Statistical Quality Control, 7th Edition International Student Version A Modern Introduction

The Seventh Edition of Statistical Quality Control provides a comprehensive treatment of the major aspects of using statistical methodology for quality control and improvement. Both traditional and modern methods are presented, including state–of–the–art techniques for statistical process monitoring and control and statistically designed experiments for process characterization, optimization, and process robustness studies. The seventh edition continues to focus on DMAIC (define, measure, analyze, improve, and control––the problem–solving strategy of six sigma) including a chapter on the implementation process. Additionally, the text includes new examples, exercises, problems, and techniques. Statistical Quality Control is best suited for students in engineering, statistics, business and management science or students in undergraduate courses.

1 MODERN QUALITY MANAGEMENT AND IMPROVEMENT 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 PROBLEM SOLVING 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 STATISTICAL MODELS OR QUALITY CONTROL AND IMPROVEMENT 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 STATISTICAL INFERENCE IN QUALITY CONTROL AND IMPROVEMENT 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 HOW SPC WORKS 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 VARIABLES CONTROL CHARTS 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 ATTRIBUTES CONTROL CHARTS 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 DETERMINING PROCESS AND MEASUREMENT SYSTEMS CAPABILITY 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 TIME–WEIGHTED 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 ADVANCED CONTROL CHARTING 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 SPC 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 PROCESS ADJUSTMENT AND PROCESS MONITORING 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 BASIC EXPERIMENTAL DESIGN FOR PROCESS 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 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 BASIC ACCEPTANCE SAMPLING PROCEDURES 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 ADDITIONAL SAMPLING PROCEDURES 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