Introduction to statistical quality control 7th edtition

C ontents
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
ix
x Contents
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 s 2 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
Contents xi
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 C p 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
xii Contents
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 PROCESS-
MONITORING 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 Non-
normality 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
Contents xiii
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 T 2 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 2 k Factorial Design 578
13.5.1 The 2 2 Design 578
13.5.2 The 2 k Design for k ≥ 3 Factors 583
13.5.3 A Single Replicate of the 2 k
Design 593
13.5.4 Addition of Center Points to
the 2 k Design 596
13.5.5 Blocking and Confounding in
the 2 k Design 599
13.6 Fractional Replication of the 2 k Design 601
13.6.1 The One-Half Fraction of the
2 k Design 601
13.6.2 Smaller Fractions: The 2 k–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
xiv Contents
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  χ 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