Visual six sigma making data analysis lean (2nd edition) by ian cox, marie gaudard

Snee Too Big to Ignore: The Business Case for Big Data by Phil Simon Trade-Based Money Laundering: The Next Frontier in International Money Laundering ment by John Cassara Enforce-The Vi

Visual Six Sigma

Wiley & SAS Business

Series

The Wiley & SAS Business Series presents books that help senior-level managers with their critical management decisions.

Titles in the Wiley & SAS Business Series include:

Agile by Design: An Implementation Guide to Analytic Lifecycle Management by Rachel

Alt-Simmons

Analytics in a Big Data World: The Essential Guide to Data Science and Its Applications by Bart

Baesens

Bank Fraud: Using Technology to Combat Losses by Revathi Subramanian

Big Data, Big Innovation: Enabling Competitive Differentiation through Business Analytics by

Evan Stubbs

Business Forecasting: Practical Problems and Solutions edited by Michael Gilliland, Len

Tashman, and Udo Sglavo

Business Intelligence Applied: Implementing an Effective Information and Communications nology Infrastructure by Michael Gendron

Tech-Business Intelligence and the Cloud: Strategic Implementation Guide by Michael S Gendron Business Transformation: A Roadmap for Maximizing Organizational Insights by Aiman Zeid Data-Driven Healthcare: How Analytics and BI Are Transforming the Industry by Laura Madsen Delivering Business Analytics: Practical Guidelines for Best Practice by Evan Stubbs

Demand-Driven Forecasting: A Structured Approach to Forecasting, Second Edition by Charles

Economic and Business Forecasting: Analyzing and Interpreting Econometric Results by John

Silvia, Azhar Iqbal, Kaylyn Swankoski, Sarah Watt, and Sam Bullard

Financial Institution Advantage and the Optimization of Information Processing by Sean C Keenan

Financial Risk Management: Applications in Market, Credit, Asset, and Liability Management and Firmwide Risk by Jimmy Skoglund and Wei Chen

Fraud Analytics Using Descriptive, Predictive, and Social Network Techniques: A Guide to Data Science for Fraud Detection by Bart Baesens, Veronique Van Vlasselaer, and Wouter Verbeke Harness Oil and Gas Big Data with Analytics: Optimize Exploration and Production with Data Driven Models by Keith Holdaway

Health Analytics: Gaining the Insights to Transform Health Care by Jason Burke

Heuristics in Analytics: A Practical Perspective of What Influences Our Analytical World by Carlos

Andre, Reis Pinheiro, and Fiona McNeill

Hotel Pricing in a Social World: Driving Value in the Digital Economy by Kelly McGuire Implement, Improve and Expand Your Statewide Longitudinal Data System: Creating a Culture of Data in Education by Jamie McQuiggan and Armistead Sapp

Killer Analytics: Top 20 Metrics Missing from your Balance Sheet by Mark Brown

Mobile Learning: A Handbook for Developers, Educators, and Learners by Scott McQuiggan,

Lucy Kosturko, Jamie McQuiggan, and Jennifer Sabourin

The Patient Revolution: How Big Data and Analytics Are Transforming the Healthcare Experience

by Krisa Tailor

Predictive Analytics for Human Resources by Jac Fitz-enz and John Mattox II

Predictive Business Analytics: Forward-Looking Capabilities to Improve Business Performance by

Lawrence Maisel and Gary Cokins

Statistical Thinking: Improving Business Performance, Second Edition by Roger W Hoerl and

Ronald D Snee

Too Big to Ignore: The Business Case for Big Data by Phil Simon

Trade-Based Money Laundering: The Next Frontier in International Money Laundering ment by John Cassara

Enforce-The Visual Organization: Data Visualization, Big Data, and the Quest for Better Decisions by

Phil Simon

Understanding the Predictive Analytics Lifecycle by Al Cordoba

Unleashing Your Inner Leader: An Executive Coach Tells All by Vickie Bevenour

Using Big Data Analytics: Turning Big Data into Big Money by Jared Dean

Visual Six Sigma, Second Edition by Ian Cox, Marie Gaudard and Mia Stephens

For more information on any of the above titles, please visit www.wiley.com.

Six Sigma

Making Data Analysis Lean

Ian Cox Marie A Gaudard Mia L Stephens

Second Edition

Copyright © 2016 by SAS Institute, Inc All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers,

MA 01923, (978) 750-8400, fax (978) 646-8600, or on the Web at www.copyright.com Requests

to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online

at http://www.wiley.com/go/permissions.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002.

Wiley publishes in a variety of print and electronic formats and by print-on-demand Some material included with standard print versions of this book may not be included in e-books or in print-on-demand If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com For more information about Wiley products, visit www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

Names: Cox, Ian, 1956–

Title: Visual six sigma : making data analysis lean / Ian Cox,

Marie A Gaudard, Mia L Stephens.

Description: Second edition | Hoboken : Wiley, 2016 | Series: Wiley and SAS

business series | Revised edition of Visual six sigma, 2010 | Includes index.

Identifiers: LCCN 2016001878 (print) | LCCN 2016003459 (ebook) |

ISBN 9781118905685 (hardback) | ISBN 9781119222262 (epdf) |

ISBN 9781119222255 (epub)

Subjects: LCSH: Six sigma (Quality control standard) | Decision support

systems | Decision making—Statistical methods | Organizational

effectiveness | BISAC: BUSINESS & ECONOMICS / Strategic Planning.

Classification: LCC HD30.213 C69 2016 (print) | LCC HD30.213 (ebook) |

DDC 658.4/013—dc23

LC record available at http://lccn.loc.gov/2016001878

Cover Design: Wiley

Cover Image: ©Studio-Pro/iStock.com

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

Preface to the Second Edition ix

Preface to the First Edition xiii

Acknowledgments xv

About the Authors xvii

Index 539

vii

Preface to the Second

Edition

The first edition of this book appeared in 2010, so we decided to produce

an updated and expanded second edition The purpose of the book remainsunchanged—to show how, using the three principles of Visual Six Sigma,you can exploit data to make better decisions more quickly and easily than youwould otherwise And, as you might expect given their power and utility, theseprinciples are also unchanged However, production of this second editionallows us to take advantage of some interim developments that make theimplementation of Visual Six Sigma even easier, further increasing the scopeand efficacy of its application It also allows us to improve and enhance thecontent and form of the first edition

The staying power of Six Sigma as a methodology can be attributed to thefact that it can provide a common language for, and approach to, project-basedimprovement initiatives Nonetheless, as we pointed out in the first edition,there is a clear need to evolve the mechanics of Six Sigma both to accommo-date the greater availability of data and to address the fact that, historically,approaches to analyzing data were overly concerned with hypothesis testing, tothe detriment of the hypothesis generation and discovery needed for improve-ment We believe that Visual Six Sigma can foster this evolution, and this is part

of our motivation for keeping this text current

At the same time, the past five years have seen the explosion of “big data,”

at least as an identifiable area that software providers and implementation sultants make strenuous efforts to market to In this language, the increaseddata availability mentioned above is measured using three dimensions: volume,variety, and velocity Even though the precise definition of big data is not alwaysclear, we think there is much for would-be data scientists to learn from the prin-ciples of Visual Six Sigma and their application In addition, if a project-basedapproach is warranted, the language of Six Sigma may also be useful

con-Although the principles of Visual Six Sigma are general, their effective andefficient adoption in practice is reliant on good enabling software The first edi-tion was tied to version 8.01 of JMP, Statistical Discovery software from SAS

ver-sion current at the time of writing, JMP 12.2.0 Generally, JMP aims to exploitthe synergy between visualization and analysis, and its continuing developmenthas opened up new possibilities for Visual Six Sigma In some cases, these aresimply matters of detail and efficiency, but in others there are important newcapabilities we can use

ix

Consistent with the requirements of Visual Six Sigma in the new era of bigdata, we have introduced two new chapters:

and addresses the management of data and data quality Data quality, at

an organizational level, is a ubiquitous topic that is often seen as stream to the point of being boring However, the importance of dataquality for project teams and anyone making decisions with data can-not be overstated As we shall see, the Visual Six Sigma context leads tosome important and interesting nuances

studies and shows how to go beyond the interactive usage of JMP fordiscovery and improvement No matter how simple or complex, theperformance of empirical models always degrades over time Onceimprovements are made, there is always the need to monitor and adaptwith an appropriate frequency In turn, this means that analyses need

to be repeated as new data arrive, and this is often best done with anelement of automation

The case studies appear in Part Two of the book Chapter 4 is appended

to Part One, making this section four chapters long Given the nature of thecontent, Chapter 11 appears as a singleton chapter in Part Three

Finally, we have tried to make the case studies easier to use by having clearer

typographic separation between the narrative (consisting of the why, the what,

and the findings of each technique as it is used in a specific context) and the

“how to” steps required in JMP As well as helping to keep things concise, thisarrangement better accommodates users with different levels of prior familiaritywith JMP, and may make it easier to use other software should this be required

or mandated

As in the first edition, we have used different fonts to help identify thenames of data tables, of columns in data tables, and commands Data table

names are shown in MeridienLTStd-Bold, the names of columns (which are

variable names) are shown in italic Helvetica, and the names of commands and

other elements of the user interface are shown in bold Helvetica.

We are now living through a time of rapid change in the world of dataanalysis We have tried to reflect this in our changes and additions We hopethat this second edition on Visual Six Sigma contains even more of interest forcurrent or would-be Six Sigma practitioners, or more generally for anyone with

in this book is available in JMP 12.2.0 or newer versions.

The data sets used in the book are available at http://support.sas.com/

visualsixsigma This folder contains a journal file, Visual Six Sigma.jrn, that

contains links to the data tables, scripts, and add-ins discussed in this book Thecolor versions of the exhibits shown in the book are also available here Exhibitsshowing JMP results were taken using JMP 12.2.0 running on Windows

Preface to the First Edition

The purpose of this book is to show how, using the principles of Visual SixSigma, you can exploit data to make better decisions more quickly and easilythan you would otherwise We emphasize that your company does not need tohave a Six Sigma initiative for this book to be useful Clearly there are manydata-driven decisions that, by necessity or by design, fall outside the scope of aSix Sigma effort, and in such cases we believe that Visual Six Sigma is ideal Weseek to show that Visual Six Sigma can be used by a lone associate, as well as ateam, to address data-driven questions, with or without the support of a formalinitiative like Six Sigma

To this end, we present six case studies that show Visual Six Sigma inaction These case studies address complex problems and opportunities faced

by individuals and teams in a variety of application areas Each case studywas addressed using the Visual Six Sigma Roadmap, described in Chapters 2and 3 As these case studies illustrate, Visual Six Sigma is about explorationand discovery, which means that it is not, and never could be, an entirelyprescriptive framework

As well as using the case studies to convey the Visual Six Sigma Roadmap,

we also want to use them to illustrate Visual Six Sigma techniques that you canreuse in your own setting To meet this goal, sometimes we have deliberatelycompromised the lean nature of the Visual Six Sigma Roadmap in order to takethe opportunity to show you extra techniques that may not be strictly nec-essary to reach the conclusion or business decision Striking the balance thisway means that you will see a wider repertoire of techniques from which tosynthesize an approach to Visual Six Sigma that works for you

Because of its visual emphasis, Visual Six Sigma opens the doors fornon-statisticians to take active roles in data-driven decision making, empow-ering them to leverage their contextual knowledge to pose relevant questions,get good answers, and make sound decisions You may find yourself working

on a Six Sigma improvement project, a design project, a data mining inquiry,

or a scientific study—all of which require decision making based on data Afterworking through this book, we hope that you will be able to make data-drivendecisions in your specific situation quickly, easily, and with greater assurance

How This Book Is Organized

This book is organized in two parts Part I contains an introductory chapter thatpresents the three Visual Six Sigma strategies, a chapter on Visual Six Sigma,

xiii

xiv P R E F A C E T O T H E F I R S T E D I T I O N

will be used throughout the case studies

Case studies are presented in Part Two These case studies follow ing real-world projects from start to finish Through these case studies, you willgain insight into how the three Visual Six Sigma strategies combine to expediteproject execution in the real world Each case study is given its own chapter,which can be read independently from the rest A concise summary of the story-line opens each case study Although these case studies are real, we use fictitiousnames for the companies and individuals to preserve confidentiality

challeng-Within each case study, visualization methods and other statistical niques are applied at various stages in the data analysis process in order to betterunderstand what the data are telling us For those not familiar with JMP, eachcase study also contains the relevant how-to steps so that you may follow alongand see Visual Six Sigma in action

tech-The data sets used in the case studies are available at http://support.sas.com/visualsixsigma Here you can also find the exhibits shown in the casestudies, allowing you to see screen captures in color Additional Visual Six Sigmaresource materials will be made available on the website, as appropriate

A Word about Software

The ideas behind Visual Six Sigma are quite general, but active learning—in ourview, the only kind of learning that works—requires that you step through thecase studies and examples in this book to try things out for yourself For moreinformation about JMP, and to download a trial version of the software, visitwww.jmp.com/demo

JMP is available on Windows, Mac, and Linux platforms The step-by-stepinstructions in this book assume that you are working in Windows Mac andLinux users should refer to the JMP documentation for details on differences.This book is based on JMP version 8.0.1

Stating the obvious, this book would not exist without its first edition Eventhough some have moved on, we remain deeply indebted to all those listedwho made the first edition possible Most importantly, we want to thank LeoWright of SAS and Phil Ramsey of the North Haven Group, LLC, our co-authors

on the first edition, who provided some of the original case studies and helped

to make this book possible

Both editions of the book were substantially improved by suggestions fromMark Bailey of SAS We greatly appreciate his time, interest, valuable feed-back, and insights We want to thank Andy Liddle, now of Process InsightConsulting Limited, who assisted with the review of the original version of “Im-proving a Polymer Manufacturing Process” (now Chapter 9) We also want tothank Volker Kraft of SAS, who provided valuable feedback in connection withupdates to this case study for the book’s second edition

This project was greatly facilitated by Stacey Hamilton and Stephenie Joyner

of SAS Publishing Their support, encouragement, and attention to detail atevery step of this adventure were invaluable

Finally, we would like to thank Jon Weisz and Curt Hinrichs of JMP fortheir support and encouragement in updating this book And, as before, a spe-cial thank-you goes to John Sall, Bradley Jones, Chris Gotwalt, Xan Gregg,Brian Corcoran, and the JMP Development Team for their continuing work

on a visionary product that makes Visual Six Sigma possible

xv

About the Authors

Ian Cox currently works in the JMP Division of SAS Before joining SAS in

1999, he worked for Digital Equipment Corporation, Motorola, and BBN ware Solutions Ltd and has been a consultant for many companies on dataanalysis, process control, and experimental design A Six Sigma Black Belt, hewas a Visiting Fellow at Cranfield University and is a Fellow of the Royal Sta-tistical Society Cox holds a Ph.D in theoretical physics

Soft-Marie A Gaudard is a consultant specializing in statistical training with the

use of JMP She is currently a statistical writer with the JMP documentationteam She earned her Ph.D in statistics in 1977 and was a professor of statistics

at the University of New Hampshire from 1977 until 2004 She has been heavilyinvolved in statistical consulting since 1981 Gaudard has worked with a vari-ety of clients in government agencies, medical areas, and manufacturing Shehas extensive experience in consulting and training in the areas of Six Sigma,Design for Six Sigma, forecasting and demand planning, and data mining

Mia L Stephens is an academic ambassador with the JMP division of SAS.

Prior to joining SAS, she was an adjunct professor at the University of NewHampshire and a partner in the North Haven Group, a statistical training and

consulting company Also a coauthor of JMP Start Statistics: A Guide to Statistics and Data Analysis Using JMP, Fifth Edition and Building Better Models with JMP Pro,

she has developed courses and training materials, taught, and consulted within

a variety of manufacturing and service industries Stephens holds an M.S instatistics from the University of New Hampshire

xvii

Visual Six Sigma

P A R T

ONE

Background

Visual Six Sigma: Making Data Analysis Lean, Second Edition Ian Cox, Marie A Gaudard, Mia L Stephens

© 2016 by SAS Institute, Inc Published by John Wiley & Sons, Inc.

C H A P T E R 1

Introduction

3

Visual Six Sigma: Making Data Analysis Lean, Second Edition Ian Cox, Marie A Gaudard, Mia L Stephens

© 2016 by SAS Institute, Inc Published by John Wiley & Sons, Inc.

4 V I S U A L S I X S I G M A

WHAT IS VISUAL SIX SIGMA?

Visual Six Sigma is about leveraging interactive and dynamic graphical displays

to help transform data into sound decisions It is not an algorithm It is a ative process that employs visual techniques in the discovery of new and usefulknowledge, leading to quicker and better decisions than do the methods ingeneral use today It signals a new generation of Six Sigma techniques

cre-At the heart of Six Sigma is the concept of data-driven decision making, that

is, of exploiting the data from measurements or simulations at various points

in the life cycle of your product or service Visual Six Sigma aims to producebetter alignment between Six Sigma practice and the key idea of discovery,providing benefits for all those who have a stake in solving problems and inmaking improvements through data

Visual Six Sigma consists of three main strategies:

1 Using dynamic visualization to literally see the sources of variation in

Sigma program provides a structure for a company’s efforts Each phase ofDMAIC comes with a list of techniques that are considered appropriate in thatphase; the team moves from one phase to another, using this sequence of tech-niques as a general guide In a similar way, Six Sigma projects aimed at design

follow various structures, such as Define, Measure, Analyze, Design, and Validate (DMADV) and Identify, Design, Optimize, and Validate (IDOV).

Visual Six Sigma is not a replacement for the DMAIC, DMADV, or IDOVframeworks Rather, Visual Six Sigma supports these frameworks by simplifyingand enhancing methods for data exploration and discovery whenever they areneeded In addition, when circumstances make a full-blown project-based orteam-based approach undesirable or unworkable, Visual Six Sigma can still beused by individual contributors such as you In a nutshell, Visual Six Sigma helps

to make the DMAIC and design structures—and data analysis in general—lean

Moving beyond Traditional Six Sigma

It is our belief that the tools, techniques, and workflows in common use withSix Sigma efforts are typically not aligned with the key idea of discovery In

I N T R O D U C T I O N 5

the early days of Six Sigma, relevant data rarely existed, and a team was oftenchallenged to collect data on its own As part of the Measure phase, a team usu-ally conducted a brainstorming session to identify which features of a processshould be measured In some sense, this brainstorming session was the team’sonly involvement in hypothesis generation The data collected were precious,and hypothesis testing methods were critical in separating signals from noise.Project teams struggling with a lack of useful data generally rely on an abun-dance of subjective input, and often require hypothesis testing to minimize therisk of bad decisions This emphasis on hypothesis testing is reasonable in anenvironment where data are sparse In contrast, today’s Six Sigma teams oftenfind warehouses of data that are relevant to their efforts Their challenge is towade through the data to discover prominent features, to separate the remark-able from the unremarkable

These data-rich environments call for a shift in emphasis from tory methods, such as hypothesis testing, to exploratory methods, with a majoremphasis on the display of data to reveal prominent features that are hidden

confirma-in the data Sconfirma-ince the human confirma-interpretation of the data context is a vital part

of the discovery process, these exploratory techniques cannot be fully mated Also, with large quantities of data, hypothesis testing itself becomes lessuseful—statistical significance comes easily and may have little to do with prac-tical importance

auto-Of course, the simple abundance of data in a warehouse does not guaranteeits relevance for improvement or problem solving In fact, it is our experiencethat teams working in what they believe to be data-rich environments some-times find that the available data are of poor quality or are largely irrelevant

to their efforts Visualization methods can be instrumental in helping teamsquickly reach this conclusion In these cases, teams need to revert to techniquessuch as brainstorming, cause-and-effect diagrams, and process maps, whichdrive efforts to collect the proper data But, as we shall see, even in situationswhere only few relevant data are available, visualization techniques, supported

as appropriate by confirmatory methods, prove invaluable in identifying tellingfeatures of the data

Making Data Analysis Lean

Discovery is largely supported by the generation of hypotheses—conjecturesabout relationships and causality Today’s Six Sigma teams, and data analysts

in the business world in general, are often trained with a heavy emphasis onhypothesis testing, with comparatively little emphasis given to hypothesis gen-eration and discovery They are often hampered in their problem-solving andimprovement efforts by the inability to exploit exploratory methods, whichcould enable them to make more rapid progress, often with less effort

6 V I S U A L S I X S I G M A

In recent times, we have seen incredible advances in visualization methods,supported by phenomenal increases in computing power We strongly believethat the approaches now allowed by these methods are underutilized in currentSix Sigma practice It is this conviction that motivated us to write the first edition

of this book and, following its success, to produce a second edition that takesadvantage of recent software advances We hope you find this book useful asyou shape and build your own real-world Six Sigma experience

Requirements of the Reader

This leads to another important point, namely, that you are “part of the system.”Discovery, whether practiced as an individual or as a team sport, involves bothdivergent and convergent thinking; both creativity and discipline are required

at different times You should bear this in mind when forming a team or whenconsulting with individuals, since each person will bring his or her own skillset, perspective, and strength to the discovery process

Given the need to be data driven, we also need to recognize one of the basicrules of using data, which is that any kind of analysis that treats data simply as alist of numbers is doomed to failure To say it differently: All data are contextual,and it is this context and the objectives set out for the project that must shapethe analysis and produce useful recommendations for action As a practitioner,your main responsibility should always be to understand what the numbers inthe data actually mean in the real world In fact, this is the only requirementfor putting the ideas in this book into practice in your workplace

C H A P T E R 2

Six Sigma and Visual Six Sigma

7

Visual Six Sigma: Making Data Analysis Lean, Second Edition Ian Cox, Marie A Gaudard, Mia L Stephens

© 2016 by SAS Institute, Inc Published by John Wiley & Sons, Inc.

8 V I S U A L S I X S I G M A

our focus is on the latter Six Sigma is a potentially huge topic, so we onlyhave space to mention some of its essential ideas There are already numer-ous well-written books and articles dealing with the many and diverse aspects

(software, databases, visual media, etc.) are leveraged extensively in Six Sigma

Our goal in this chapter is to provide an overview of Six Sigma so that youstart to see how Visual Six Sigma fits into this picture However, it is worthpointing out in advance that you can only gain a proper appreciation of thepower of visualization techniques by working with data that relate to real prob-lems in the real world

BACKGROUND: MODELS, DATA, AND VARIATION

There is no doubt that science and technology have transformed the lives ofmany and will continue to do so Like many fields of human endeavor, science

proceeds by building pictures, or models, of what we think is happening These

models can provide a framework in which we attempt to influence or controlinputs so as to provide better outputs Unlike the models used in some otherareas, the models used in science are usually constructed using data that arisefrom measurements made in the real world

At the heart of the scientific approach is the explicit recognition that we may

be wrong in our current world view Saying this differently, we recognize that

our models will always be imperfect, but by confronting them with data, we canstrive to make them better and more useful Echoing the words of George Box,one of the pioneers of industrial statistics, we can say, “Essentially, all models

MODELS

The models of interest in this book can be conceptualized as shown inExhibit 2.1 This picture demands a few words of explanation:

are denoted with a Y For example, Y1 in Exhibit 2.1 could represent theevent that someone will apply for a new credit card after receiving anoffer from a credit card company

example, X1 may denote the age of the person receiving the creditcard offer

the recipient to influence the chance that he or she will apply for a credit

S I X S I G M A A N D V I S U A L S I X S I G M A 9

Causes We Don’t Understand, Know About, or Care About

Measured Effects

or Outcomes of Interest

Exhibit 2.1 Modeling of Causes before Improvement

card after receiving an offer,” we can just write Y = f(X) Here, f is called

a function, and Y = f(X) describes how Y changes as X changes If we think

that Y depends on more than one X, we simply write an expression like

Y = f(X1, X2) Since the function f describes how the inputs X1 and X2

affect Y, the function f is called a signal function.

in the diagram with solid arrows, and (X4, X5, X6), shown with ted arrows The causes with dotted arrows are the causes that we donot know about or care about, or causes that it is impossible or uneco-

dot-nomic to control Often, these are called nuisance or noise variables For

example, X4 could be the number of credit cards that the recipient ofthe offer already has, or the time since the recipient received a similaroffer The function that represents the combined effect of the noise vari-

ables on Y is called a noise function, and the result is sometimes referred

to simply as error.

that they do not influence Y If X4, X5, or X6 change, as they typically

will, then they will necessarily lead to some apparently inexplicable ation in the outcome Y, even when we do our best to keep X1, X2, and X3

vari-fixed For example, whether an offer recipient applies for a new creditcard may well be influenced by the number of credit cards that the recip-ient already has

As you can see in the exhibit, a key aspect of such a model is that it focuses

on some specific aspects (i.e., X1, X2, and X3) in order to better understandthem By intention or simply lack of current knowledge, the model necessarilyomits some aspects that may actually be important (X4, X5, and X6)

Depending on whether you are being optimistic or pessimistic, Six Sigmacan be associated with improvement or problem solving Very often, an explicitmodel relating the Ys to Xs may not exist; to effect an improvement or to solve

a problem, you need to develop such a model The process of developing this

10 V I S U A L S I X S I G M A

Causes We Don’t Understand, Know About, or Care About

Measured Effects

or Outcomes of Interest

X5 X6

Exhibit 2.2 Modeling of Causes after Improvement

model first requires arriving at a starting model and then confronting that modelwith data to try to refine it Later in this chapter, in the section “Visual Six Sigma:Strategies, Process, Roadmap, and Guidelines,” we discuss a process for refiningthe model

If you succeed in refining it, then the new model might be represented asshown in Exhibit 2.2 Now X4 has a solid arrow rather than a dotted arrow and

is within the scope of the signal function rather than the noise function When

we gain a new understanding of a noise variable, we gain leverage in explainingthe outcome (Y) and so can often make the outcome more favorable to us Inother words, we are able to make an improvement

The use of the term error to refer to a noise function has technical origins, and its use is pervasive, though noise might be a better term Useful models

that encompass variation rely on making a correct separation of the noise andthe signal implied by the data Indeed, the inclusion of noise in the model is

essentially the definition of a statistical model (see the section “Variation and Statistics”), and in such models the relevance or statistical significance of a signal

variable is assessed in relation to the noise

MEASUREMENTS

The use of data-driven models to encapsulate and predict how important aspects

of a business operate is still a new frontier Moreover, there is a sense in which

a scientific approach to business is more challenging than the pursuit of ence itself In science, the prevailing notion is that knowledge is valuable forits own sake But for any business striving to deliver value to its customersand stakeholders—usually in competition with other businesses doing the same

sci-thing—knowledge does not necessarily have an intrinsic value This is particularly

so since the means to generate, store, and use data and knowledge are in selves value-consuming, including database and infrastructure costs, trainingcosts, cycle time lost to making measurements, and so on

them-S I X them-S I G M A A N D V I them-S U A L them-S I X them-S I G M A 11

Therefore, for a business, the only legitimate driving force behind a

scien-tific, data-driven approach that includes modeling is a failure to produce or deliver what is required This presupposes that the business can assess and monitor what

is needed, which is a nontrivial problem for at least two reasons:

1 A business is often a cacophony of voices, expressing different views as

to the purpose of the business and needs of the customer

2 A measurement process implies that a value is placed on what is beingmeasured, and it can be very difficult to determine what should bevalued

It follows that developing a useful measurement scheme can be a difficult,but vital, exercise Moreover, the analysis of the data that arise when mea-surements are actually made gives us new insights that often suggest the needfor making new measurements We will see some of this thinking in the casestudies that follow

OBSERVATIONAL VERSUS EXPERIMENTAL DATA

Before continuing, it is important to note that the data we will use come in twotypes, depending on how the measurements of Xs and Ys are made: observa-tional data and experimental data Exhibit 2.1 allows us to explain the crucialdifference between these two types of data

1 Observational data arise when, as we record values of the Ys, the values

of the Xs are allowed to change at will This occurs when a process runsnaturally and without interference

2 Experimental data arise when we deliberately manipulate the Xs and then

record the corresponding Ys

Observational data are collected with no control over associated Xs Often

we simply assume that the Xs are essentially constant over the observationalperiod, but sometimes the values of a set of Xs are recorded along with thecorresponding Y values

In contrast, the collection of experimental data requires us to force variation

in the Xs This involves designing a plan that tells us exactly how to change

the Xs in the best way, leading to the topic of experimental design, or design

of experiments (DOE) DOE is a powerful and far-reaching approach that has

The book Optimal Design of Experiments: A Case Study Approach guides readers in

In both manufacturing and nonmanufacturing settings, DOE is starting to

12 V I S U A L S I X S I G M A

In such experiments, users or potential users of a product or service are giventhe chance to compare attributes and express their preferences or choices Thisallows market researchers and developers to take a more informed approach

to tailoring and trading off the attributes of the product or service in advance.Because one attribute can be price, such methods allow you to address an impor-tant question: What will users pay money for? We note that JMP has extensive,easy-to-use facilities for both the design and analysis of choice models

Even in situations where DOE is relevant, preliminary analysis of tional data is advised to set the stage for designing the most appropriate andpowerful experiment The case studies in this book deal predominantly withthe treatment of observational data, but Chapters 7 and 9 feature aspects ofDOE as well

observa-SIX SIGMA

Some common perceptions and definitions of Six Sigma include:

opportunities

In spite of this diversity of perspectives, there seems to be broad agreementthat a Six Sigma initiative involves a variety of stakeholders and is a project-based method utilizing cross-functional teams A performance gap is the onlylegitimate reason for spending the time and resources needed to execute a SixSigma project From this point of view, questions such as the following are vital

to a Six Sigma deployment:

S I X S I G M A A N D V I S U A L S I X S I G M A 13

However, for reasons of space, our brief discussion will only address thesteps that are followed in a typical Six Sigma project once it has been kicked off.Using the background presented in the beginning of this chapter, we offerour own succinct definition of Six Sigma:

Six Sigma is the management of sources of variation in relation to performance requirements.

Here, management refers to some appropriate modeling activity fed by data.

Depending on both the business objectives and the current level of ing, management of sources of variation can mean:

A Six Sigma deployment effort typically starts with the following structure:

the necessary impetus and alignment by assuming a leadership role

the senior executive, oversees the Six Sigma deployment

indi-vidual is usually a member of the executive committee and has enoughinfluence to remove obstacles or allocate resources without having toappeal to a more senior individual

improve-ments to operations

This individual is a full-time change agent who is allocated to severalprojects A black belt is usually a quality professional, but is often not anexpert on the operational processes within the scope of the project

project

green belts), often provides training, and advises the executive tee A master black belt must have a proven track record of effectingchange and be a known and trusted figure This track record is estab-lished by having successfully completed and led numerous Six Sigmaprojects, ideally within the same organization

commit-14 V I S U A L S I X S I G M A

To guide Six Sigma projects that seek to deliver bottom-line results in the

short or medium term, black belts typically use the Define, Measure, Analyze, Improve, and Control (DMAIC) structure, where DMAIC is an acronym for the

five phases involved:

1 Define Define the problem or opportunity that the project seeks to

address, along with the costs, benefits, and the customer impact Definethe team, the specific project goals, the project timeline, and the process

if needed Brainstorm or otherwise identify as many Xs as possible, inorder to include the Xs that represent root causes

3 Analyze Use process knowledge and data to determine which Xs

repre-sent root causes of variation in the Ys

4 Improve Find the settings for Xs that deliver the best possible values

for the Ys, develop a plan to implement process changes, pilot the cess changes to verify improvement in the Ys, and institutionalize thechanges

pro-5 Control Lock in the performance gains from the Improve phase.

Depending on the state of the process, product, or service addressed by theproject, a different set of steps is sometimes used For instance, for products or

processes that are being designed or redesigned, the Define, Measure, Analyze, Design, Verify (DMADV) or the Identify, Design, Optimize, Validate (IDOV) frame-

work is often used These structures form the basis of Design for Six Sigma

1 Define Similar to the Define phase of DMAIC.

2 Measure Determine internal and external customer requirements,

mea-sure baseline performance against these requirements, and benchmarkagainst competitors and industry standards

3 Analyze Explore product and process design options for satisfying

cus-tomer requirements, evaluate these options, and select the best design(s)

4 Design Create detailed designs of the product and process, pilot these,

and evaluate the ability to meet customer requirements

5 Verify Verify that the performance of the product and process meets

cus-tomer requirements

This brings us back full circle to our own definition of Six Sigma:management of sources of variation in relation to performance requirements

S I X S I G M A A N D V I S U A L S I X S I G M A 15

With a little thought, perhaps you can see how large parts of DMAIC, DMADV,

or IDOV involve different ways to manage variation For example, a DFSSproject would involve techniques and tools to “anticipate sources of variation”

in the product, process, or service

VARIATION AND STATISTICS

In the previous section, we mentioned the following aspects of managingvariation:

The first point, “Identify and quantify sources of variation,” is a vital stepand typically precedes the others In fact, Six Sigma efforts aside, many busi-nesses can derive useful new insights and better knowledge of their processesand products simply by understanding what their data represent and by inter-

acting with their data to literally see what has not been seen before

Identifi-cation of sources of variation is a necessary step before starting any modelingassociated with the other Six Sigma steps Even in those rare situations wherethere is already a high level of understanding about the data and the model, itwould be very unwise to begin modeling without first investigating the data.Every set of data is unique, and in the real world, change is ubiquitous, includ-ing changes in the patterns of variation

Given that the study of variation plays a central role in Six Sigma, it would

be useful if there were already a body of knowledge that we could apply to

help us make progress Luckily, there is: statistics! One of the more enlightened definitions of statistics is learning in the face of uncertainty; since variation is a

result of uncertainty, then the relevance of statistics becomes immediately clear.However, statistics tends to be underutilized in understanding uncertainty

We believe that one of the reasons is that the fundamental difference between

an exploratory study and a confirmatory study is not sufficiently emphasized or

understood This difference can be loosely expressed as the difference between

statistics as detective and statistics as lawyer Part of the difficulty with fully appreciating the relevance of statistics as detective is that the process of discovery

it addresses cannot fully be captured within an algorithmic or theoreticalframework Rather, producing new and valuable insights from data relies onheuristics, rules of thumb, serendipity, and contextual knowledge In contrast,

statistics as lawyer relies on deductions that follow from a structured body of

knowledge, formulas, statistical tests, and p-values

The lack of appreciation of statistics as detective is part of our motivation in

writing this book A lot of traditional Six Sigma training overly emphasizes

16 V I S U A L S I X S I G M A

statistics as lawyer This generally gives an unbalanced view of what Six Sigma

should be, as well as making unrealistic and overly time-consuming demands

on practitioners and organizations

Six Sigma is one of many applications where learning in the face of tainty is required In any situation where statistics is applied, the analyst willfollow a process, more or less formal, to reach findings, recommendations, and

1 Exploratory Data Analysis

2 Confirmatory Data Analysis

Exploratory Data Analysis (EDA) is nothing more than a fancy name for tics as detective, whereas Confirmatory Data Analysis (CDA) is simply statistics as lawyer In technical jargon, the emphasis in EDA is on hypothesis generation In

statis-EDA efforts, the analyst searches for clues in the data that help identify theories

about underlying behavior In contrast, the focus of CDA is hypothesis testing and inference CDA consists of confirming these theories and behaviors CDA fol- lows EDA, and together they make up statistical modeling A paper by Jeroen de

Mast and Albert Trip provides a detailed discussion of the crucial role of EDA in

or shifting the scope of the investigation as knowledge is developed So it is withgenerating hypotheses through EDA

We have seen that the first and sometimes only step in managing tainty is to identify and quantify sources of variation Building on the old adagethat “a picture is worth a thousand words,” it is clear that graphical displaysshould play a key role here This is especially desirable when the software allowsyou to interact freely with these graphical views Thanks to the advance of tech-nology, most Six Sigma practitioners now have capabilities on their desktopsthat were only the province of researchers 10 years ago, and were not evenforeseen 30 years ago Although it is not entirely coincidental, we are fortunatethat the wide availability of this capability comes at a time when data volumescontinue to escalate

uncer-Incidentally, many of the statistical methods that fall under CDA, whichare in routine use by the Six Sigma community, were originally developed for

squeezing the most out of a small volume of data, often with the use of

noth-ing more than a calculator or a pen and paper Increasnoth-ingly, the Six Sigma

S I X S I G M A A N D V I S U A L S I X S I G M A 17

practitioner is faced with a quite different challenge: The sheer volume of data(rows and columns) can make the nạve application of statistical testing, should

it be needed, difficult and questionable

At this point, let us consider the appropriate role of visualization and, gentially, data mining within Six Sigma Visualization, which has a long andinteresting history of its own, is conventionally considered valuable in three

1 Checking raw data for anomalies (EDA)

2 Exploring data to discover plausible models (EDA)

3 Checking model assumptions (CDA)

Given the crucial role of communication in Six Sigma, we can add twoadditional ways in which visualization has value:

1 Investigating model outcomes (EDA and CDA)

2 Communicating results to others (EDA and CDA)

There are a wide variety of ways to display data visually Many of these,such as histograms, scatterplots, Pareto plots, and box plots, are already inwidespread use However, the simple idea of providing multiple linked views ofdata with which you can interact via software takes current Six Sigma analysis

to another level of efficiency and effectiveness For example, imagine clicking

on a bar in a Pareto chart and seeing the corresponding points in a scatterplotbecome highlighted Imagine what can be learned! Unfortunately, however, alot of software is still relatively static, offering little more than a computerizedversion of what is possible on the printed page In contrast, we see the dynamicaspect of good visualization software as critical to the detective work of EDA,which relies on an unfolding, rather than preplanned, set of steps

Visualization remains an active area of research, particularly when data

For example, the parallel coordinates plots used for visualizing data with manycolumns are well known within the visualization community, but have not yet

Additionally, although there are established principles about the correctways to represent data graphically, the fact that two individuals will perceivepatterns differently means that good software should present a wide repertoire

to demonstrate through the case studies that this comprehensive dynamic ing is a powerful capability for hypothesis generation To emphasize this desir-

link-able aspect, from now on, we will refer to dynamic visualization, rather than

simply visualization

Not only does dynamic visualization support EDA when data volumes arelarge, but it is also our experience that dynamic visualization is very powerful

18 V I S U A L S I X S I G M A

when data volumes are modest For instance, if the distributions of two or more

variables are linked together, you can quickly and easily see the balance of the

data, that is, which values or levels of one variable occur with those of another

If the data are perfectly balanced, then tabulation may also provide the sameinsight, but if the data are only nearly balanced or if they are unbalanced, as ismore often the case, the linked distributions will usually be much more easilyinterpreted With dynamic visualization, we can assess many views of the dataquickly and efficiently

The mention of large data volumes inevitably raises the topic of data mining.

This is a rapidly moving field, so a precise definition is difficult Essentially, data

mining (also known as predictive analytics) is the process of sorting through large

amounts of data and picking out relevant information using techniques from

two sets, and a model is built using one set, then validated or tested on the

second set Once the model is built, it is used to score new data as they arrive,

thereby making (hopefully) useful predictions

As with traditional statistical analysis, there are several processes that you

automates each step in the process, usually involving some prescribed stoppingrule to determine when there is no further structure in the data to model Assuch, many data-mining efforts have a strong flavor of CDA However, EDA canbring high value to data-mining applications, especially in Six Sigma settings

In our case studies, we will see two such applications

VISUAL SIX SIGMA: STRATEGIES, PROCESS, ROADMAP,

AND GUIDELINES

In this section, we will explore the three strategies that underlie Visual SixSigma We then present the Visual Six Sigma Data Analysis Process that supportsthese strategies through six steps and define the Visual Six Sigma Roadmap thatexpands on three of the key steps This section closes with guidelines that helpyou assess your performance as a Visual Six Sigma practitioner

Visual Six Sigma Strategies

As mentioned earlier, Visual Six Sigma exploits the following three keystrategies to support the goal of managing variation in relation to performancerequirements:

1 Using dynamic visualization to literally see the sources of variation in

your data

2 Using exploratory data analysis techniques to identify key drivers and els, especially for situations with many variables

mod-S I X mod-S I G M A A N D V I mod-S U A L mod-S I X mod-S I G M A 19

3 Using confirmatory statistical methods only when the conclusions arenot obvious

Note that with reference to the section “Variation and Statistics,” Strategy 1

falls within what was called EDA, or statistics as detective Strategy 3 falls within what we defined as CDA, or statistics as lawyer Strategy 2 has aspects of both

EDA and CDA

Earlier, we stressed that by working in the EDA mode of statistics as detective

we have to give up the possibility of a neat conceptual and analytical

frame-work Rather, the proper analysis of our data has to be driven by a set of informal rules

or heuristics that allow us to make new, useful discoveries However, there are still

some useful principles that can guide us Jeroen de Mast and Albert Trip offer anexcellent articulation and positioning of these principles in the Six Sigma con-

and appear in a modified form in the Visual Six Sigma Roadmap presented later(Exhibit 2.4)

If you recall from Chapter 1, one of the goals of Visual Six Sigma is to equipusers who know their business with some simple ideas and tools to get from data

to decisions easily and quickly Indeed, we would argue that the only uisite for a useful analysis, other than having high-quality data, is knowledge

prereq-of what the different variables that are being analyzed actually represent Wecannot emphasize strongly enough this need for contextual knowledge to guideinterpretation; it is not surprising that this is one of the key principles listed by

de Mast and Trip

As mentioned earlier, a motivating factor for this book is our convictionthat the balance in emphasis between EDA and CDA in Six Sigma is not alwayscorrect Yet another motivation for this book is to address the perception that ateam must strictly adhere to the phases of DMAIC, even when the data or prob-lem context does not warrant doing so The use of the three key Visual Six Sigmastrategies provides the opportunity to reengineer the process of going from data

to decisions In part, this is accomplished by freeing you, the practitioner, fromthe need to conduct unnecessary analyses

Visual Six Sigma Data Analysis Process

We have found the simple process shown in Exhibit 2.3 to be effective in many

real-world situations We refer to this in the remainder of the book as the Visual Six Sigma (VSS) Data Analysis Process.

This process gives rise to the subtitle of this book, Making Data Analysis Lean.

As the exhibit shows, it may not always be necessary to engage in the “ModelRelationships” activity This is reflective of the third Visual Six Sigma strategy

An acid test for a Six Sigma practitioner is to ask, “If I did have a model of Ys

20 V I S U A L S I X S I G M A

Statistics as Detective (EDA)

Utilize Knowledge

Revise Knowledge

Model Relationships

Statistics as

Lawyer (CDA)

Exhibit 2.3 Visual Six Sigma Data Analysis Process

against Xs from CDA, how would it change my recommended actions for thebusiness?”

The steps in the VSS Data Analysis Process may be briefly described asfollows:

1 Frame Problem Identify the specific failure to produce what is required

(see prior section titled “Measurements”) Identify your general strategyfor improvement, estimate the time and resources needed, and calculatethe likely benefit if you succeed Identify the Y or Ys of interest

2 Collect Data Identify potential Xs using techniques such as brainstorming,

process maps, data mining, failure modes and effects analysis (FMEA),and subject matter knowledge Passively or actively collect data thatrelate these to the Ys of interest

3 Uncover Relationships Assess your data’s strengths, weaknesses, and

rele-vance to your problem Using exploratory tools and your understanding

of the data context, generate hypotheses and explore whether and howthe Xs relate to the Ys

4 Model Relationships Build statistical models relating the Xs to the Ys.

Determine statistically which Xs explain variation in the Ys and mayrepresent causal factors

5 Revise Knowledge Optimize settings of the Xs to give the best values for the

Ys Explore the distribution of Ys as the Xs are allowed to shift a little fromtheir optimal settings Collect new data to verify that the improvement

is real

S I X S I G M A A N D V I S U A L S I X S I G M A 21

6 Utilize Knowledge Implement the improvement and monitor or review

the Ys with an appropriate frequency to see that the improvement ismaintained

Visual Six Sigma Roadmap: Uncover Relationships, Model

Relationships, and Revise Knowledge

In this section, we expand on the three steps in the VSS Data Analysis Processthat benefit the most from the power of visual methods: Uncover Relationships,Model Relationships, and Revise Knowledge These activities are reflective ofwhere we see the biggest opportunities for removing waste from the process ofgoing from data to decisions

The Visual Six Sigma Roadmap in Exhibit 2.4 guides you through thesethree important steps Given that the displays used for visualization and discov-ery depend upon your own perceptive and cognitive style, the Visual Six Sigma

Roadmap focuses on the goal, or the what, of each step However, in Chapter 3,

we will make specific suggestions about how each step can be accomplished

using JMP

This Roadmap uses the Six Sigma convention that a variable is usuallyassigned to a Y role (an outcome or effect of interest) or to an X role (a pos-

sible cause that may influence a Y) The phrase Hot X in Exhibit 2.4 relates to

the fact that according to the available data this variable really does appear tohave an impact on the Y of interest Of course, in order to make such a deter-mination, this X variable must have been included in your initial picture of

Exhibit 2.4 The Visual Six Sigma Roadmap: What We Do Visual Six Sigma Roadmap—What We Do

Uncover Relationships

Dynamically visualize the variables one at a timeDynamically visualize the variables two at a timeDynamically visualize the variables more than two at a timeVisually determine the Hot Xs that affect variation in the Ys

Model Relationships

For each Y, identify the Hot Xs to include in the signal functionModel Y as a function of the Hot Xs; check the noise function

If needed, revise the model

If required, return to the Collect Data step and use DOE

Revise Knowledge

Identify the best Hot X settingsVisualize the effect on the Ys should these Hot X settings varyVerify improvement using a pilot study or confirmation trials

22 V I S U A L S I X S I G M A

how the process operates Those X variables that are not Hot Xs, in spite ofprior expectations, can be thought of as being moved into the noise function

for that Y Other terms for Hot X are Red X and Vital X Whatever terminology

is used, it is important to understand that for any given Y, there may be more than one X that has an impact, and, in such cases, it is important to understand the joint impact of these Xs.

Note that, although the designations of Y or X for a particular variable areuseful, whether a variable is a Y or an X depends both on how the problem isframed and on the stage of the analysis Processes are often modeled as both

serial (a set of connected steps) and hierarchical (an ordered grouping of levels

of steps, where one step at a higher level comprises a series of steps at a lowerlevel) Indeed, one of the tough choices to be made in the Frame Problemstep (Exhibit 2.3) is to decide on an appropriate level of detail and granularityfor usefully modeling the process Even when a manufacturing process is onlymoderately complex, it is often necessary to use a divide-and-conquer approach

in process and product improvement and design projects, which are often divided into pieces that reflect how the final product is made and operates Intransactional situations, modeling the process is usually more straightforward

sub-Uncover Relationships and Model Relationships

Earlier, we used the phrase “data of high quality.” Although data cleansing isoften presented as an initial step prior to any data analysis, we feel that it is bet-ter to include this vital activity as part of the Uncover and Model Relationshipssteps (Exhibit 2.3), particularly when there are large numbers of variables Forexample, it is perfectly possible to have a multivariate outlier that is not outlying

in any single variable Therefore the assessment of data quality and any requiredremedial action is understood to be woven into the Visual Six Sigma Roadmap.Chapter 4, “Managing Data and Data Quality,” shows some examples

The Uncover and Model Relationships steps also require a sound standing and validation of the measurement process for each variable in your

under-data You can address measurement process variation using a Gauge Repeatability and Reproducibility (Gauge R&R) study or a Measurement System Analysis (MSA)

study Whatever your approach, addressing measurement variability is criticallyimportant It is only when you understand the pattern of variation resulting

from repeatedly measuring the same item that you can correctly interpret the

In many ways, an MSA is best seen as an application of DOE to a ment process, and properly the subject of a Visual Six Sigma effort of its own

measure-To generalize, we would say that:

sophisticated

S I X S I G M A A N D V I S U A L S I X S I G M A 23

sophisticated enough

As an example of the second point: If the process to measure a small feature

is automated, involving robot handling and vision systems, then the two Rs in

Gauge R&R (corresponding to repeatability and reproducibility variation) maynot be of interest Instead we may be concerned with the variation when therobot loads and orients the part, when the camera tracks to supposedly fixedlocations, and when the laser scans in a given pattern to examine the feature

Revise Knowledge

The Revise Knowledge activity is where we integrate what we have learned

in the Uncover Relationships and possibly the Model Relationships steps withwhat we already know There are many aspects to this, and most of them areparticular to the specific context

Regardless, one of the vital tasks associated with the Revise Knowledge step

is to consider how, or if, our new findings will generalize Note that Step 4 inModel Relationships already alerts us to this kind of problem, but this represents

an extreme case

Perhaps unsurprisingly, the best way to tackle this issue is to collect

addi-tional, new data via confirmatory runs to check how these fit with what we

now expect This is particularly important when we have changed the settings

of the Hot Xs to achieve what appear to be better outcomes As we acquireand investigate more and more data under the new settings, we have moreand more assurance that we did indeed make a real improvement Many busi-nesses develop elaborate protocols to manage the risk of making such changes.Although there are some statistical aspects, there are at least as many contextualones, so it is difficult to give general guidance

In any case, confirmatory runs, no matter how they are chosen, are anexpression of the fact that learning should be cumulative Assuming that theperformance gap continues to justify it, the continued application of the VSSData Analysis Process (Exhibit 2.3) gives us the possibility of a virtuous circle

Guidelines

Finally, the following are some guidelines that may help you as a practitioner

of Visual Six Sigma:

context and objectives for all the analyses you conduct

control, reduction, and/or anticipation of sources of variation

24 V I S U A L S I X S I G M A

the capability of your measurement process, then you are still guessing

Visual Six Sigma, then your information system needs to be carefullyexamined

constructing a set of data should be driven by your current process orproduct understanding and the objectives that have been set

about how your findings are likely to generalize to other similarsituations

to just manipulate numbers will always fail

visualization

not involve a formal model

error in constructing it

stakehold-ers, then you have failed

anal-ysis was pointless

CONCLUSION

In this chapter, we have given an overview of Six Sigma and Visual SixSigma The “Six Sigma” section presented our definition of Six Sigma asthe management of variation in relation to performance requirements, andbriefly described some wider aspects of Six Sigma The section “Variation and

Statistics” emphasized the key role of statistics as detective, namely, EDA The

next section dealt briefly with dynamic visualization as a prerequisite for cessful detective work while the section “Visual Six Sigma: Strategies, Process,Roadmap, and Guidelines” aimed to summarize the three key strategies andthe process that will allow you to solve data mysteries more quickly and withless effort Through the Visual Six Sigma Data Analysis Process and the VisualSix Sigma Roadmap, the application of these strategies will be illustrated in thecase studies

suc-S I X suc-S I G M A A N D V I suc-S U A L suc-S I X suc-S I G M A 25

Chapter 3 aims to familiarize you a little with JMP, the enabling technology

we use for Visual Six Sigma Its purpose is to equip you to follow the JMPusage in the Visual Six Sigma case studies that form the heart of this book.With the background in Chapter 3 and the step-by-step details given in the casestudies, you will be able to work through the case study chapters, reproducingthe appropriate graphs and reports Maybe you will even venture beyond theseanalyses to discover new knowledge on your own! In any case, you will learn

to use a large repertoire of techniques that you can then apply to your own dataand projects

NOTES

1 Mikel Harry and Richard Schroeder, Six Sigma: The Breakthrough Management Strategy izing the World’s Top Corporations (New York, NY: Random House, 2006); Thomas Pyzdek, The Six Sigma Handbook: A Complete Guide for Greenbelts, Blackbelts and Managers at All Levels (New York, NY: McGraw-Hill, 2003); and George Eckes, The Six Sigma Revolution: How General Electric and Others Turned Process into Profits (New York, NY: John Wiley & Sons, Inc., 2003).

Revolution-2 http://www.bptrends.com/publicationfiles/12-03 ART Digital Six Sigma-Smith-Fingar1.pdf (accessed 10 February 2016).

3 George E P Box and Norman R Draper, Empirical Model-Building and Response Surfaces

(New York, NY: John Wiley & Sons, Inc., 1987), 424.

4 George E P Box, William G Hunter, and Stuart J Hunter, Statistics for Experimenters: Design, Innovation, and Discovery (Hoboken, NJ: John Wiley & Sons, Inc., 2005); Marvin Lentner and Thomas Bishop, Experimental Design and Analysis, 2nd Edition (Blacksburg, VA:Valley Book Co., 1986); Ronald Moen, Thomas W Nolan, and Lloyd P Provost, Improving Quality through Planned Experimentation (New York, NY: McGraw-Hill, 1991); and Douglas C Montgomery, Design and Analysis of Experiments, 6th Edition (Hoboken, NJ: John Wiley & Sons, Inc., 2005).

5 Charles W Holland and David W Cravens, “Fractional Factorial Experimental Designs in

Marketing Research,” Journal of Marketing Research 10, no 3 (1973): 270–276; and Forrest

W Breyfogle, Implementing Six Sigma: Smarter Solutions Using Statistical Methods, 2nd Edition

(Hoboken, NJ: John Wiley & Sons, Inc., 2003).

6 Peter Goos and Bradley Jones, Optimal Design of Experiments: A Case Study Approach

2005).

9 There are many variations of this process, but one example, not too far removed from Six

Sigma, can be found in Chris Chatfield, Problem Solving: A Statistician’s Guide, 2nd Edition

(New York, NY: Chapman & Hall, 1995).

10 Jeroen de Mast and Albert Trip, “Exploratory Data Analysis in Quality Improvement Projects,”

Journal of Quality Technology 4, no 39 (2007): 301–311.

11 See article at the York University Consulting Service website www.math.yorku.ca/SCS/ Gallery/historical.html (accessed 13 June 2015); Leland Wilkinson and Anand Anushka,

“High-Dimensional Visual Analytics: Interactive Exploration Guided by Pairwise Views of

Point Distributions,” IEEE Transactions on Visualization and Computer Graphics 12, no 6 (2006):

1363–1372.

12 For an example, see Antony Unwin, Martin Theus, and Heike Hofmann, Graphics of Large Datasets: Visualizing a Million (New York, NY: Springer, 2006).

26 V I S U A L S I X S I G M A

13 Alfred Inselberg, Parallel Coordinates: Visual Multidimensional Geometry and Its Applications

(New York, NY: Springer, 2008).

14 Edward R Tufte, The Visual Display of Quantitative Information, 2nd Edition (Cheshire, CT:

Graphics Press, 2001).

15 See, for example, Trevor Hastie, R Tibshirani, and J H Freidman, The Elements of Statistical Learning: Data Mining, Inference and Prediction (New York, NY: Springer, 2001).

16 Wikipedia, “SEMMA,” https://en.wikipedia.org/wiki/SEMMA (accessed 26 June 2015).

17 de Mast and Trip, “Exploratory Data Analysis in Quality Improvement Projects.”

18 Larry B Barrentine, Concepts for R&R Studies, 2nd Edition (Milwaukee, WI: ASQ Quality Press, 2002); and Richard K Burdick, Connie M Borror, and Douglas C Montgomery, Design and Analysis of Gauge R&R Studies: Making Decisions with Confidence Intervals in Random and Mixed ANOVA Models (Philadelphia, PA: Society for Industrial and Applied Mathematics, 2005).

C H A P T E R 3

A First Look at JMP

27

Visual Six Sigma: Making Data Analysis Lean, Second Edition Ian Cox, Marie A Gaudard, Mia L Stephens

© 2016 by SAS Institute, Inc Published by John Wiley & Sons, Inc.