Statistics for Six Sigma Black Belts

Matthew A. Barsalou

Description

This book is written for the Six Sigma Black Belt who needs an understanding of many statistical methods but does not use all of these methods every day. It is intended to be used as a quick reference, providing basic details, step-by-step instructions, and Minitab statistical software instructions.
Six Sigma Black Belts typically use a statistical program such as Minitab to perform calculations, but an understanding of the underlying statistics is still needed. Anybody can type data into a program; a Black Belt must be capable of understanding which hypothesis test is appropriate for a given use, as well as the assumptions that must be met to correctly perform the hypothesis test.
The methods presented here are laid out according to the Six Sigma DMAIC (Define, Measure, Analyze, Improve, Control) phases in which they are typically used. However, these methods can also be applied outside of a Six Sigma project, such as when one simply needs to determine whether there is a difference in the means of two processes producing the same parts.
A Six Sigma Black Belt using Statistics for Six Sigma Black Belts will be able to quickly zero in on appropriate methods and follow the examples to reach the correct statistical conclusions.

Sujets

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

Informations

• Publié par: ASQ Quality Press
• Date de parution: 14 novembre 2014
• Nombre de lectures: 0
• EAN13: 9780873891653
• Langue: English

Extrait

Statistics for Six Sigma Black Belts
Matthew A. Barsalou
ASQ Quality Press
Milwaukee, Wisconsin
American Society for Quality, Quality Press, Milwaukee 53203
© 2015 by ASQ
All rights reserved.
Library of Congress Cataloging-in-Publication Data
Barsalou, Matthew A., 1975–
Statistics for six sigma black belts / Matthew A. Barsalou.
pages cm
Includes bibliographical references and index.
ISBN 978-0-87389-892-8 (alk. paper)
1. Six sigma (Quality control standard) 2. Quality control—Statistical methods. I. Title
effectiveness. I. Title.
TS156.B4316 2015
658.5 ′620218 —dc23
2014038327
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: Lynelle Korte
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Dedicated to my father, Gilbert L. Barsalou, my brother, Mark A. Barsalou, and two dear friends whom I lost while writing this, Michael W. “Pugsly” Adams and Sarah Jung.
Preface
J ust over half a decade before the arrival of Six Sigma, William J. Diamond (1981) wrote, “The best experiment designs result from the combined efforts of a skilled experimenter, who has had basic training in experiment design methods, and of a skilled statistician, who has had training in engineering or science. The statistician alone cannot design good experiments in every possible discipline; neither can the scientist or engineer who is untrained in statistical experiment design be a good experiment designer.” Today, Six Sigma Black Belts are expected to have the skills of a good experimenter, possessing both a deep understanding of statistics and a knowledge of the industry in which they work.
This does not mean a Six Sigma Black Belt must know everything; the Six Sigma project team should include experts with the required detailed technical knowledge of the process being improved. A Six Sigma Black Belt can also consult with a Master Black Belt or a statistician for additional support with statistical methods.
Statistics for Six Sigma Black Belts is written for the Six Sigma Black Belt who needs an understanding of many statistical methods but does not use all of these methods every day. A Six Sigma Black Belt who has not had to use a specific statistical test in several years should be able to quickly review the test and perform it using the examples presented here. This book is intended to be used as a quick reference, providing basic details as well as step-by-step instructions for using Minitab ® statistical software.
Six Sigma Black Belts typically use a statistical program to perform calculations, but an understanding of the underlying statistics is still needed. Anybody can type data into a program; a Black Belt must be capable of understanding which hypothesis test is appropriate for a given use as well as the assumptions that must be met to correctly perform the hypothesis test.
The methods presented here are laid out according to the Six Sigma DMAIC (Define, Measure, Analyze, Improve, Control) phases in which they are typically used. However, these methods can also be applied outside of a Six Sigma project, such as when one simply needs to determine whether there is a difference in the means of two processes producing the same parts. In such a case, the flowchart in Appendix A could be used to quickly identify the correct test based on the intended use and available data.
A Six Sigma Black Belt using Statistics for Six Sigma Black Belts will be able to quickly zero in on the appropriate method and follow the examples to reach the correct statistical conclusion.
Acknowledgments
This book would not have been possible without the support of many people. I would like to thank Lynetta Campbell ( [e-mail] ) for keeping my statistics straight. I would also like to thank Jim Frost from Minitab for his assistance in providing clear conclusions for hypothesis tests, and Eston Martz and Michelle Paret from Minitab for providing me with a DOE data set. I am also grateful to Dean Christolear of CpkInfo.com for letting me use his Z-score table, and Rick Haynes of Smarter Solutions ( www.smartersolutions.com ) for providing me with the templates to create the other statistical tables.
Portions of information contained in this book are printed with permission of Minitab, Inc. All such material remains the exclusive property and copyright of Minitab, Inc. All rights reserved.
Introduction
S ix Sigma projects have five phases: Define, Measure, Analyze, Improve, and Control. The statistical methods presented here are laid out according to the phase in which they are typically used. This book is intended to present the statistics of Six Sigma; however, it would be negligent to fail to mention the phases in which the methods are applied.
Chapter 1 briefly covers the Define phase. Chapter 2 covers the Measure phase, where baseline performance is determined. Here, basic statistical concepts as well as types of data and measurement scales are introduced. Samples and populations are described and basic probability is explained. The binomial distribution and Bayes’ theorem are described. The chapter then covers descriptive statistics including measures of central tendency, variability, and shape before going into process capability and performance and measurement system analysis.
Chapter 3 deals with methods used during the Analyze phase of a Six Sigma project. Hypothesis testing is detailed, including error types and the five steps for hypothesis testing. Hypothesis tests presented include Z-tests, t-tests, and tests for both population and sample proportions. Also included are confidence intervals for means, the chi-square test of population variance, and the F-test of the variance of two samples, as well as simple linear regression and analysis of variance (ANOVA) for testing the differences between means.
Design of experiments (DOE) for use during the Improve phase of a Six Sigma project is detailed in Chapter 4. Chapter 5, which covers the Control phase, presents statistical process control (SPC), including the I-mR chart, the and S chart, and the and R chart for variable data, and the c chart, u chart, p chart, and np chart for attribute data.
Appendix A includes a flowchart that provides the correct statistical test for a given use and type of data. Also included are flowcharts depicting the five steps for hypothesis testing. Appendix B contains the statistical formulas in tables to serve as a quick reference. A Black Belt who only needs to look up a formula can find it in the tables; if the Black Belt is unsure how to apply the formula, he or she can follow the instructions in the appropriate chapter. The statistical tables are located in Appendix C. These include tables for the Z score, t distribution, F distribution, and chi-square distribution. Appendix D provides the SPC constants. Appendix E is a quick reference for those unfamiliar with Minitab. A detailed glossary is included as Appendix F.
Table of Contents
Preface
Introduction
Chapter 1
Define
Chapter 2
Measure
Types of Data and Measurement Scales
Samples and Populations
Probability
Binomial Distribution
Bayes’ Theorem
Descriptive Statistics
Capability and Performance Studies
Measurement System Analysis
Chapter 3
Analyze
Hypothesis Testing
Tests of Population Means
Confidence Intervals for Means
Chi-Square Test of Population Variance
F-Test for the Variance of Two Samples
Simple Linear Regression
Test of Differences Between Means (ANOVA)
Chapter 4
Improve
Design of Experiments
Chapter 5
Control
Statistical Process Control
Chapter 6
Conclusion
Appendix A
Hypothesis Test Selection
Appendix B
Quick Reference for Formulas
Appendix C
Statistical Tables
Appendix D
Statistical Process Control Constants
Appendix E
Minitab Quick Reference
Appendix F
Glossary
References



Chapter 1
Define
T he Define phase is the first phase of a Six Sigma project. Typical Define phase activities include creating a project charter that lays out the project’s goals and timeline and a clear project statement (George et al. 2005). The project statement should clearly communicate the problem and its impact on the business, and it should include goals and strategic objectives. It should also help the project team to focus on the core issue (Breyfogle 2008). The scope of the project should also be determined; this involves defining what is part of the project and what is clearly outside the bounds of the project.
Project management tools such as Gantt and PERT charts are often created during the Define phase. These are used to identify and track project milestones. An activity tracking list may also be created at this time to track the status of delegated project tasks.



Chapter 2
Measure
T he current level of performance is assessed during the Measure phase of a Six Sigma pr