Introduction To Statistical Quality Control
The correct bibliographic citation for this manual is as follows: Ramirez, Brenda S., M.S., and Jose G., Ramirez, Ph.D. 2018.Douglas Montgomery’s Introduction to Statistical Quality Control: A JMP Companion. Cary, NC: SAS Institute Inc.Douglas Montgomery’s Introduction to Statistical Quality Control: A JMP CompanionCopyright 2018, SAS Institute Inc., Cary, NC, USA978-1-63526-022-9 (Hard copy)978-1-63526-825-6 (Web PDF)978-1-63526-823-2 (epub)978-1-63526-824-9 (mobi)All Rights Reserved. Produced in the United States of America.For a hard copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in anyform or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of thepublisher, SAS Institute Inc.For a web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at thetime you acquire this publication.The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of thepublisher is illegal and punishable by law. Please purchase only authorized electronic editions and do not participate in orencourage electronic piracy of copyrighted materials. Your support of others’ rights is appreciated.U.S. Government License Rights; Restricted Rights: The Software and its documentation is commercial computersoftware developed at private expense and is provided with RESTRICTED RIGHTS to the United States Government. Use,duplication, or disclosure of the Software by the United States Government is subject to the license terms of this Agreementpursuant to, as applicable, FAR 12.212, DFAR 227.7202-1(a), DFAR 227.7202-3(a), and DFAR 227.7202-4, and, to the extentrequired under U.S. federal law, the minimum restricted rights as set out in FAR 52.227-19 (DEC 2007). If FAR 52.227-19 isapplicable, this provision serves as notice under clause (c) thereof and no other notice is required to be affixed to theSoftware or documentation. The Government’s rights in Software and documentation shall be only those set forth in thisAgreement.SAS Institute Inc., SAS Campus Drive, Cary, NC 27513-2414October 2018SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc.in the USA and other countries. indicates USA registration.Other brand and product names are trademarks of their respective companies.SAS software may be provided with certain third-party software, including but not limited to open-source software, which islicensed under its applicable third-party software license agreement. For license information about third-party softwaredistributed with SAS software, refer to http://support.sas.com/thirdpartylicenses.
ContentsForeword . vAbout This Book . viiAcknowledgments . xiiiChapter 1: Using This Book .1Overview .1Chapter Contents .1Chapter Layout.7JMP Software and JMP Tables .9Typographical Conventions .12Chapter 2: Overview of Statistical Quality Control Topics and JMP.15Overview .15Statistical Process Control .15Measurement System Analysis .24Process Health Assessment .30Chapter 3: Control Charts for Variables .37Overview .37Variables Control Chart Review .37JMP Variables Control Chart Platforms .38Examples from ISQC Chapter 6 .39Statistical Insights.61Chapter 4: Control Charts for Attributes .75Overview .75Attributes Control Chart Review .75JMP Attributes Control Chart Platforms.77Examples from ISQC Chapter 7 .77Statistical Insights.116Chapter 5: Process and Measurement System Capability Analysis.127Overview .127Process and Measurement System Capability Analysis Review .127JMP Process Capability and MSA Platforms.129Examples from ISQC Chapter 8 .131Statistical Insights.172
ivContentsChapter 6: Process Health Assessment.183Overview . 183Process Health Assessment Review . 183JMP Platforms for Process Health Assessments . 185Examples for Chapter 6 . 186Statistical Insights . 217Chapter 7: Cumulative Sum and Exponentially Weighted Moving Average Control Charts .225Overview . 225CUSUM and EWMA Control Chart Review . 225JMP Small Shift Detection Control Chart Platforms. 227Examples from ISQC Chapter 9 . 228Statistical Insights . 253Chapter 8: Other Univariate Statistical Process Monitoring and Control Techniques .267Overview . 267Special Topics Review . 267JMP Platforms for Monitoring Autocorrelated Processes . 269Examples from ISQC Chapter 10 . 270Statistical Insights . 285Chapter 9: Multivariate Process Monitoring and Control .307Overview . 307Multivariate Process Monitoring Review . 307JMP Multivariate Monitoring Platforms . 308Examples from ISQC Chapter 11 . 309Statistical Insights . 331References .339
About This BookWhy Statistical Quality Control?What comes to mind when you think of statistical quality control (SQC)? The EncyclopediaBritannica defines this phrase as “the use of statistical methods in the monitoring andmaintaining of the quality of products and services.” This definition is in line with our initialexposure to SQC during our college years, in classes like Statistical Process Control. These ideascontinued to take shape when we studied for the American Society for Quality Certified QualityEngineering exam, which had us memorize numerous facts about different statistical qualitytools. But it was not until we started using these tools and techniques in a real-worldmanufacturing environment that we truly understood their impact on improving products andprocesses.Thirty years and several industries later, we have become great stewards of SQC techniques, andtheir use and application have become second nature. Therefore, when we were asked to author acompanion book to Prof. Montgomery’s Introduction to Statistical Quality Control (ISQC), weenthusiastically agreed. Like many, we were introduced to his work through his many books.They are among our favorites because they are very readable, practical, and relevant, not only tothe industries that we have worked in but also to the engineers and scientists with whom weoften interact. This is no coincidence since Professor Montgomery holds BS, MS, and PhDdegrees, all in engineering, and has spent many years both as a professor of IndustrialEngineering and Statistics at Arizona State University and as a practitioner collaborating withpeople in industry.The synergy between engineering, science, and statistics is always found in Prof. Montgomery’steachings. Take ISQC, for example. This book provides applications for many of the common SPCtechniques using data sources from well-known manufacturing and business processes. Forexample, the book educates the reader about XBar and Range charts using dimensionalmeasurements from a Hard-Bake process, C charts are applied to nonconformities on a printedcircuit board, and we interpret the results of an attribute gauge capability analysis to understandthe consistency of a manual underwriting process for mortgage loan applications. ISQC Chapter10, “Other Univariate Statistical Process-Monitoring and Control Techniques,” contains manyuseful monitoring techniques that are very effective in practice but may be overlooked ormisunderstood. We encourage you to check out his discussions for how to adapt SPC charts forthe following scenarios: short production runs, nonstationary and autocorrelated output, changepoint models, profile monitoring, and multistream processes.Following in Prof. Montgomery’s footsteps, we have written a companion book that is gearedtoward the practitioner of SQC, one who is using these techniques to monitor and improveproducts and processes. One of our goals in writing this book is to share valuable lessons that wehave learned from applying SQC techniques to solve problems in a variety of industries,including semiconductors, electronics, chemical, and biotechnology.
viii Douglas Montgomery’s Introduction to Statistical Quality Control: A JMP CompanionFinally, to fully answer the question of why SQC, we must turn our attention to JMP software.We have been avid JMP users for almost as long as we have been industrial statisticians andknow the software well. JMP not only has powerful SQC tools that are easy to use, but it also hasplenty of state-of-the-art analysis and visualization tools if the need arises. We have includedmore than 20 JMP SQC platforms in our book, with step-by-step instructions and tips and tricksWhat Does This Book Cover?As the title suggests, this book is a JMP companion to Introduction to Statistical Quality Control,Seventh Edition by Douglas C. Montgomery, which we refer to as ISQC throughout this book.However, the main emphasis of this book is on statistical process control and capability analysis.Therefore, we focus on the techniques provided in ISQC Part 3, “Basic Methods of StatisticalProcess Control and Capability Analysis,” and ISQC Part 4, “Other Statistical Process Monitoringand Control Techniques.” These include topics such as Statistical Process Control (SPC), ProcessCapability Analysis (PCA), Measurement System Analysis (MSA), and Advanced StatisticalProcess Control (SPC).For ISQC Chapters 6, 7, 8, 9, 10, and 11, we systematically reproduce the examples and relevantoutput using JMP. We provide the reader with easy step-by-step instructions, screen captures,and tips and tricks to follow along with. This book is useful for the practitioner because weemphasize the interpretation of the output and provide practical advice for how to navigatecommon challenges when using these techniques, based on our many years of experience usingSPC.Some recent advances in JMP related to these topics are highlighted in this book. This includes athorough review of the Control Chart Builder and CUSUM Control Chart, which are relativelynew additions to the Quality and Process menu. We are also excited to include a chapter on theProcess Screening platform, new to JMP version 13, which includes the Stability Ratio in B.Ramírez and G. Runger (2006), and JMP Process Performance Graph, based on the processperformance dashboard of J. Ramírez. This information is used to identify the overall health of aprocess through a Process Health Assessment (PHA).Is This Book for You?The main audience for this book is you, the practitioner, who uses these valuable quality andproductivity statistical techniques and for which JMP provides a state-of-the-art implementationof them. This book provides the reader with an overview of concepts and tools used tostatistically monitor process output, determine the ability of a process to meet specification limits,understand measurement system variability, and assess and prioritize the overall health of manyprocesses. These techniques are used to aid development and manufacturing activities in avariety of industries, including, but not limited to, the automotive, biotechnology, electronics,pharmaceutical, medical devices, chemical, military, and aerospace industries.
About this Book ixThis book is also suitable for anyone using Prof. Montgomery’s Introduction to Statistical QualityControl book to increase your knowledge of these techniques. This includes students taking aSQC course with ISQC as the textbook. In addition to emphasizing the key topic-related contentof ISQC, we also provide additional analyses that offer insight to effectively implementing theseimportant tools. Finally, for those who want to learn how to use JMP to more easily explore yourdata using tools associated with SPC, PCA, MSA, and Advanced SPC, this book is a must.What Are the Prerequisites for This Book?Although we provide an overview of each statistical quality tool introduced in this book, we referthe reader to Prof. Montgomery’s Introduction to Statistical Quality Control for detailed discussionson theory and concepts. We also assume a familiarity with the basic functions of JMP, such asimporting and manipulating data, navigating around the JMP menus and windows, and usingthe basic JMP tools. A summary of related JMP help and resources is provided in the subsequentsection called JMP Software.What Should You Know about the Examples?For most of the examples presented in ISQC Parts 3 and 4, step-by-step instructions are providedfor the reader to follow along, with lots of JMP screen captures. A discussion of the analysisresults is also included, and the output is interpreted in the context of the analysis goals.Supplementary examples are provided in the Statistical Insights section in each chapter toillustrate additional JMP functionality not previously covered or to elaborate on importantpoints. A summary of the examples used in this book is provided in Chapter 1.Software Used to Develop the Book’s ContentThis book was written using JMP version 14. We have included more than 20 JMP SQC platformsin our book, which are primarily part of the Quality and Process menu. As mentionedpreviously, we are aware of two platforms discussed in this book that were added in the lastseveral versions, Process Screening (version 13) and CUSUM Control Chart (version 14). Asummary of the JMP platforms used in this book is shown in Chapter 1.Example DataThe data used in this book is available at http://support.sas.com/jramirez orhttp://support.sas.com/bramirez. Users can download the JMP tables and follow along.
x Douglas Montgomery’s Introduction to Statistical Quality Control: A JMP CompanionAbout the AuthorsBrenda S. Ramírez, MS, is an industrial statistician with many years ofexperience working in the semiconductor, chemical, and biotechnologyindustries. In this role, Brenda partners with engineers and scientists to bringnew products to market, sustain manufacturing operations, and guide processimprovements through the union of science and statistics. She has spent hercareer using and promoting Statistical Quality Control techniques, such as SPCand Process Stability metrics. Brenda received an MS in applied statistics fromWorcester Polytechnic Institute and an MS in industrial and managementengineering from Rensselaer Polytechnic Institute. She is an avid user of SAS and JMP statisticalsoftware from SAS. Her book, Analyzing and Interpreting Continuous Data Using JMP: A Step-byStep Guide, written with her husband José Ramírez, won the 2010 Award of Excellence in theSociety for Technical Communications International Technical Publications Competition.José G. Ramírez, PhD, is a statistical engineer with years of experience in thesemiconductor, electronics and biotech industries. A JMP user for more than 25years, he works closely with engineers and scientists to help them make senseof data, and through collaborative education, helps promote statistical thinkingand JMP usage. He received a degree in mathematics from Universidad SimónBolívar in Caracas, Venezuela, and both an MS in applied statistics and a PhDin statistics from the University of Wisconsin-Madison. He was one of thefounding members of the Center for Quality and Productivity Improvement atthe University of Wisconsin-Madison. At the 1998 international SAS users conference, Ramírezwon the best contributed statistics paper, and in 2002 he received the SAS User Feedback Award.His book, Analyzing and Interpreting Continuous Data Using JMP: A Step-by-Step Guide, writtenwith his wife Brenda Ramírez, won the 2010 Award of Excellence in the Society for TechnicalCommunications International Technical Publications Competition.Learn more about these authors by visiting their author pages, where you can download freebook excerpts, access example code and data, read the latest reviews, get updates, and upport.sas.com/jose-ramirez
About this Book xiWe Want to Hear from YouSAS Press books are written by SAS users for SAS users. We welcome your participation in theirdevelopment and your feedback on SAS Press books that you are using. Please visit sas.com/booksto do the following: Sign up to review a book Recommend a topic Request information on how to become a SAS Press author Provide feedback on a bookDo you have questions about a SAS Press book that you are reading? Contact the author throughsaspress@sas.com or https://support.sas.com/author feedback.SAS has many resources to help you find answers and expand your knowledge. If you needadditional help, see our list of resources: sas.com/books.
xii Douglas Montgomery’s Introduction to Statistical Quality Control: A JMP Companion
Chapter 3: Control Charts for VariablesOverview .37Variables Control Chart Review .37JMP Variables Control Chart Platforms .38Examples from ISQC Chapter 6 .39ISQC Example 6.1 Flow Width .39ISQC Example 6.3 Piston Ring Diameter .48ISQC Example 6.4 Piston Ring Diameter .50ISQC Example 6.5 Loan Processing Costs .51ISQC Example 6.6 Resistivity of Silicon Wafers .56ISQC Example 6.11 Vane Height of an Aerospace Casting .59Statistical Insights .61Operating Characteristic Curve .61Phase Chart.63Lognormal Probability Limits.653-Way Control Chart and Variance Components .70Rational Subgrouping .73OverviewThis chapter illustrates how to generate control charts using examples from Chapter 6, “ControlCharts for Variables,” of Introduction to Statistical Quality Control (ISQC), as well as some of thefundamental ideas behind statistical process control (SPC).These control chart techniques are presented for data measured on a quantitative scale and arereferred to as variable control charts. They include the X and Range, X and Standard Deviation,and Individual Measurement and Moving Range control charts.Two JMP platforms are highlighted in this chapter: the Control Chart Builder and the ControlChart.Variables Control Chart ReviewMost books on control charts are partitioned into two buckets: control charts for variable data andcontrol charts for attribute data. This distinction is important to select the most effective controlchart to adequately represent the data of interest. In general, variable data is a measurement that isobtained on a continuous scale, such as temperature, pressure, or thickness. For a thoroughdiscussion of measurement scales, see Chapter 2 in Ramírez and Ramírez (2009).The most common control charts for variable data include the X and Range, the X and StandardDeviation, and the Individual Measurement and Moving Range (XmR). The first Shewhart controlchart, the X and Range, is the landmark chart of SPC as we have come to know it today. This chartis appropriate when the natural grouping of the measurements taken in a process is greater than
38 Douglas Montgomery’s Introduction to Statistical Quality Control: A JMP Companionone, also referred to as the subgroup size, n. The X chart plots the subgroup averages and is usedto understand the homogeneity of a process by determining if the subgroup-to-subgroup averagesare consistent, as compared to the within-subgroup variation. The Range chart plots the subgroupranges (maximum value – minimum value) and looks for consistent within-subgroup variationfrom subgroup to subgroup.The X and Standard Deviation chart is also used to monitor subgroup averages andwithin-subgroup variation. However, instead of using the subgroup ranges, the chart displays thesample standard deviation to monitor the variation within each subgroup. It is a more appropriatechoice when the number of measurements in a subgroup is larger (for example, n 5). The controllimits for the X chart are calculated using an estimate of the within-subgroup variation (ranges orstandard deviations).The third chart that is covered in this chapter is the one for individual measurements, referred toas XmR. This chart is appropriate when the natural subgroup size is one, and the data arecontinuous in nature. For example, if one thickness measurement is taken per hour or perequipment run, then an XmR chart is appropriate. The control limits for this chart are constructedfrom an estimate of the variation from consecutive moving ranges.The control charts described here are built on statistical assumptions, including the basic modelfor the observations yi µ εi, where εi i.i.d. N(µ, σ). Although these charts are robust tomoderate departures in these assumptions, we emphasize several examples from ISQC tounderstand the impact of certain departures on the performance of the chart. For example, a3-way control chart is used to widen inappropriately tight limits on an X chart due to a lack ofindependence among the subgroup measurements, and probability limits from a lognormaldistribution are used to accommodate a skewed distribution.JMP Variables Control Chart PlatformsTwo platforms are used to create variables control charts such as X and Range, X and StandardDeviation, and XmR charts. One is the legacy Control Chart platform and the other one is theControl Chart Builder. The Control Chart Builder is part of the new generation of JMP qualitytools, which makes it easier to design, create, and evaluate control charts. These platforms wereintroduced in Chapter 2. In this chapter, we focus on the use of these platforms for variables data.Table 3.1 provides a summary of the features we find most useful from both platforms.Table 3.1 Comparison of Features for JMP Variables Control Chart PlatformsFeatureControl chart typesSave limitsSave summariesControl Chart Builder X and Range X and Standard DeviationXmRIn Column and in new TableYesControl Chart X and Range X and Standard Deviation XmRIn Column and in new TableYes
Chapter 3: Control Charts for VariablesFeatureSave sigmaAnnotat
Introduction to Statistical Quality Control, Seventh Edition by Douglas C. Montgomery, which we refer to as ISQC throughout this book. However, the main emphasis of this book is on statistical process control and capability analysis. Therefore, we focus on the techniques provided in ISQC Part 3, “Basic Methods of Statistical
1.3 Statistical Methods for Quality Control and Improvement Chapter 1 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. 15 . Scientists and Engineers to lecture on statistical quality control t
be in statistical control. A process that is operating in the presence of assignable causes is said to be out of control. 5.2 Chance and Assignable Causes of Variation. Chapter 5 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. 5
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Statistical Process Control (SPC) applies statistical methods to monitor and control a process to operate at full potential. Statistical process control is a collection of tools that when used together can result in process stability and variance reduction. Control charts are used in SPC for measuring the variation in the process and that can be
statistical process control functions. Organization of This Manual This manual is organized as follows: Chapter 1, Introduction to Statistical Process Control in LabVIEW, contains installation instructions, gives an overview of Statistical Process Control (SPC), and discuss
statistical process control functions. Organization of This Manual This manual is organized as follows: Chapter 1, Introduction to Statistical Process Control in LabVIEW, contains installation instructions, gives an overview of Statistical Process Control (SPC), and discusses the LabVIEW SPC Toolkit VIs and examples. Chapter 2,
This section discusses the basic concepts of statistical process control, quality control and process capability. 1. How did Statistical Quality Control Begin? 2. What are Process Control Techniques? 3. What is Process Control? 4. What to do if the process is "Out of Control"? 5. What to do if "In Control" but Unacceptable? 6. What is Process .
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