Table of Contents

PART 1 INTRODUCTION 1
1 QUALITY IMPROVEMENT IN THE MODERN BUSINESS ENVIRONMENT
3


Chapter Overview and Learning Objectives 3


1.1 The Meaning of Quality and Quality Improvement 4


1.1.1 Dimensions of Quality 4


1.1.2 Quality Engineering Terminology 8


1.2 A Brief History of Quality Control and Improvement 9


1.3 Statistical Methods for Quality Control and Improvement
13


1.4 Management Aspects of Quality Improvement 16


1.4.1 Quality Philosophy and Management Strategies 17


1.4.2 The Link Between Quality and Productivity 35


1.4.3 Supply Chain Quality Management 36


1.4.4 Quality Costs 38


1.4.5 Legal Aspects of Quality 44


1.4.6 Implementing Quality Improvement 45


2 THE DMAIC PROCESS 48


Chapter Overview and Learning Objectives 48


2.1 Overview of DMAIC 49


2.2 The Define Step 52


2.3 The Measure Step 54


2.4 The Analyze Step 55


2.5 The Improve Step 56


2.6 The Control Step 57


2.7 Examples of DMAIC 57


2.7.1 Litigation Documents 57


2.7.2 Improving On-Time Delivery 59


2.7.3 Improving Service Quality in a Bank 62


PART 2 STATISTICAL METHODS USEFUL IN QUALITY CONTROL AND
IMPROVEMENT 65


3 MODELING PROCESS QUALITY 67


Chapter Overview and Learning Objectives 68


3.1 Describing Variation 68


3.1.1 The Stem-and-Leaf Plot 68


3.1.2 The Histogram 70


3.1.3 Numerical Summary of Data 73


3.1.4 The Box Plot 75


3.1.5 Probability Distributions 76


3.2 Important Discrete Distributions 80


3.2.1 The Hypergeometric Distribution 80


3.2.2 The Binomial Distribution 81


3.2.3 The Poisson Distribution 83


3.2.4 The Negative Binomial and Geometric Distributions 86


3.3 Important Continuous Distributions 88


3.3.1 The Normal Distribution 88


3.3.2 The Lognormal Distribution 90


3.3.3 The Exponential Distribution 92


3.3.4 The Gamma Distribution 93


3.3.5 The Weibull Distribution 95


3.4 Probability Plots 97


3.4.1 Normal Probability Plots 97


3.4.2 Other Probability Plots 99


3.5 Some Useful Approximations 100


3.5.1 The Binomial Approximation to the Hypergeometric 100


3.5.2 The Poisson Approximation to the Binomial 100


3.5.3 The Normal Approximation to the Binomial 101


3.5.4 Comments on Approximations 102


4 INFERENCES ABOUT PROCESS QUALITY 108


Chapter Overview and Learning Objectives 109


4.1 Statistics and Sampling Distributions 110


4.1.1 Sampling from a Normal Distribution 111


4.1.2 Sampling from a Bernoulli Distribution 113


4.1.3 Sampling from a Poisson Distribution 114


4.2 Point Estimation of Process Parameters 115


4.3 Statistical Inference for a Single Sample 117


4.3.1 Inference on the Mean of a Population, Variance Known
118


4.3.2 The Use of P-Values for Hypothesis Testing 121


4.3.3 Inference on the Mean of a Normal Distribution, Variance
Unknown 122


4.3.4 Inference on the Variance of a Normal Distribution 126


4.3.5 Inference on a Population Proportion 128


4.3.6 The Probability of Type II Error and Sample Size Decisions
130


4.4 Statistical Inference for Two Samples 133


4.4.1 Inference for a Difference in Means, Variances Known
134


4.4.2 Inference for a Difference in Means of Two Normal
Distributions, Variances Unknown 136


4.4.3 Inference on the Variances of Two Normal Distributions
143


4.4.4 Inference on Two Population Proportions 145


4.5 What If There Are More Than Two Populations? The Analysis of
Variance 146


4.5.1 An Example 146


4.5.2 The Analysis of Variance 148


4.5.3 Checking Assumptions: Residual Analysis 154


4.6 Linear Regression Models 156


4.6.1 Estimation of the Parameters in Linear Regression Models
157


4.6.2 Hypothesis Testing in Multiple Regression 163


4.6.3 Confidance Intervals in Multiple Regression 169


4.6.4 Prediction of New Observations 170


4.6.5 Regression Model Diagnostics 171


PART 3 BASIC METHODS OF STATISTICAL PROCESS CONTROL AND
CAPABILITY ANALYSIS 185


5 METHODS AND PHILOSOPHY OF STATISTICAL PROCESS CONTROL
187


Chapter Overview and Learning Objectives 187


5.1 Introduction 188


5.2 Chance and Assignable Causes of Quality Variation 189


5.3 Statistical Basis of the Control Chart 190


5.3.1 Basic Principles 190


5.3.2 Choice of Control Limits 197


5.3.3 Sample Size and Sampling Frequency 199


5.3.4 Rational Subgroups 201


5.3.5 Analysis of Patterns on Control Charts 203


5.3.6 Discussion of Sensitizing Rules for Control Charts 205


5.3.7 Phase I and Phase II of Control Chart Application 206


5.4 The Rest of the Magnificent Seven 207


5.5 Implementing SPC in a Quality Improvement Program 213


5.6 An Application of SPC 214


5.7 Applications of Statistical Process Control and Quality
Improvement Tools in Transactional and Service Businesses 221


6 CONTROL CHARTS FOR VARIABLES 234


Chapter Overview and Learning Objectives 235


6.1 Introduction 235


6.2 Control Charts for ?x and R 236


6.2.1 Statistical Basis of the Charts 236


6.2.2 Development and Use of ?x and R Charts 239


6.2.3 Charts Based on Standard Values 250


6.2.4 Interpretation of ?x and R Charts 251


6.2.5 The Effect of Nonnormality on ?x and R Charts
254


6.2.6 The Operating-Characteristic Function 254


6.2.7 The Average Run Length for the ?x Chart 257


6.3 Control Charts for ?x and s 259


6.3.1 Construction and Operation of ?x and s Charts
259


6.3.2 The ?x and s Control Charts with Variable Sample
Size 263


6.3.3 The s2 Control Chart 267


6.4 The Shewhart Control Chart for Individual Measurements
267


6.5 Summary of Procedures for ?x , R, and s Charts 276


6.6 Applications of Variables Control Charts 276


7 CONTROL CHARTS FOR ATTRIBUTES 297


Chapter Overview and Learning Objectives 297


7.1 Introduction 298


7.2 The Control Chart for Fraction Nonconforming 299


7.2.1 Development and Operation of the Control Chart 299


7.2.2 Variable Sample Size 310


7.2.3 Applications in Transactional and Service Businesses
315


7.2.4 The Operating-Characteristic Function and Average Run
Length Calculations 315


7.3 Control Charts for Nonconformities (Defects) 317


7.3.1 Procedures with Constant Sample Size 318


7.3.2 Procedures with Variable Sample Size 328


7.3.3 Demerit Systems 330


7.3.4 The Operating-Characteristic Function 331


7.3.5 Dealing with Low Defect Levels 332


7.3.6 Nonmanufacturing Applications 335


7.4 Choice Between Attributes and Variables Control Charts
335


7.5 Guidelines for Implementing Control Charts 339


8 PROCESS AND MEASUREMENT SYSTEM CAPABILITY ANALYSIS
355


Chapter Overview and Learning Objectives 356


8.1 Introduction 356


8.2 Process Capability Analysis Using a Histogram or a
Probability Plot 358


8.2.1 Using the Histogram 358


8.2.2 Probability Plotting 360


8.3 Process Capability Ratios 362


8.3.1 Use and Interpretation of Cp 362


8.3.2 Process Capability Ratio for an Off-Center Process 365


8.3.3 Normality and the Process Capability Ratio 367


8.3.4 More about Process Centering 368


8.3.5 Confidence Intervals and Tests on Process Capability
Ratios 370


8.4 Process Capability Analysis Using a Control Chart 375


8.5 Process Capability Analysis Using Designed Experiments
377


8.6 Process Capability Analysis with Attribute Data 378


8.7 Gauge and Measurement System Capability Studies 379


8.7.1 Basic Concepts of Gauge Capability 379


8.7.2 The Analysis of Variance Method 384


8.7.3 Confidence Intervals in Gauge R & R Studies 387


8.7.4 False Defectives and Passed Defectives 388


8.7.5 Attribute Gauge Capability 392


8.7.6 Comparing Customer and Supplier Measurement Systems
394


8.8 Setting Specification Limits on Discrete Components 396


8.8.1 Linear Combinations 397


8.8.2 Nonlinear Combinations 400


8.9 Estimating the Natural Tolerance Limits of a Process 401


8.9.1 Tolerance Limits Based on the Normal Distribution 402


8.9.2 Nonparametric Tolerance Limits 403


PART 4 OTHER STATISTICAL PROCESSMONITORING AND CONTROL
TECHNIQUES 411


9 CUMULATIVE SUM AND EXPONENTIALLY WEIGHTED MOVING AVERAGE
CONTROL CHARTS 413


Chapter Overview and Learning Objectives 414


9.1 The Cumulative Sum Control Chart 414


9.1.1 Basic Principles: The CUSUM Control Chart for Monitoring
the Process Mean 414


9.1.2 The Tabular or Algorithmic CUSUM for Monitoring the
Process Mean 417


9.1.3 Recommendations for CUSUM Design 422


9.1.4 The Standardized CUSUM 424


9.1.5 Improving CUSUM Responsiveness for Large Shifts 424


9.1.6 The Fast Initial Response or Headstart Feature 424


9.1.7 One-Sided CUSUMs 427


9.1.8 A CUSUM for Monitoring Process Variability 427


9.1.9 Rational Subgroups 428


9.1.10 CUSUMs for Other Sample Statistics 428


9.1.11 The V-Mask Procedure 429


9.1.12 The Self-Starting CUSUM 431


9.2 The Exponentially Weighted Moving Average Control Chart
433


9.2.1 The Exponentially Weighted Moving Average Control Chart
for Monitoring the Process Mean 433


9.2.2 Design of an EWMA Control Chart 436


9.2.3 Robustness of the EWMA to Nonnormality 438


9.2.4 Rational Subgroups 439


9.2.5 Extensions of the EWMA 439


9.3 The Moving Average Control Chart 442


10 OTHER UNIVARIATE STATISTICAL PROCESS-MONITORING AND
CONTROL TECHNIQUES 448


Chapter Overview and Learning Objectives 449


10.1 Statistical Process Control for Short Production Runs
450


10.1.1 ?x and R Charts for Short Production Runs 450


10.1.2 Attributes Control Charts for Short Production Runs
452


10.1.3 Other Methods 452


10.2 Modified and Acceptance Control Charts 454


10.2.1 Modified Control Limits for the ?x Chart 454


10.2.2 Acceptance Control Charts 457


10.3 Control Charts for Multiple-Stream Processes 458


10.3.1 Multiple-Stream Processes 458


10.3.2 Group Control Charts 458


10.3.3 Other Approaches 460


10.4 SPC With Autocorrelated Process Data 461


10.4.1 Sources and Effects of Autocorrelation in Process Data
461


10.4.2 Model-Based Approaches 465


10.4.3 A Model-Free Approach 473


10.5 Adaptive Sampling Procedures 477


10.6 Economic Design of Control Charts 478


10.6.1 Designing a Control Chart 478


10.6.2 Process Characteristics 479


10.6.3 Cost Parameters 479


10.6.4 Early Work and Semieconomic Designs 481


10.6.5 An Economic Model of the ??x Control Chart
482


10.6.6 Other Work 487


10.7 Cuscore Charts 488


10.8 The Changepoint Model for Process Monitoring 490


10.9 Profile Monitoring 491


10.10 Control Charts in Health Care Monitoring and Public Health
Surveillance 496


10.11 Overview of Other Procedures 497


10.11.1 Tool Wear 497


10.11.2 Control Charts Based on Other Sample Statistics 498


10.11.3 Fill Control Problems 498


10.11.4 Precontrol 499


10.11.5 Tolerance Interval Control Charts 500


10.11.6 Monitoring Processes with Censored Data 501


10.11.7 Monitoring Bernoulli Processes 501


10.11.8 Nonparametric Control Charts 502


11 MULTIVARIATE PROCESS MONITORING AND CONTROL 509


Chapter Overview and Learning Objectives 509


11.1 The Multivariate Quality-Control Problem 510


11.2 Description of Multivariate Data 512


11.2.1 The Multivariate Normal Distribution 512


11.2.2 The Sample Mean Vector and Covariance Matrix 513


11.3 The Hotelling T2 Control Chart 514


11.3.1 Subgrouped Data 514


11.3.2 Individual Observations 521


11.4 The Multivariate EWMA Control Chart 524


11.5 Regression Adjustment 528


11.6 Control Charts for Monitoring Variability 531


11.7 Latent Structure Methods 533


11.7.1 Principal Components 533


11.7.2 Partial Least Squares 538


12 ENGINEERING PROCESS CONTROL AND SPC 542


Chapter Overview and Learning Objectives 542


12.1 Process Monitoring and Process Regulation 543


12.2 Process Control by Feedback Adjustment 544


12.2.1 A Simple Adjustment Scheme: Integral Control 544


12.2.2 The Adjustment Chart 549


12.2.3 Variations of the Adjustment Chart 551


12.2.4 Other Types of Feedback Controllers 554


12.3 Combining SPC and EPC 555


PART 5 PROCESS DESIGN AND IMPROVEMENT WITH DESIGNED
EXPERIMENTS 561


13 FACTORIAL AND FRACTIONAL FACTORIAL EXPERIMENTS FOR PROCESS
DESIGN AND IMPROVEMENT 563


Chapter Overview and Learning Objectives 564


13.1 What is Experimental Design? 564


13.2 Examples of Designed Experiments In Process and Product
Improvement 566


13.3 Guidelines for Designing Experiments 568


13.4 Factorial Experiments 570


13.4.1 An Example 572


13.4.2 Statistical Analysis 572


13.4.3 Residual Analysis 577


13.5 The 2k Factorial Design 578


13.5.1 The 22 Design 578


13.5.2 The 2k Design for k ? 3 Factors 583


13.5.3 A Single Replicate of the 2k Design 593


13.5.4 Addition of Center Points to the 2k Design 596


13.5.5 Blocking and Confounding in the 2k Design 599


13.6 Fractional Replication of the 2k Design 601


13.6.1 The One-Half Fraction of the 2k Design 601


13.6.2 Smaller Fractions: The 2k?p Fractional Factorial
Design 606


14 PROCESS OPTIMIZATION WITH DESIGNED EXPERIMENTS 617


Chapter Overview and Learning Objectives 617


14.1 Response Surface Methods and Designs 618


14.1.1 The Method of Steepest Ascent 620


14.1.2 Analysis of a Second-Order Response Surface 622


14.2 Process Robustness Studies 626


14.2.1 Background 626


14.2.2 The Response Surface Approach to Process Robustness
Studies 628


14.3 Evolutionary Operation 634


PART 6 ACCEPTANCE SAMPLING 647


15 LOT-BY-LOT ACCEPTANCE SAMPLING FOR ATTRIBUTES 649


Chapter Overview and Learning Objectives 649


15.1 The Acceptance-Sampling Problem 650


15.1.1 Advantages and Disadvantages of Sampling 651


15.1.2 Types of Sampling Plans 652


15.1.3 Lot Formation 653


15.1.4 Random Sampling 653


15.1.5 Guidelines for Using Acceptance Sampling 654


15.2 Single-Sampling Plans for Attributes 655


15.2.1 Definition of a Single-Sampling Plan 655


15.2.2 The OC Curve 655


15.2.3 Designing a Single-Sampling Plan with a Specified OC
Curve 660


15.2.4 Rectifying Inspection 661


15.3 Double, Multiple, and Sequential Sampling 664


15.3.1 Double-Sampling Plans 665


15.3.2 Multiple-Sampling Plans 669


15.3.3 Sequential-Sampling Plans 670


15.4 Military Standard 105E (ANSI/ASQC Z1.4, ISO 2859) 673


15.4.1 Description of the Standard 673


15.4.2 Procedure 675


15.4.3 Discussion 679


15.5 The Dodge?Romig Sampling Plans 681


15.5.1 AOQL Plans 682


15.5.2 LTPD Plans 685


15.5.3 Estimation of Process Average 685


16 OTHER ACCEPTANCE-SAMPLING TECHNIQUES 688


Chapter Overview and Learning Objectives 688


16.1 Acceptance Sampling by Variables 689


16.1.1 Advantages and Disadvantages of Variables Sampling
689


16.1.2 Types of Sampling Plans Available 690


16.1.3 Caution in the Use of Variables Sampling 691


16.2 Designing a Variables Sampling Plan with a Specified OC
Curve 691


16.3 MIL STD 414 (ANSI/ASQC Z1.9) 694


16.3.1 General Description of the Standard 694


16.3.2 Use of the Tables 695


16.3.3 Discussion of MIL STD 414 and ANSI/ASQC Z1.9 697


16.4 Other Variables Sampling Procedures 698


16.4.1 Sampling by Variables to Give Assurance Regarding the Lot
or Process Mean 698


16.4.2 Sequential Sampling by Variables 699


16.5 Chain Sampling 699


16.6 Continuous Sampling 701


16.6.1 CSP-1 701


16.6.2 Other Continuous-Sampling Plans 704


16.7 Skip-Lot Sampling Plans 704


APPENDIX 709


I. Summary of Common Probability Distributions Often Used in
Statistical Quality Control 710


II. Cumulative Standard Normal Distribution 711


III. Percentage Points of the ?2 Distribution 713


IV. Percentage Points of the t Distribution 714


V. Percentage Points of the F Distribution 715


VI. Factors for Constructing Variables Control Charts 720


VII. Factors for Two-Sided Normal Tolerance Limits 721


VIII. Factors for One-Sided Normal Tolerance Limits 722


BIBLIOGRAPHY 723


ANSWERS TO SELECTED EXERCISES 739


INDEX 749

About the Author

DOUGLAS C. MONTGOMERY, PhD, is Regents Professor of Industrial Engineering and Statistics at Arizona State University. Dr. Montgomery is a Fellow of the American Statistical Association, the American Society for Quality, the Royal Statistical Society, and the Institute of Industrial Engineers and has more than thirty years of academic and consulting experience. He has devoted his research to engineering statistics, specifically the design and analysis of experiments, statistical methods for process monitoring and optimization, and the analysis of time-oriented data. Dr. Montgomery is the coauthor of Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition and Introduction to Time Series Analysis and Forecasting, both published by Wiley.