loyal customers, 31

Mmain effects, 297, 300–303maintainability, design for, 417MAMR (moving average and moving range)

control charts, 383–389considerations when using, 383–384constructing, 384–385

Mann-Whitney test, 266t, 275–277one-tail critical values for, 556–557two-tail critical values, 558–559

MANOVA (multiple analysis of variance), 198, 204–208

manufacturing, design for, 417

margin, 32market share, 32Master Black Belts (MBBs), 18matrix diagram, 56, 56fmean(s), 127–128, 128t, 358–359

commonly used symbol for, 122tconfidence intervals for, 237–240,

238–239thypothesis tests for, 244–248, 245–247t

measurement error, causes of, 120–121measurement scales, 91

interval, 91nominal, 91ordinal, 91ratio, 91

measurement systemscomponents of, 99in enterprises, 118–119re-analysis of, 403–405

measurement systems analysis, 97–99attributes, 111–118variables, 99–111

measurement tools, 95–97examples of, 96–97

measures of central tendency, 128median, 127–128, 128tmedian ranks table, 539–541method of least squares, 188–189metrology, 119–121micrometers, 96Minitab, 107–109

rules for out-of-control conditions, 390mode, 127–128, 128tmodels, 348Mood’s median test, 264–268, 265tmoving average and moving range (MAMR)

control charts, 383–389considerations when using, 383–384constructing, 384–385

moving range charts. See individual and moving range chart

multiple analysis of variance (MANOVA), 198, 204–208

multiple linear regression, 196–197multivariate analysis, 197

discriminant analysis, 198, 201–204factor analysis, 197, 200–201multiple analysis of variance (MANOVA),

198, 204–208principal components analysis, 197,

198–200multi-vari studies, 208–217multivoting, 51, 55


I�� 615

must-be requirements, 70mutually exclusive events, 145

Nn, defined, 295natural process limits, 178net present value (NPV), 33–34neutral characteristics, 70NGT (nominal group technique), 50Nippondenso, 400noise factors

defined, 295planning experiments and, 310for robust design, 418–420

nominal group technique (NGT), 50nominal logistics regression, 218, 224–226nominal scales, 91non-normal data, process capability for,

174–175non-parametric tests, 264, 265–266t

Kruskal-Wallis test, 266t, 272–275Levene’s test, 269–272Mann-Whitney test, 266t, 275–277Mood’s Median test, 264–268

non-value-added, defined, 8normal distributions, 148–151, 149t

cumulative standard table, 499–501standard table, 496–498

normal probability plots, 135–137, 136normal scores table, 543–545norms, team, 44–45Norton, David P., 28np chart, 370–375NPV. See net present value (NPV)

Oobjectives, statement of, for teams, 44observed value, defined, 294Ohno, Taiichi, 332one-dimensional requirements, 70one-factor experiments, 311–319

completely randomized, 311Latin square designs, 315–319randomized complete block design

(RCBD), 311one-sided tolerance limits, factors for,

546–549one-way ANOVA designs, 256–258, 311, 312t

source tables for, 314tsums of squares for, 315t

ongoing evaluation, 411–412

optical comparators, 96order, 297, 298

run, 299standard, 298

ordinal logistic regression, 218, 226–229ordinal scales, 91organizational memory, 408–409out-of-control rules, 389

of Automotive Industry Action Group (AIAG), 390, 396–399

Minitab, 390, 391–396

PPareto charts, 72, 285–288, 286fPareto principle, 131–132parts per million (PPM), 179, 180–181payback period, 33p chart, 368–370PDPC (process decision program chart),

56–57percent agreement, 99percent defective, equivalent sigma levels

and, 554–555perspectives

customer, 28financial, 28internal, 29learning and growth, 29

PERT (Project Evaluation and Review Technique), 76

PEST (political, economic, social, and technological) analysis, 354

phone interviews, for customer feedback, 63pilot runs, 348Plackett-Burman designs, 310planning, strategic, 424–426

tactical, 426–430point estimates, 237Poisson distributions, 149t, 152–153

cumulative table, 489–495table, 481–487

poka-yoke, 335–336population, 122population parameters, 122Porter, Michael, 425Porter’s five forces, 425portfolio architecting, 425positional variation, 208power

defined, 230power, sample size and, 297–298PPM (parts per million), 179, 180–181


616 Index

practical significance, statistical significance vs., 231

precisioncomponents of, 98–99defined, 98

precision protractors, 96precision-to-tolerance ratio (PTR), 99prediction intervals, 195, 235–236prevention costs, 34principal components analysis, 197,

198–200prioritization matrix, 54–56, 55fprobability

addition rule of, 139–141classic definition, 138complementary rule of, 139conditional, 143–144multiplication rule of, 145–147relative-frequency definition, 138rules of, 147t

problem statements, 71procedures, written, 84–85, 85f, 86process analysis tools, 83–89

flowcharts, 84, 84fprocess maps, 84, 84fspaghetti diagrams, 88, 88fvalue stream maps, 85–88, 87fwritten procedures, 84–85, 85f, 86f

process capabilityfor attributes data, 175–176defined, 167for non-normal data, 174–175

process capability indices, 167–171process capability studies, 176–177

conducting, 177process decision program chart (PDPC),

56–57processes

defined, 80metrics for evaluating flow in, 81–83, 82fSIPOC tool for, 80–81, 81f

processes, business, 10process flowcharts, 10, 10fprocess flow metrics, 81–83process FMEA (PFMEA), 278process improvement teams, 38process logs, 389process maps, 72, 84, 84fprocess owners, 18–19process performance

defined, 171specification vs., 178–181

process performance indices, 171–173

process performance metrics, 179–181defects per million opportunities

(DPMO), 179, 180defects per unit (DPU), 179, 180parts per million (PPM), 179, 180–181rolled throughput yield (RTY), 179, 181throughput yield, 179, 180

process-related training plans, developing, 410

process stakeholders, 22–23process variation, sources of, 359producibility, design for, 417profitable customers, 31project charters

defined, 71goals and objectives for, 73performance measures for, 74problem statements, 71project scope, 72–73

Project Evaluation and Review Technique (PERT), 76

project tracking, 73–77proportions

confidence intervals for, 241–243, 242thypothesis tests for, 250–255, 251t

prototypes, 348PTR (precision-to-tolerance ratio), 99Pugh analysis, 429–430pull systems, 333–334push systems, 339p-value

defined, 230

Qquality circles, 5tquality costs, 34quality function deployment (QFD), 66–69,

67f, 68fquality improvement, history of, 2–6quartiles, 130

Rrandomization, 297, 299

planning experiments and, 310randomized complete block design (RCBD),

311, 312tsource tables for, 314tsums of squares for, 315t

random sampling, 93range, 127, 128trapid continuous improvement (RCI), 337


I�� 617

rapid exchange of tooling and dies (RETAD), 340

rational subgroups, choosing, 360–361ratio scales, 91RCBD (randomized complete block design),

340RCI (rapid continuous improvement), 337re-analysis, of measurement systems,

403–405recognition, as team motivation technique,

42recorders

duties of, 40reengineering, 5tregression

binary logistic, 218–223nominal logistic, 218, 224–226ordinal logistic, 218, 226–229

regression analysis, 188–197confidence intervals for, 194–195hypothesis tests for, 196method of least squares, 192–194multiple linear regression, 196–197prediction intervals for, 195simple linear regression, 189–192

relationships within teams, as motivation technique, 43

repeatability, 98repeated measures, 297, 298repetition, 298replication, 297, 298reproducibility, 98–99requirements

attractive, 70must-be, 70one-dimensional, 70

residuals, 188–189resolution, 99, 297, 307–308

planning experiments and, 310response variable, defined, 294RETAD (rapid exchange of tooling and dies),

340return on investment (ROI), 32–33revenue growth, 32reversal characteristics, 70rewards, as team motivation technique, 42ring gages, 96risk analysis, 351–352roadblocks, organizational, 14–15robustness, 5

design for, 417Rockwell method, 97ROI (return on investment), 32–33

rolled throughput yield (RTY), 179, 180root cause analysis, 284

cause-and-effect diagrams, 285, 285f, 286ffault tree analysis, 288–290, 289f5 whys technique, 284–285Pareto charts, 285–288, 286f

RTY (rolled throughput yield), 179, 180run charts, 130t, 132–133, 133frun order, 299

Ssample homogeneity, 93sample size, 231–234

commonly used symbol for, 122tformulas for, 232tpower and, 297–298

sample standard deviation, 127, 128tsampling methods, 92–93scales

interval, 91nominal, 91ordinal, 91ratio, 91

scatter diagrams, 130t, 133–135, 134tscope, defining, 72–73screening designs, 310scribes

duties of, 40self-directed teams, 38setup time, 836Ms, 1207Ms, 120–121Shewhart, Walter A., 2Shingo, Shigeo, 340Shingo methodology, 340short-run control charts, 376–382, 377f

constructing, 380–381rules for, 380summary of formulas for, 378–379t

short-term capability, 173–174sigma levels, equivalent, 554–555significance

statistical vs. practical, 231simple linear regression, 189–192simulations, 348sine bars, 96single minute exchange of dies (SMED), 340SIPOC (suppliers, inputs, process, outputs,

customers) tool, 80–81, 81fSix Sigma, 6t

defined, 6–7integrating Lean and, 8–9


618 Index

projects, 16–17responsibilities, 17–19roles, 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 projectseffective, 23impact on stakeholders and, 23storyboards for, 77teams and, 23

skewness, 127SMART (specific, measurable, achievable,

relevant, timely) goal statements, 73SMED (single minute exchange of dies), 340source tables

for full factorial experiments, 327tspaghetti diagrams, 88, 88fSPC (statistical process control), 5t

objectives of tools for, 358–359special causes, 359specification

limits, 178–179process performance vs., 178–181

sponsor entityduties of, 39

SQC (statistical quality control), 2stability, of measurement system, defined, 97stakeholders, 22–23

general, 22impact of Six Sigma projects on, 23process, 22–23

standard deviation, 358–359commonly used symbol for, 122tsample, 127, 128t

standard error of the estimate, 194standard operating procedures (SOPs),

documenting, 411standard order, 298standard work, 334statement of goals and objectives, for teams,

44statistical conclusions

descriptive, 137inferential, 137

statistical control, state of, 167statistical process control (SPC), 5t

objectives of tools for, 358–359statistical quality control (SQC), 2statistical significance, practical significance

vs., 231

statistics, 122commonly used symbols, 122t

stem-and-leaf diagrams, 129t, 130storyboards, 77

for Six Sigma projects, 77strategic planning, 424

hoshin planning, 425–426Porter’s five forces model, 425portfolio architecting model, 425

stratified sampling, 93Student’s t distribution, 149t, 156–157subgroups, choosing rational, 360–361substance-field involvement, law of, 428sums of squares

for full factorial experiments, 328tfor Latin square designs, 315tone-way ANOVA designs, 315tfor randomized complete block design,

315tsuppliers

external, 22internal, 22

surveysfor customer feedback, 63

SWOT (strengths, weaknesses, opportunities, and threats) analysis, 353

symbols, statistical, commonly used, 122tsystematic design, 428systems, business, 10

Ttactical planning, 426–430

axiomatic design, 428critical parameter management,

428–429Pugh analysis, 429–430systematic design, 428TRIZ, 427–428

Taguchi, Genichi, 5takt time, 82, 83

defined, 338tallies, 129tt distribution (Student’s t distribution), 149t,

156–157table, 502–503

team leaders, duties of, 39team members

duties of, 40selecting, 40

team motivation, techniques for, 42–43team roles, 39–40


I�� 619

teams, 44fcommon obstacles and solutions for,

47–48fcommunication and, 44–45decision-making tools for, 50–51dynamics of, 46growth stages of, 43informal, 38launching, 41norms for, 44–45performance criteria for, 58process improvement, 38rewards for, 58–59selecting members for, 40self-directed, 38statement of objectives for, 44time management for, 49virtual, 38work group, 38

temporal variation, 20810:1 ratio rule, 404test, design for, 417theory of constraints (TOC), 344–346

impact of, 346thread snap gages, 96throughput, 83throughput yield, 179time management, for teams, 49TOC. See theory of constraints (TOC)tolerance design, 420tolerance intervals, 236–237tolerance limits

one-sided, factors for, 546–549two-sided, factors for, 550–553

tolerances, statisticalcapability and, 423conventional, 420, 421–422statistical, 420, 422–423

tolerant customers, 31total productive maintenance (TPM), 400–401total quality control, 4touch time, 82Toyota Production System (TPS), 8TPM (total productive maintenance),

400–401tracking, project, 73–77training

initial, 409recurring, 409

training plansconsiderations, 410developing process-related, 410

transfer devices, 96transition from macro to micro, law of, 428transition to super system, law of, 428treatment, defined, 295tree diagrams, 54, 54f

CTQ, 25fTRIZ (Teorija Rezbenija Izobretaltelshih Zadach),

427–428Tukey, John, 130two-level fractional factorial experiments,

319–325two-sided tolerance limits, factors for, 550–553two-way ANOVA, 258–259Type I error, 231

defined, 230Type II error, 231

defined, 230

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

Vvalue-added, 332value-added time, 83value stream maps, 85–88, 87fvariables control charts, 361–362, 389variables data, 95variables method, of measurement systems

analysis, 99–111ANOVA method, 107–109control chart method, 109–111GR&R study, 100–107

variables selection, for control charts, 360variances

confidence intervals for, 240–241hypothesis tests for, 248–250

virtual teams, 38visual controls, 402visual factory, 401–402voice of customer (VOC), 62, 66–67

Wwaste analysis, sources of, 290–291waste elimination, 332–336

5S system for, 333–334kaizen for, 336


620 Index

kanban systems for, 332–333poka-yoke for, 335–336pull systems for, 333–334standard work for, 334

Weibull distributions, 160t, 165–166Whitney, Eli, 8Wilcoxon signed-rank test, critical values for,

560within-system variation, 98work group teams, 38work in progress (WIP), 82

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

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

Zzero defects concept, 3


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