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Introduction to statistical quality cont douglas c. montgomery


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Introduction to statistical quality cont douglas c. montgomery

  1. 1. I Sixth Edition ntroduction to Statistical Quality Control DOUGLAS C. MONTGOMERY Arizona State University John Wiley & Sons, Inc.
  2. 2. Executive Publisher: Don Fowley Associate Publisher: Daniel Sayer Acquisitions Editor: Jennifer Welter Marketing Manager: Christopher Ruel Production Manager: Dorothy Sinclair Production Editor: Sandra Dumas Senior Designer: Kevin Murphy New Media Editor: Lauren Sapira Editorial Assistant: Mark Owens Production Management Services: Elm Street Publishing Services Composition Services: Aptara, Inc. This book was typeset in 10/12 Times by Aptara, Inc., and printed and bound by R. R. Donnelley (Jefferson City). The cover was printed by R. R. Donnelley (Jefferson City). The paper in this book was manufactured by a mill whose forest management programs include sustained yield harvesting of its timberlands. Sustained yield harvesting principles ensure that the number of trees cut each year does not exceed the amount of new growth. This book is printed on acid-free paper. Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. 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 Sections 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, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470. 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, E-mail: PERMREQ@WILEY.COM. To order books or for customer service, call 1-800-CALL-WILEY(225-5945). Montgomery, Douglas, C. Introduction to Statistical Quality Control, Sixth Edition 978-0-470-16992-6 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1
  3. 3. About the Author Douglas C. Montgomery is Regents’ Professor of Industrial Engineering and Statistics and the Arizona State University Foundation Professor of Engineering. He received his B.S., M.S., and Ph.D. degrees from Virginia Polytechnic Institute, all in engineering. From 1969 to 1984 he was a faculty member of the School of Industrial & Systems Engineering at the Georgia Institute of Technology; from 1984 to 1988 he was at the University of Washington, where he held the John M. Fluke Distinguished Chair of Manufacturing Engineering, was Professor of Mechanical Engineering, and was Director of the Program in Industrial Engineering. Dr. Montgomery has research and teaching interests in engineering statistics including statistical quality-control techniques, design of experiments, regression analysis and empirical model building, and the application of operations research methodology to problems in manufacturing systems. He has authored and coauthored more than 190 technical papers in these fields and is the author of twelve other books. Dr. Montgomery is a Fellow of the American Society for Quality, a Fellow of the American Statistical Association, a Fellow of the Royal Statistical Society, a Fellow of the Institute of Industrial Engineers, an elected member of the International Statistical Institute, and an elected Academican of the International Academy of Quality. He is a Shewhart Medalist of the American Society for Quality, and he also has received the Brumbaugh Award, the Lloyd S. Nelson Award, the William G. Hunter Award, and two Shewell Awards from the ASQ. He is a recipient of the Ellis R. Ott Award. He is a former editor of the Journal of Quality Technology, is one of the current chief editors of Quality and Reliability Engineering International, and serves on the editorial boards of several journals. iii
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  5. 5. Preface Introduction This book is about the use of modern statistical methods for quality control and improvement. It provides comprehensive coverage of the subject from basic principles to state-of-the-art concepts and applications. The objective is to give the reader a sound understanding of the principles and the basis for applying them in a variety of situations. Although statistical techniques are emphasized throughout, the book has a strong engineering and management orientation. Extensive knowledge of statistics is not a prerequisite for using this book. Readers whose background includes a basic course in statistical methods will find much of the material in this book easily accessible. Audience The book is an outgrowth of more than 35 years of teaching, research, and consulting in the application of statistical methods for industrial problems. It is designed as a textbook for students enrolled in colleges and universities, who are studying engineering, statistics, management, and related fields and are taking a first course in statistical quality control. The basic quality-control course is often taught at the junior or senior level. All of the standard topics for this course are covered in detail. Some more advanced material is also available in the book, and this could be used with advanced undergraduates who have had some previous exposure to the basics or in a course aimed at graduate students. I have also used the text materials extensively in programs for professional practitioners, including quality and reliability engineers, manufacturing and development engineers, product designers, managers, procurement specialists, marketing personnel, technicians and laboratory analysts, inspectors, and operators. Many professionals have also used the material for self-study. Chapter Organization and Topical Coverage The book contains five parts. Part I is introductory. The first chapter is an introduction to the philosophy and basic concepts of quality improvement. It notes that quality has become a major business strategy and that organizations that successfully improve quality can increase their productivity, enhance their market penetration, and achieve greater profitability and a strong competitive advantage. Some of the managerial and implementation aspects of quality improvement are included. Chapter 2 describes DMAIC, an acronym for define, measure, analyze, improve, and control. The DMAIC process is an excellent framework to use in conducting quality improvement projects. DMAIC often is associated with six-sigma, but regardless of the approach taken by an organization strategically, DMAIC is an excellent tactical tool for quality professionals to employ. Part II is a description of statistical methods useful in quality improvement. Topics include sampling and descriptive statistics, the basic notions of probability and probability distributions, point and interval estimation of parameters, and statistical hypothesis testing. These topics are usually covered in a basic course in statistical methods; however, their presentation in this text v
  6. 6. vi Preface is from the quality-engineering viewpoint. My experience has been that even readers with a strong statistical background will find the approach to this material useful and somewhat different from a standard statistics textbook. Part III contains four chapters covering the basic methods of statistical process control (SPC) and methods for process capability analysis. Even though several SPC problem-solving tools are discussed (including Pareto charts and cause-and-effect diagrams, for example), the primary focus in this section is on the Shewhart control chart. The Shewhart control chart certainly is not new, but its use in modern-day business and industry is of tremendous value. There are four chapters in Part IV that present more advanced SPC methods. Included are the cumulative sum and exponentially weighted moving average control charts (Chapter 9), several important univariate control charts such as procedures for short production runs, autocorrelated data, and multiple stream processes (Chapter 10), multivariate process monitoring and control (Chapter 11), and feedback adjustment techniques (Chapter 12). Some of this material is at a higher level than Part III, but much of it is accessible by advanced undergraduates or firstyear graduate students. This material forms the basis of a second course in statistical quality control and improvement for this audience. Part V contains two chapters that show how statistically designed experiments can be used for process design, development, and improvement. Chapter 13 presents the fundamental concepts of designed experiments and introduces factorial and fractional factorial designs, with particular emphasis on the two-level system of designs. These designs are used extensively in the industry for factor screening and process characterization. Although the treatment of the subject is not extensive and is no substitute for a formal course in experimental design, it will enable the reader to appreciate more sophisticated examples of experimental design. Chapter 14 introduces response surface methods and designs, illustrates evolutionary operation (EVOP) for process monitoring, and shows how statistically designed experiments can be used for process robustness studies. Chapters 13 and 14 emphasize the important interrelationship between statistical process control and experimental design for process improvement. Two chapters deal with acceptance sampling in Part VI. The focus is on lot-by-lot acceptance sampling, although there is some discussion of continuous sampling and MIL STD 1235C in Chapter 14. Other sampling topics presented include various aspects of the design of acceptance-sampling plans, a discussion of MIL STD 105E, MIL STD 414 (and their civilian counterparts, ANSI/ASQC ZI.4 and ANSI/ASQC ZI.9), and other techniques such as chain sampling and skip-lot sampling. Throughout the book, guidelines are given for selecting the proper type of statistical technique to use in a wide variety of situations. Additionally, extensive references to journal articles and other technical literature should assist the reader in applying the methods described. I also have showed how the different techniques presented are used in the DMAIC process. Supporting Text Materials Computer Software The computer plays an important role in a modern quality-control course. This edition of the book uses Minitab as the primary illustrative software package. I strongly recommend that the course have a meaningful computing component. To request this book with a student version of Minitab included, contact your local Wiley representative at and click on the tab for “Who’s My Rep?” The student version of Minitab has limited functionality and does not include DOE capability. If your students will need DOE capability, they can download the fully functional 30-day trial at or purchase a fully functional time-limited version from
  7. 7. Preface vii Supplemental Text Material I have written a set of supplemental materials to augment many of the chapters in the book. The supplemental material contains topics that could not easily fit into a chapter without seriously disrupting the flow. The topics are shown in the Table of Contents for the book and in the individual chapter outlines. Some of this material consists of proofs or derivations, new topics of a (sometimes) more advanced nature, supporting details concerning remarks or concepts presented in the text, and answers to frequently asked questions. The supplemental material provides an interesting set of accompanying readings for anyone curious about the field. It is available at Student Resource Manual The text contains answers to most of the odd-numbered exercises. A Student Resource Manual is available from John Wiley & Sons that presents comprehensive annotated solutions to these same odd-numbered problems. This is an excellent study aid that many text users will find extremely helpful. The Student Resource Manual may be ordered in a set with the text or purchased separately. Contact your local Wiley representative to request the set for your bookstore or purchase the Student Resource Manual from the Wiley Web site. Instructor’s Materials The instructor’s section of the textbook Web site contains the following: 1. 2. 3. 4. 5. Solutions to the text problems The supplemental text material described above A set of Microsoft® PowerPoint® slides for the basic SPC course Data sets from the book, in electronic form Image Gallery, illustrations from the book in electronic format The instructor’s section is for instructor use only and is password-protected. Visit the Instructor Companion Site portion of the Web site, located at, to register for a password. The World Wide Web Page The Web page for the book is accessible through the Wiley home page. It contains the supplemental text material and the data sets in electronic form. It will also be used to post items of interest to text users. The Web site address is Click on the cover of the text you are using. ACKNOWLEDGMENTS Many people have generously contributed their time and knowledge of statistics and quality improvement to this book. I would like to thank Dr. Bill Woodall, Dr. Doug Hawkins, Dr. Joe Sullivan, Dr. George Runger, Dr. Bert Keats, Dr. Bob Hogg, Mr. Eric Ziegel, Dr. Joe Pignatiello, Dr. John Ramberg, Dr. Ernie Saniga, Dr. Enrique Del Castillo, Dr. Sarah Streett, and Dr. Jim Alloway for their thorough and insightful comments on this and previous editions. They generously shared many of their ideas and teaching experiences with me, leading to substantial improvements in the book. Over the years since the first edition was published, I have received assistance and ideas from a great many other people. A complete list of colleagues with whom I have interacted
  8. 8. viii Preface would be impossible to enumerate. However, some of the major contributors and their professional affiliations are as follows: Dr. Mary R. Anderson-Rowland, Dr. Dwayne A. Rollier, Dr. Norma F. Hubele, and Dr. Murat Kulahci, Arizona State University; Mr. Seymour M. Selig, formerly of the Office of Naval Research; Dr. Lynwood A. Johnson, Dr. Russell G. Heikes, Dr. David E. Fyffe, and Dr. H. M. Wadsworth, Jr., Georgia Institute of Technology; Dr. Sharad Prabhu and Dr. Robert Rodriguez, SAS Institute; Dr. Scott Kowalski, Minitab; Dr. Richard L. Storch and Dr. Christina M. Mastrangelo, University of Washington; Dr. Cynthia A. Lowry, formerly of Texas Christian University; Dr. Smiley Cheng, Dr. John Brewster, Dr. Brian Macpherson, and Dr. Fred Spiring, the University of Manitoba; Dr. Joseph D. Moder, University of Miami; Dr. Frank B. Alt, University of Maryland; Dr. Kenneth E. Case, Oklahoma State University; Dr. Daniel R. McCarville, Dr. Lisa Custer, Dr. Pat Spagon, and Mr. Robert Stuart, all formerly of Motorola; Dr. Richard Post, Intel Corporation; Dr. Dale Sevier, San Diego State University; Mr. John A. Butora, Mr. Leon V. Mason, Mr. Lloyd K. Collins, Mr. Dana D. Lesher, Mr. Roy E. Dent, Mr. Mark Fazey, Ms. Kathy Schuster, Mr. Dan Fritze, Dr. J. S. Gardiner, Mr. Ariel Rosentrater, Mr. Lolly Marwah, Mr. Ed Schleicher, Mr. Amiin Weiner, and Ms. Elaine Baechtle, IBM; Mr. Thomas C. Bingham, Mr. K. Dick Vaughn, Mr. Robert LeDoux, Mr. John Black, Mr. Jack Wires, Dr. Julian Anderson, Mr. Richard Alkire, and Mr. Chase Nielsen, the Boeing Company; Ms. Karen Madison, Mr. Don Walton, and Mr. Mike Goza, Alcoa; Mr. Harry PetersonNedry, Ridgecrest Vineyards and The Chehalem Group; Dr. Russell A. Boyles, formerly of Precision Castparts Corporation; Dr. Sadre Khalessi and Mr. Franz Wagner, Signetics Corporation; Mr. Larry Newton and Mr. C. T. Howlett, Georgia Pacific Corporation; Mr. Robert V. Baxley, Monsanto Chemicals; Dr. Craig Fox, Dr. Thomas L. Sadosky, Mr. James F. Walker, and Mr. John Belvins, the Coca-Cola Company; Mr. Bill Wagner and Mr. Al Pariseau, Litton Industries; Mr. John M. Fluke, Jr., John Fluke Manufacturing Company; Dr. Paul Tobias, formerly of IBM and Semitech; Dr. William DuMouchel and Ms. Janet Olson, BBN Software Products Corporation. I would also like to acknowledge the many contributions of my late partner in Statistical Productivity Consultants, Mr. Sumner S. Averett. All of these individuals and many others have contributed to my knowledge of the quality improvement field. Other acknowledgments go to the editorial and production staff at Wiley, particularly Ms. Charity Robey and Mr. Wayne Anderson, with whom I worked for many years, and Ms. Jenny Welter; they have had much patience with me over the years and have contributed greatly toward the success of this book. Dr. Cheryl L. Jennings made many valuable contributions by her careful checking of the manuscript and proof materials. I also thank Dr. Gary Hogg and Dr. Ron Askin, former and current chairs of the Department of Industrial Engineering at Arizona State University, for their support and for providing a terrific environment in which to teach and conduct research. I thank the various professional societies and publishers who have given permission to reproduce their materials in my text. Permission credit is acknowledged at appropriate places in this book. I am also indebted to the many organizations that have sponsored my research and my graduate students for a number of years, including the member companies of the National Science Foundation/Industry/University Cooperative Research Center in Quality and Reliability Engineering at Arizona State University, the Office of Naval Research, the National Science Foundation, the Semiconductor Research Corporation, the Aluminum Company of America, and the IBM Corporation. Finally, I would like to thank the many users of the previous editions of this book, including students, practicing professionals, and my academic colleagues. Many of the changes and improvements in this edition of the book are the direct result of your feedback. DOUGLAS C. MONTGOMERY Tempe, Arizona
  9. 9. Contents 2.7 1 PART INTRODUCTION 1 1 QUALITY IMPROVEMENT IN THE MODERN BUSINESS ENVIRONMENT Chapter Overview and Learning Objectives 1.1 The Meaning of Quality and Quality Improvement 1.1.1 Dimensions of Quality 1.1.2 Quality Engineering Terminology 1.2 A Brief History of Quality Control and Improvement 1.3 Statistical Methods for Quality Control and Improvement 1.4 Management Aspects of Quality Improvement 1.4.1 Quality Philosophy and Management Strategies 1.4.2 The Link Between Quality and Productivity 1.4.3 Quality Costs 1.4.4 Legal Aspects of Quality 1.4.5 Implementing Quality Improvement 2 THE DMAIC PROCESS Chapter Overview and Learning Objectives 2.1 Overview of DMAIC 2.2 The Define Step 2.3 The Measure Step 2.4 The Analyze Step 2.5 The Improve Step 2.6 The Control Step 3 3 4 4 8 Examples of DMAIC 2.7.1 Litigation Documents 2.7.2 Improving On-Time Delivery 2.7.3 Improving Service Quality in a Bank 13 16 17 35 36 41 42 45 45 45 49 50 52 53 54 59 2 PART STATISTICAL METHODS USEFUL IN QUALITY CONTROL AND IMPROVEMENT 3 MODELING PROCESS QUALITY 9 54 54 56 Chapter Overview and Learning Objectives 3.1 Describing Variation 3.1.1 The Stem-and-Leaf Plot 3.1.2 The Histogram 3.1.3 Numerical Summary of Data 3.1.4 The Box Plot 3.1.5 Probability Distributions 3.2 Important Discrete Distributions 3.2.1 The Hypergeometric Distribution 3.2.2 The Binomial Distribution 3.2.3 The Poisson Distribution 3.2.4 The Pascal and Related Distributions 3.3 Important Continuous Distributions 3.3.1 The Normal Distribution 3.3.2 The Lognormal Distribution 3.3.3 The Exponential Distribution 3.3.4 The Gamma Distribution 3.3.5 The Weibull Distribution 3.4 Probability Plots 3.4.1 Normal Probability Plots 3.4.2 Other Probability Plots 3.5 Some Useful Approximations 3.5.1 The Binomial Approximation to the Hypergeometric 61 63 63 64 64 66 69 71 72 76 76 77 79 80 81 81 86 88 89 91 93 93 95 96 96 ix
  10. 10. x Contents 3.5.2 3.5.3 3.5.4 The Poisson Approximation to the Binomial The Normal Approximation to the Binomial Comments on Approximations 4.6.2 96 4.6.3 97 98 4.6.4 4.6.5 Hypothesis Testing in Multiple Regression Confidance Intervals in Multiple Regression Prediction of New Observations Regression Model Diagnostics 157 163 164 165 4 INFERENCES ABOUT PROCESS QUALITY 103 Chapter Overview and Learning Objectives 4.1 Statistics and Sampling Distributions 4.1.1 Sampling from a Normal Distribution 4.1.2 Sampling from a Bernoulli Distribution 4.1.3 Sampling from a Poisson Distribution 4.2 Point Estimation of Process Parameters 4.3 Statistical Inference for a Single Sample 4.3.1 Inference on the Mean of a Population, Variance Known 4.3.2 The Use of P-Values for Hypothesis Testing 4.3.3 Inference on the Mean of a Normal Distribution, Variance Unknown 4.3.4 Inference on the Variance of a Normal Distribution 4.3.5 Inference on a Population Proportion 4.3.6 The Probability of Type II Error and Sample Size Decisions 4.4 Statistical Inference for Two Samples 4.4.1 Inference for a Difference in Means, Variances Known 4.4.2 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown 4.4.3 Inference on the Variances of Two Normal Distributions 4.4.4 Inference on Two Population Proportions 4.5 What If There Are More Than Two Populations? The Analysis of Variance 4.5.1 An Example 4.5.2 The Analysis of Variance 4.5.3 Checking Assumptions: Residual Analysis 4.6 Linear Regression Models 4.6.1 Estimation of the Parameters in Linear Regression Models 104 104 105 108 109 110 112 113 116 117 120 122 124 127 128 130 137 139 140 140 142 148 150 151 3 PART BASIC METHODS OF STATISTICAL PROCESS CONTROL AND CAPABILITY ANALYSIS 177 5 METHODS AND PHILOSOPHY OF STATISTICAL PROCESS CONTROL 179 Chapter Overview and Learning Objectives 5.1 Introduction 5.2 Chance and Assignable Causes of Quality Variation 5.3 Statistical Basis of the Control Chart 5.3.1 Basic Principles 5.3.2 Choice of Control Limits 5.3.3 Sample Size and Sampling Frequency 5.3.4 Rational Subgroups 5.3.5 Analysis of Patterns on Control Charts 5.3.6 Discussion of Sensitizing Rules for Control Charts 5.3.7 Phase I and Phase II of Control Chart Application 5.4 The Rest of the Magnificent Seven 5.5 Implementing SPC in a Quality Improvement Program 5.6 An Application of SPC 5.7 Applications of Statistical Process Control and Quality Improvement Tools in Transactional and Service Businesses 179 180 181 182 182 189 191 193 195 197 198 199 205 206 213 6 CONTROL CHARTS FOR VARIABLES Chapter Overview and Learning Objectives 6.1 Introduction 226 226 227
  11. 11. Contents 6.2 6.3 6.4 6.5 6.6 Control Charts for – and R x 6.2.1 Statistical Basis of the Charts 6.2.2 Development and Use of – and x R Charts 6.2.3 Charts Based on Standard Values 6.2.4 Interpretation of – and R x Charts 6.2.5 The Effect of Nonnormality on – x and R Charts 6.2.6 The Operating-Characteristic Function 6.2.7 The Average Run Length for the – Chart x Control Charts for – and s x 6.3.1 Construction and Operation of – x and s Charts 6.3.2 The – and s Control Charts with x Variable Sample Size 6.3.3 The s2 Control Chart The Shewhart Control Chart for Individual Measurements Summary of Procedures for – R, x, and s Charts Applications of Variables Control Charts 231 7.4 242 7.5 243 246 246 249 251 251 255 259 259 268 268 7 CONTROL CHARTS FOR ATTRIBUTES Chapter Overview and Learning Objectives 7.1 Introduction 7.2 The Control Chart for Fraction Nonconforming 7.2.1 Development and Operation of the Control Chart 7.2.2 Variable Sample Size 7.2.3 Applications in Transactional and Service Businesses 7.2.4 The Operating-Characteristic Function and Average Run Length Calculations 7.3 Control Charts for Nonconformities (Defects) 7.3.1 Procedures with Constant Sample Size 7.3.2 Procedures with Variable Sample Size 7.3.3 Demerit Systems 7.3.4 228 228 288 288 289 289 290 301 304 306 308 309 319 321 The Operating-Characteristic Function 7.3.5 Dealing with Low Defect Levels 7.3.6 Nonmanufacturing Applications Choice Between Attributes and Variables Control Charts Guidelines for Implementing Control Charts xi 322 323 326 326 330 8 PROCESS AND MEASUREMENT SYSTEM CAPABILITY ANALYSIS Chapter Overview and Learning Objectives 8.1 Introduction 8.2 Process Capability Analysis Using a Histogram or a Probability Plot 8.2.1 Using the Histogram 8.2.2 Probability Plotting 8.3 Process Capability Ratios 8.3.1 Use and Interpretation of Cp 8.3.2 Process Capability Ratio for an Off-Center Process 8.3.3 Normality and the Process Capability Ratio 8.3.4 More about Process Centering 8.3.5 Confidence Intervals and Tests on Process Capability Ratios 8.4 Process Capability Analysis Using a Control Chart 8.5 Process Capability Analysis Using Designed Experiments 8.6 Process Capability Analysis with Attribute Data 8.7 Gauge and Measurement System Capability Studies 8.7.1 Basic Concepts of Gauge Capability 8.7.2 The Analysis of Variance Method 8.7.3 Confidence Intervals in Gauge R & R Studies 8.7.4 False Defectives and Passed Defectives 8.7.5 Attribute Gauge Capability 8.8 Setting Specification Limits on Discrete Components 8.8.1 Linear Combinations 8.8.2 Nonlinear Combinations 344 345 345 347 347 349 351 351 354 356 357 359 364 366 367 368 368 373 376 377 381 383 384 387
  12. 12. xii 8.9 Contents Estimating the Natural Tolerance Limits of a Process 8.9.1 Tolerance Limits Based on the Normal Distribution 8.9.2 Nonparametric Tolerance Limits 9.2.2 388 389 390 9.3 4 PART OTHER STATISTICAL PROCESSMONITORING AND CONTROL TECHNIQUES Chapter Overview and Learning Objectives 9.1 The Cumulative Sum Control Chart 9.1.1 Basic Principles: The Cusum Control Chart for Monitoring the Process Mean 9.1.2 The Tabular or Algorithmic Cusum for Monitoring the Process Mean 9.1.3 Recommendations for Cusum Design 9.1.4 The Standardized Cusum 9.1.5 Improving Cusum Responsiveness for Large Shifts 9.1.6 The Fast Initial Response or Headstart Feature 9.1.7 One-Sided Cusums 9.1.8 A Cusums for Monitoring Process Variability 9.1.9 Rational Subgroups 9.1.10 Cusums for Other Sample Statistics 9.1.11 The V-Mask Procedure 9.1.12 The Self-Starting Cusum 9.2 The Exponentially Weighted Moving Average Control Chart 9.2.1 The Exponentially Weighted Moving Average Control Chart for Monitoring the Process Mean 422 424 425 425 428 10 397 9 CUMULATIVE SUM AND EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHARTS Design of an EWMA Control Chart 9.2.3 Robustness of the EWMA to Nonnormality 9.2.4 Rational Subgroups 9.2.5 Extensions of the EWMA The Moving Average Control Chart 399 400 400 400 403 408 410 410 410 413 413 414 414 415 417 419 419 OTHER UNIVARIATE STATISTICAL PROCESS MONITORING AND CONTROL TECHNIQUES 433 Chapter Overview and Learning Objectives 10.1 Statistical Process Control for Short Production Runs 10.1.1 – and R Charts for Short x Production Runs 10.1.2 Attributes Control Charts for Short Production Runs 10.1.3 Other Methods 10.2 Modified and Acceptance Control Charts 10.2.1 Modified Control Limits for the – Chart x 10.2.2 Acceptance Control Charts 10.3 Control Charts for Multiple-Stream Processes 10.3.1 Multiple-Stream Processes 10.3.2 Group Control Charts 10.3.3 Other Approaches 10.4 SPC With Autocorrelated Process Data 10.4.1 Sources and Effects of Autocorrelation in Process Data 10.4.2 Model-Based Approaches 10.4.3 A Model-Free Approach 10.5 Adaptive Sampling Procedures 10.6 Economic Design of Control Charts 10.6.1 Designing a Control Chart 10.6.2 Process Characteristics 10.6.3 Cost Parameters 10.6.4 Early Work and Semieconomic Designs 10.6.5 An Economic Model of the – x Control Chart 10.6.6 Other Work 10.7 Cuscore Charts 10.8 The Changepoint Model for Process Monitoring 10.9 Profile Monitoring 434 435 435 437 437 439 439 442 443 443 443 445 446 446 450 458 462 463 463 464 464 466 467 472 473 475 476
  13. 13. Contents 10.10 Control Charts in Health Care Monitoring and Public Health Surveillance 10.11 Overview of Other Procedures 10.11.1 Tool Wear 10.11.2 Control Charts Based on Other Sample Statistics 10.11.3 Fill Control Problems 10.11.4 Precontrol 10.11.5 Tolerance Interval Control Charts 10.11.6 Monitoring Processes with Censored Data 10.11.7 Nonparametric Control Charts 481 482 482 482 484 484 Chapter Overview and Learning Objectives 11.1 The Multivariate Quality-Control Problem 11.2 Description of Multivariate Data 11.2.1 The Multivariate Normal Distribution 11.2.2 The Sample Mean Vector and Covariance Matrix 11.3 The Hotelling T 2 Control Chart 11.3.1 Subgrouped Data 11.3.2 Individual Observations 11.4 The Multivariate EWMA Control Chart 11.5 Regression Adjustment 11.6 Control Charts for Monitoring Variability 11.7 Latent Structure Methods 11.7.1 Principal Components 11.7.2 Partial Least Squares 485 486 487 13 494 494 495 497 497 498 499 499 506 509 513 516 518 518 523 12 ENGINEERING PROCESS CONTROL AND SPC Chapter Overview and Learning Objectives 12.1 Process Monitoring and Process Regulation 12.2 Process Control by Feedback Adjustment 12.2.1 A Simple Adjustment Scheme: Integral Control 12.2.2 The Adjustment Chart 12.2.3 Variations of the Adjustment Chart 539 540 5 PART PROCESS DESIGN AND IMPROVEMENT WITH DESIGNED EXPERIMENTS 11 MULTIVARIATE PROCESS MONITORING AND CONTROL 12.2.4 Other Types of Feedback Controllers 12.3 Combining SPC and EPC xiii 527 527 528 529 529 534 536 FACTORIAL AND FRACTIONAL FACTORIAL EXPERIMENTS FOR PROCESS DESIGN AND IMPROVEMENT Chapter Overview and Learning Objectives 13.1 What is Experimental Design? 13.2 Examples of Designed Experiments In Process and Product Improvement 13.3 Guidelines for Designing Experiments 13.4 Factorial Experiments 13.4.1 An Example 13.4.2 Statistical Analysis 13.4.3 Residual Analysis 13.5 The 2k Factorial Design 13.5.1 The 22 Design 13.5.2 The 2k Design for k ≥ 3 Factors 13.5.3 A Single Replicate of the 2k Design 13.5.4 Addition of Center Points to the 2k Design 13.5.5 Blocking and Confounding in the 2k Design 13.6 Fractional Replication of the 2k Design 13.6.1 The One-Half Fraction of the 2k Design 13.6.2 Smaller Fractions: The 2 k–p Fractional Factorial Design 547 549 550 550 552 554 556 558 558 563 564 564 569 579 582 585 587 587 592 14 PROCESS OPTIMIZATION WITH DESIGNED EXPERIMENTS Chapter Overview and Learning Objectives 14.1 Response Surface Methods and Designs 14.1.1 The Method of Steepest Ascent 602 602 603 605
  14. 14. xiv Contents 14.1.2 Analysis of a Second-Order Response Surface 14.2 Process Robustness Studies 14.2.1 Background 14.2.2 The Response Surface Approach to Process Robustness Studies 14.3 Evolutionary Operation 607 611 611 613 619 6 PART ACCEPTANCE SAMPLING 629 15 LOT-BY-LOT ACCEPTANCE SAMPLING FOR ATTRIBUTES Chapter Overview and Learning Objectives 15.1 The Acceptance-Sampling Problem 15.1.1 Advantages and Disadvantages of Sampling 15.1.2 Types of Sampling Plans 15.1.3 Lot Formation 15.1.4 Random Sampling 15.1.5 Guidelines for Using Acceptance Sampling 15.2 Single-Sampling Plans for Attributes 15.2.1 Definition of a Single-Sampling Plan 15.2.2 The OC Curve 15.2.3 Designing a Single-Sampling Plan with a Specified OC Curve 15.2.4 Rectifying Inspection 15.3 Double, Multiple, and Sequential Sampling 15.3.1 Double-Sampling Plans 15.3.2 Multiple-Sampling Plans 15.3.3 Sequential-Sampling Plans 15.4 Military Standard 105E (ANSI/ ASQC Z1.4, ISO 2859) 15.4.1 Description of the Standard 15.4.2 Procedure 15.4.3 Discussion 15.5 The Dodge–Romig Sampling Plans 15.5.1 AOQL Plans 15.5.2 LTPD Plans 15.5.3 Estimation of Process Average 631 631 632 633 634 635 635 636 637 637 637 642 643 646 647 651 652 655 655 657 661 663 664 667 667 16 OTHER ACCEPTANCE-SAMPLING TECHNIQUES 670 Chapter Overview and Learning Objectives 16.1 Acceptance Sampling by Variables 16.1.1 Advantages and Disadvantages of Variables Sampling 16.1.2 Types of Sampling Plans Available 16.1.3 Caution in the Use of Variables Sampling 16.2 Designing a Variables Sampling Plan with a Specified OC Curve 16.3 MIL STD 414 (ANSI/ASQC Z1.9) 16.3.1 General Description of the Standard 16.3.2 Use of the Tables 16.3.3 Discussion of MIL STD 414 and ANSI/ASQC Z1.9 16.4 Other Variables Sampling Procedures 16.4.1 Sampling by Variables to Give Assurance Regarding the Lot or Process Mean 16.4.2 Sequential Sampling by Variables 16.5 Chain Sampling 16.6 Continuous Sampling 16.6.1 CSP-1 16.6.2 Other Continuous-Sampling Plans 16.7 Skip-Lot Sampling Plans APPENDIX Summary of Common Probability Distributions Often Used in Statistical Quality Control II. Cumulative Standard Normal Distribution III. Percentage Points of the χ2 Distribution IV. Percentage Points of the t Distribution V. Percentage Points of the F Distribution VI. Factors for Constructing Variables Control Charts VII. Factors for Two-Sided Normal Tolerance Limits VIII. Factors for One-Sided Normal Tolerance Limits 670 671 671 672 673 673 676 676 677 679 680 680 681 681 683 683 686 686 691 I. 692 693 695 696 697 702 703 704 BIBLIOGRAPHY 705 ANSWERS TO SELECTED EXERCISES 721 INDEX 729
  15. 15. PART 1 Introduction Controlling and improving quality has become an important business strategy for many organizations; manufacturers, distributors, transportation companies, financial services organizations; health care providers, and government agencies. Quality is a competitive advantage. A business that can delight customers by improving and controlling quality can dominate its competitors. This book is about the technical methods for achieving success in quality control and improvement, and offers guidance on how to successfully implement these methods. Part 1 contains two chapters. Chapter 1 contains the basic definitions of quality and quality improvement, provides a brief overview of the tools and methods discussed in greater detail in subsequent parts of the book, and discusses the management systems for quality improvement. Chapter 2 is devoted to the DMAIC (define, measure, analyze, improve, and control) problemsolving process, which is an excellent framework for implementing quality improvement. We also show how the methods discussed in the book are used in DMAIC.
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  17. 17. 1Q uality Improvement in the Modern Business Environment CHAPTER OUTLINE 1.1 THE MEANING OF QUALITY AND QUALITY IMPROVEMENT 1.1.1 Dimensions of Quality 1.1.2 Quality Engineering Terminology 1.2 A BRIEF HISTORY OF QUALITY CONTROL AND IMPROVEMENT 1.3 STATISTICAL METHODS FOR QUALITY CONTROL AND IMPROVEMENT CHAPTER OVERVIEW AND 1.4 MANAGEMENT ASPECTS OF QUALITY IMPROVEMENT 1.4.1 Quality Philosophy and Management Strategies 1.4.2 The Link Between Quality and Productivity 1.4.3 Quality Costs 1.4.4 Legal Aspects of Quality 1.4.5 Implementing Quality Improvement LEARNING OBJECTIVES This book is about the use of statistical methods and other problem-solving techniques to improve the quality of the products used by our society. These products consist of manufactured goods such as automobiles, computers, and clothing, as well as services such as the generation and distribution of electrical energy, public transportation, banking, retailing, and health care. Quality improvement methods can be applied to any area within a company or organization, including manufacturing, process development, engineering design, finance and accounting, marketing, distribution and logistics, customer service, and field service of products. This text presents the technical tools that are needed to achieve quality improvement in these organizations. In this chapter we give the basic definitions of quality, quality improvement, and other quality engineering terminology. We also discuss the historical development of quality 3
  18. 18. 4 Chapter 1 ■ Quality Improvement in the Modern Business Environment improvement methodology and overview the statistical tools essential for modern professional practice. A brief discussion of some management and business aspects for implementing quality improvement is also given. After careful study of this chapter you should be able to do the following: 1. 2. 3. 4. 5. 6. 7. 8. 9. Define and discuss quality and quality improvement Discuss the different dimensions of quality Discuss the evolution of modern quality improvement methods Discuss the role that variability and statistical methods play in controlling and improving quality Describe the quality management philosophies of W. Edwards Deming, Joseph M. Juran, and Armand V. Feigenbaum Discuss total quality management, the Malcolm Baldrige National Quality Award, six-sigma, and quality systems and standards Explain the links between quality and productivity and between quality and cost Discuss product liability Discuss the three functions: quality planning, quality assurance, and quality control and improvement 1.1 The Meaning of Quality and Quality Improvement We may define quality in many ways. Most people have a conceptual understanding of quality as relating to one or more desirable characteristics that a product or service should possess. Although this conceptual understanding is certainly a useful starting point, we will give a more precise and useful definition. Quality has become one of the most important consumer decision factors in the selection among competing products and services. The phenomenon is widespread, regardless of whether the consumer is an individual, an industrial organization, a retail store, a bank or financial institution, or a military defense program. Consequently, understanding and improving quality are key factors leading to business success, growth, and enhanced competitiveness. There is a substantial return on investment from improved quality and from successfully employing quality as an integral part of overall business strategy. In this section we provide operational definitions of quality and quality improvement. We begin with a brief discussion of the different dimensions of quality and some basic terminology. 1.1.1 Dimensions of Quality The quality of a product can be described and evaluated in several ways. It is often very important to differentiate these different dimensions of quality. Garvin (1987) provides an excellent discussion of eight components or dimensions of quality. We summarize his key points concerning these dimensions of quality as follows: 1. Performance (Will the product do the intended job?) Potential customers usually evaluate a product to determine if it will perform certain specific functions and determine how well it performs them. For example, you could evaluate spreadsheet software packages for a PC to determine which data manipulation operations they perform. You may discover that one outperforms another with respect to the execution speed.
  19. 19. 1.1 The Meaning of Quality and Quality Improvement 5 2. Reliability (How often does the product fail?) Complex products, such as many appliances, automobiles, or airplanes, will usually require some repair over their service life. For example, you should expect that an automobile will require occasional repair, but if the car requires frequent repair, we say that it is unreliable. There are many industries in which the customer’s view of quality is greatly impacted by the reliability dimension of quality. 3. Durability (How long does the product last?) This is the effective service life of the product. Customers obviously want products that perform satisfactorily over a long period of time. The automobile and major appliance industries are examples of businesses where this dimension of quality is very important to most customers. 4. Serviceability (How easy is it to repair the product?) There are many industries in which the customer’s view of quality is directly influenced by how quickly and economically a repair or routine maintenance activity can be accomplished. Examples include the appliance and automobile industries and many types of service industries (how long did it take a credit card company to correct an error in your bill?). 5. Aesthetics (What does the product look like?) This is the visual appeal of the product, often taking into account factors such as style, color, shape, packaging alternatives, tactile characteristics, and other sensory features. For example, soft-drink beverage manufacturers have relied on the visual appeal of their packaging to differentiate their product from other competitors. 6. Features (What does the product do?) Usually, customers associate high quality with products that have added features; that is, those that have features beyond the basic performance of the competition. For example, you might consider a spreadsheet software package to be of superior quality if it had built-in statistical analysis features while its competitors did not. 7. Perceived Quality (What is the reputation of the company or its product?) In many cases, customers rely on the past reputation of the company concerning quality of its products. This reputation is directly influenced by failures of the product that are highly visible to the public or that require product recalls, and by how the customer is treated when a quality-related problem with the product is reported. Perceived quality, customer loyalty, and repeated business are closely interconnected. For example, if you make regular business trips using a particular airline, and the flight almost always arrives on time and the airline company does not lose or damage your luggage, you will probably prefer to fly on that carrier instead of its competitors. 8. Conformance to Standards (Is the product made exactly as the designer intended?) We usually think of a high-quality product as one that exactly meets the requirements placed on it. For example, how well does the hood fit on a new car? Is it perfectly flush with the fender height, and is the gap exactly the same on all sides? Manufactured parts that do not exactly meet the designer’s requirements can cause significant quality problems when they are used as the components of a more complex assembly. An automobile consists of several thousand parts. If each one is just slightly too big or too small, many of the components will not fit together properly, and the vehicle (or its major subsystems) may not perform as the designer intended. We see from the foregoing discussion that quality is indeed a multifaceted entity. Consequently, a simple answer to questions such as “What is quality?” or “What is quality improvement?” is not easy. The traditional definition of quality is based on the viewpoint that products and services must meet the requirements of those who use them.
  20. 20. 6 Chapter 1 ■ Quality Improvement in the Modern Business Environment Definition Quality means fitness for use. There are two general aspects of fitness for use: quality of design and quality of conformance. All goods and services are produced in various grades or levels of quality. These variations in grades or levels of quality are intentional, and, consequently, the appropriate technical term is quality of design. For example, all automobiles have as their basic objective providing safe transportation for the consumer. However, automobiles differ with respect to size, appointments, appearance, and performance. These differences are the result of intentional design differences among the types of automobiles. These design differences include the types of materials used in construction, specifications on the components, reliability obtained through engineering development of engines and drive trains, and other accessories or equipment. The quality of conformance is how well the product conforms to the specifications required by the design. Quality of conformance is influenced by a number of factors, including the choice of manufacturing processes, the training and supervision of the workforce, the types of process controls, tests, and inspection activities that are employed, the extent to which these procedures are followed, and the motivation of the workforce to achieve quality. Unfortunately, this definition has become associated more with the conformance aspect of quality than with design. This is in part due to the lack of formal education most designers and engineers receive in quality engineering methodology. This also leads to much less focus on the customer and more of a “conformance-to-specifications” approach to quality, regardless of whether the product, even when produced to standards, was actually “fit-foruse” by the customer. Also, there is still a widespread belief that quality is a problem that can be dealt with solely in manufacturing, or that the only way quality can be improved is by “gold-plating” the product. We prefer a modern definition of quality: Definition Quality is inversely proportional to variability. Note that this definition implies that if variability1 in the important characteristics of a product decreases, the quality of the product increases. As an example of the operational effectiveness of this definition, a few years ago, one of the automobile companies in the United States performed a comparative study of a transmission that was manufactured in a domestic plant and by a Japanese supplier. An analysis of warranty claims and repair costs indicated that there was a striking difference between the two sources of production, with the Japanese-produced transmission having much lower costs, as shown in Fig. 1.1. As part of the study to discover the cause of this difference in cost and performance, the company selected random samples of transmissions from each plant, disassembled them, and measured several critical quality characteristics. 1 We are referring to unwanted or harmful variability. There are situations in which variability is actually good. As my good friend Bob Hogg has pointed out, “I really like Chinese food, but I don’t want to eat it every night.”
  21. 21. 1.1 The Meaning of Quality and Quality Improvement 7 Japan $ United States 0 United States ■ FIGURE 1.1 transmissions. Japan LSL Warranty costs for Target USL ■ FIGURE 1.2 Distributions of critical dimensions for transmissions. Figure 1.2 is generally representative of the results of this study. Note that both distributions of critical dimensions are centered at the desired or target value. However, the distribution of the critical characteristics for the transmissions manufactured in the United States takes up about 75% of the width of the specifications, implying that very few nonconforming units would be produced. In fact, the plant was producing at a quality level that was quite good, based on the generally accepted view of quality within the company. In contrast, the Japanese plant produced transmissions for which the same critical characteristics take up only about 25% of the specification band. As a result, there is considerably less variability in the critical quality characteristics of the Japanese-built transmissions in comparison to those built in the United States. This is a very important finding. Jack Welch, the retired chief executive officer of General Electric, has observed that your customer doesn’t see the mean of your process (the target in Fig. 1.2), he only sees the variability around that target that you have not removed. In almost all cases, this variability has significant customer impact. There are two obvious questions here: Why did the Japanese do this? How did they do this? The answer to the “why” question is obvious from examination of Fig. 1.1. Reduced variability has directly translated into lower costs (the Japanese fully understood the point made by Welch). Furthermore, the Japanese-built transmissions shifted gears more smoothly, ran more quietly, and were generally perceived by the customer as superior to those built domestically. Fewer repairs and warranty claims means less rework and the reduction of wasted time, effort, and money. Thus, quality truly is inversely proportional to variability. Furthermore, it can be communicated very precisely in a language that everyone (particularly managers and executives) understands—namely, money. How did the Japanese do this? The answer lies in the systematic and effective use of the methods described in this book. It also leads to the following definition of quality improvement. Definition Quality improvement is the reduction of variability in processes and products. Excessive variability in process performance often results in waste. For example, consider the wasted money, time, and effort that is associated with the repairs represented in Fig. 1.1. Therefore, an alternate and frequently very useful definition is that quality improvement is the reduction of waste. This definition is particularly effective in service industries, where there may not be as many things that can be directly measured (like the transmission