The Certified Six Sigma Black Belt Handbook

T C S S B B H

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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 controlStatistical methodsHandbooks, manuals, etc. I. Benbow, Donald W., 1936 II. Title.

TS156.B4653 2008 658.4013--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 OMaraProduction 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 daysometimes 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 lifes 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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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 X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 IIX

Certified Six Sigma Black BeltSimulated Exam

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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 matrixfirst step. . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 13.5 Example of a prioritization matrixsecond 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 StudyANOVA method: source tables. . . . . . . . . . . . . . . . . . . . . . 108

Figure 20.7 Gage R&R studyANOVA method: components of variation. . . . . . . . . . . . 109

Figure 20.8 Minitab session window output of the R&R studyX/R method:

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

Figure 20.9 Graphical results of the GR&R studyX/R method:

X and R

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

Table 20.1 Attribute agreement analysisdata 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 studydata 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 22.422.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 = 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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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xviii List of Figures and Tables

Figure 24.4 Scatter diagram from Figure 24.3 with two proposed lines. . . . . . . . . . . . . . . 191

Table 24.2 Computed values for the proposed lines in Figure 24.4. . . . . . . . . . . . . . . . . . 192

Table 24.3 Computed values for the proposed lines given in Figure 24.4 with residual values added. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

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 Moods 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 Levenes test for Example 25.16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

Table 25.22 Levenes test for Example 25.16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

Table 25.23 Levenes 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 231 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 241 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 241 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 analogyno rope. . . . . . . . . . . . . . 345

Figure 32.2 The Drum- Buffer-Rope subordinate step analogywith 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 35.2X 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 35.3individual 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 35.4p chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

Figure 35.7 p chart for data given in Table 35.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

Table 35.4 Data for Example 35.5np chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

Figure 35.8 np chart for data given in Table 35.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

Table 35.5 Data for Example 35.6c chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

Figure 35.9 c chart for data given in Table 35.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

Table 35.6 Data for Example 35.7u 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 certificationbased 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 2933 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 presentfor 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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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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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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1Part I

Part IEnterprise-Wide Deployment

Chapter 1 Enterprise-Wide ViewChapter 2 Leadership

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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


C 1: E-W V 3Part I.A

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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 processesquality planning, quality control, and quality improvementfor use in managing for quality. Juran wrote hundreds of papers and 12 books, includ-ing Jurans Quality Control Handbook (1999), Jurans 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), Lets Talk Quality (1990), and Leading: The Art of Becoming an Executive (1990). Crosbys 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 Ishikawas philosophy:

Quality firstnot short- term profit first.

Consumer orientationnot producer orientation. Think from the standpoint of the other party.

The next process is your customerbreaking down the barrier of sectionalism.

Using facts and data to make presentationsutilization of statistical methods.

Respect for humanity as a management philosophyfull 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 19791981 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 1987present 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 19961997 A breakthrough approach involving the restructuring of an entire organization and its processes.

Benchmarking 19881996 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

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

Continued



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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 organizations 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

1987present 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 Departments National Institute of Standards and Technology manages the award, and ASQ administers it.

Six Sigma 1995present As described in Chapter 1.

Lean manufacturing

2000present As described in Chapter 1.

Lean-Six Sigma 2002present 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-panys bottom line.

Opinions on the definition of Six Sigma differ:

PhilosophyThe 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 toolsSix 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.

MethodologyThe 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.

MetricsIn 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:



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.A.4

A systematic approach to identifying and eliminating waste (non-value-added activities) through continuous improvement by flowing the product at the pull of the customer in pursuit of perfection.

ASQ defines the phrase non-value-added as follows:

A term that describes a process step or function that is not required for the direct achievement of process output. This step or function is identified and examined for potential elimination.

This represents a shift in focus for manufacturing engineering, which has tradition-ally studied ways to improve value- added functions and activities (for example, how can this process run faster and more precisely). Lean thinking doesnt 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, Youre not just talking about Six Sigma; youre 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.

Documents

The Certified Six Sigma Black Belt Handbook