Statistical Quality Control
7th Edition
Published on 19. June 2012
Book
Hardback
768 pages
978-1-118-14681-1 (ISBN)
Description
The Seventh Edition of Introduction to 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 upper-division students in engineering, statistics, business and management science or students in graduate courses.
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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.
Content
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
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