كتاب Introduction to Statistical Quality Control - Sixth Edition

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Introduction to Statistical Quality Control - Sixth Edition
DOUGLAS C. MONTGOMERY
Arizona State University

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Contents
PART 1
INTRODUCTION
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 Quality Costs 36
1.4.4 Legal Aspects of Quality 41
1.4.5 Implementing Quality Improvement 42
2
THE DMAIC PROCESS 45
Chapter Overview and Learning Objectives 45
2.1 Overview of DMAIC 45
2.2 The Define Step 49
2.3 The Measure Step 50
2.4 The Analyze Step 52
2.5 The Improve Step 53
2.6 The Control Step 54
2.7 Examples of DMAIC 54
2.7.1 Litigation Documents 54
2.7.2 Improving On-Time Delivery 56
2.7.3 Improving Service Quality
in a Bank 59
PART 2
STATISTICAL METHODS USEFUL
IN QUALITY CONTROL
AND IMPROVEMENT 61
3
MODELING PROCESS QUALITY 63
Chapter Overview and Learning Objectives 63
3.1 Describing Variation 64
3.1.1 The Stem-and-Leaf Plot 64
3.1.2 The Histogram 66
3.1.3 Numerical Summary of Data 69
3.1.4 The Box Plot 71
3.1.5 Probability Distributions 72
3.2 Important Discrete Distributions 76
3.2.1 The Hypergeometric Distribution 76
3.2.2 The Binomial Distribution 77
3.2.3 The Poisson Distribution 79
3.2.4 The Pascal and Related Distributions 80
3.3 Important Continuous Distributions 81
3.3.1 The Normal Distribution 81
3.3.2 The Lognormal Distribution 86
3.3.3 The Exponential Distribution 88
3.3.4 The Gamma Distribution 89
3.3.5 The Weibull Distribution 91
3.4 Probability Plots 93
3.4.1 Normal Probability Plots 93
3.4.2 Other Probability Plots 95
3.5 Some Useful Approximations 96
3.5.1 The Binomial Approximation to
the Hypergeometric 963.5.2 The Poisson Approximation to
the Binomial 96
3.5.3 The Normal Approximation to
the Binomial 97
3.5.4 Comments on Approximations 98
4
INFERENCES ABOUT
PROCESS QUALITY 103
Chapter Overview and Learning Objectives 104
4.1 Statistics and Sampling Distributions 104
4.1.1 Sampling from a Normal
Distribution 105
4.1.2 Sampling from a Bernoulli
Distribution 108
4.1.3 Sampling from a Poisson
Distribution 109
4.2 Point Estimation of Process Parameters 110
4.3 Statistical Inference for a Single Sample 112
4.3.1 Inference on the Mean of a
Population, Variance Known 113
4.3.2 The Use of P-Values for
Hypothesis Testing 116
4.3.3 Inference on the Mean of a Normal
Distribution, Variance Unknown 117
4.3.4 Inference on the Variance of
a Normal Distribution 120
4.3.5 Inference on a Population
Proportion 122
4.3.6 The Probability of Type II Error
and Sample Size Decisions 124
4.4 Statistical Inference for Two Samples 127
4.4.1 Inference for a Difference in
Means, Variances Known 128
4.4.2 Inference for a Difference in Means
of Two Normal Distributions,
Variances Unknown 130
4.4.3 Inference on the Variances of Two
Normal Distributions 137
4.4.4 Inference on Two
Population Proportions 139
4.5 What If There Are More Than Two
Populations? The Analysis of Variance 140
4.5.1 An Example 140
4.5.2 The Analysis of Variance 142
4.5.3 Checking Assumptions:
Residual Analysis 148
4.6 Linear Regression Models 150
4.6.1 Estimation of the Parameters
in Linear Regression Models 151
x Contents
4.6.2 Hypothesis Testing in Multiple
Regression 157
4.6.3 Confidance Intervals in Multiple
Regression 163
4.6.4 Prediction of New Observations 164
4.6.5 Regression Model Diagnostics 165
PART 3
BASIC METHODS OF STATISTICAL
PROCESS CONTROL AND
CAPABILITY ANALYSIS 177
5
METHODS AND PHILOSOPHY OF
STATISTICAL PROCESS
CONTROL 179
Chapter Overview and Learning Objectives 179
5.1 Introduction 180
5.2 Chance and Assignable Causes of
Quality Variation 181
5.3 Statistical Basis of the Control Chart 182
5.3.1 Basic Principles 182
5.3.2 Choice of Control Limits 189
5.3.3 Sample Size and Sampling
Frequency 191
5.3.4 Rational Subgroups 193
5.3.5 Analysis of Patterns on Control
Charts 195
5.3.6 Discussion of Sensitizing Rules
for Control Charts 197
5.3.7 Phase I and Phase II of Control
Chart Application 198
5.4 The Rest of the Magnificent Seven 199
5.5 Implementing SPC in a Quality
Improvement Program 205
5.6 An Application of SPC 206
5.7 Applications of Statistical Process
Control and Quality Improvement Tools
in Transactional and Service Businesses 213
6
CONTROL CHARTS
FOR VARIABLES 226
Chapter Overview and Learning Objectives 226
6.1 Introduction 2276.2 Control Charts for – x and R 228
6.2.1 Statistical Basis of the Charts 228
6.2.2 Development and Use of – x and
R Charts 231
6.2.3 Charts Based on Standard
Values 242
6.2.4 Interpretation of – x and R
Charts 243
6.2.5 The Effect of Nonnormality on – x
and R Charts 246
6.2.6 The Operating-Characteristic
Function 246
6.2.7 The Average Run Length for
the – x Chart 249
6.3 Control Charts for – x and s 251
6.3.1 Construction and Operation of – x
and s Charts 251
6.3.2 The – x and s Control Charts with
Variable Sample Size 255
6.3.3 The s2 Control Chart 259
6.4 The Shewhart Control Chart for Individual
Measurements 259
6.5 Summary of Procedures for – x, R,
and s Charts 268
6.6 Applications of Variables Control
Charts 268
7
CONTROL CHARTS
FOR ATTRIBUTES 288
Chapter Overview and Learning Objectives 288
7.1 Introduction 289
7.2 The Control Chart for Fraction
Nonconforming 289
7.2.1 Development and Operation of
the Control Chart 290
7.2.2 Variable Sample Size 301
7.2.3 Applications in Transactional
and Service Businesses 304
7.2.4 The Operating-Characteristic
Function and Average Run Length
Calculations 306
7.3 Control Charts for Nonconformities
(Defects) 308
7.3.1 Procedures with Constant Sample
Size 309
7.3.2 Procedures with Variable Sample
Size 319
7.3.3 Demerit Systems 321
Contents xi
7.3.4 The Operating-Characteristic
Function 322
7.3.5 Dealing with Low Defect Levels 323
7.3.6 Nonmanufacturing Applications 326
7.4 Choice Between Attributes and Variables
Control Charts 326
7.5 Guidelines for Implementing Control
Charts 330
8
PROCESS AND MEASUREMENT
SYSTEM CAPABILITY ANALYSIS 344
Chapter Overview and Learning Objectives 345
8.1 Introduction 345
8.2 Process Capability Analysis Using a
Histogram or a Probability Plot 347
8.2.1 Using the Histogram 347
8.2.2 Probability Plotting 349
8.3 Process Capability Ratios 351
8.3.1 Use and Interpretation of C
p 351
8.3.2 Process Capability Ratio for an
Off-Center Process 354
8.3.3 Normality and the Process
Capability Ratio 356
8.3.4 More about Process Centering 357
8.3.5 Confidence Intervals and
Tests on Process Capability
Ratios 359
8.4 Process Capability Analysis Using a
Control Chart 364
8.5 Process Capability Analysis Using
Designed Experiments 366
8.6 Process Capability Analysis with Attribute
Data 367
8.7 Gauge and Measurement System
Capability Studies 368
8.7.1 Basic Concepts of Gauge
Capability 368
8.7.2 The Analysis of Variance
Method 373
8.7.3 Confidence Intervals in Gauge
R & R Studies 376
8.7.4 False Defectives and Passed
Defectives 377
8.7.5 Attribute Gauge Capability 381
8.8 Setting Specification Limits on Discrete
Components 383
8.8.1 Linear Combinations 384
8.8.2 Nonlinear Combinations 3878.9 Estimating the Natural Tolerance Limits
of a Process 388
8.9.1 Tolerance Limits Based on the
Normal Distribution 389
8.9.2 Nonparametric Tolerance Limits 390
PART 4
OTHER STATISTICAL PROCESSMONITORING AND CONTROL
TECHNIQUES 397
9
CUMULATIVE SUM AND
EXPONENTIALLY WEIGHTED
MOVING AVERAGE CONTROL
CHARTS 399
Chapter Overview and Learning Objectives 400
9.1 The Cumulative Sum Control Chart 400
9.1.1 Basic Principles: The Cusum
Control Chart for Monitoring the
Process Mean 400
9.1.2 The Tabular or Algorithmic
Cusum for Monitoring the
Process Mean 403
9.1.3 Recommendations for Cusum
Design 408
9.1.4 The Standardized Cusum 410
9.1.5 Improving Cusum
Responsiveness for Large
Shifts 410
9.1.6 The Fast Initial Response or
Headstart Feature 410
9.1.7 One-Sided Cusums 413
9.1.8 A Cusums for Monitoring
Process Variability 413
9.1.9 Rational Subgroups 414
9.1.10 Cusums for Other Sample
Statistics 414
9.1.11 The V-Mask Procedure 415
9.1.12 The Self-Starting Cusum 417
9.2 The Exponentially Weighted Moving
Average Control Chart 419
9.2.1 The Exponentially Weighted
Moving Average Control
Chart for Monitoring the
Process Mean 419
xii Contents
9.2.2 Design of an EWMA Control
Chart 422
9.2.3 Robustness of the EWMA to Nonnormality 424
9.2.4 Rational Subgroups 425
9.2.5 Extensions of the EWMA 425
9.3 The Moving Average Control Chart 428
10
OTHER UNIVARIATE STATISTICAL
PROCESS MONITORING AND
CONTROL TECHNIQUES 433
Chapter Overview and Learning Objectives 434
10.1 Statistical Process Control for Short
Production Runs 435
10.1.1 – x and R Charts for Short
Production Runs 435
10.1.2 Attributes Control Charts for
Short Production Runs 437
10.1.3 Other Methods 437
10.2 Modified and Acceptance Control Charts 439
10.2.1 Modified Control Limits for
the – x Chart 439
10.2.2 Acceptance Control Charts 442
10.3 Control Charts for Multiple-Stream
Processes 443
10.3.1 Multiple-Stream Processes 443
10.3.2 Group Control Charts 443
10.3.3 Other Approaches 445
10.4 SPC With Autocorrelated Process Data 446
10.4.1 Sources and Effects of
Autocorrelation in Process Data 446
10.4.2 Model-Based Approaches 450
10.4.3 A Model-Free Approach 458
10.5 Adaptive Sampling Procedures 462
10.6 Economic Design of Control Charts 463
10.6.1 Designing a Control Chart 463
10.6.2 Process Characteristics 464
10.6.3 Cost Parameters 464
10.6.4 Early Work and Semieconomic
Designs 466
10.6.5 An Economic Model of the – x
Control Chart 467
10.6.6 Other Work 472
10.7 Cuscore Charts 473
10.8 The Changepoint Model for Process
Monitoring 475
10.9 Profile Monitoring 47610.10 Control Charts in Health Care Monitoring
and Public Health Surveillance 481
10.11 Overview of Other Procedures 482
10.11.1 Tool Wear 482
10.11.2 Control Charts Based on Other
Sample Statistics 482
10.11.3 Fill Control Problems 484
10.11.4 Precontrol 484
10.11.5 Tolerance Interval Control
Charts 485
10.11.6 Monitoring Processes with
Censored Data 486
10.11.7 Nonparametric Control Charts 487
11
MULTIVARIATE PROCESS
MONITORING AND CONTROL 494
Chapter Overview and Learning Objectives 494
11.1 The Multivariate Quality-Control
Problem 495
11.2 Description of Multivariate Data 497
11.2.1 The Multivariate Normal
Distribution 497
11.2.2 The Sample Mean Vector and
Covariance Matrix 498
11.3 The Hotelling T 2 Control Chart 499
11.3.1 Subgrouped Data 499
11.3.2 Individual Observations 506
11.4 The Multivariate EWMA Control Chart 509
11.5 Regression Adjustment 513
11.6 Control Charts for Monitoring Variability 516
11.7 Latent Structure Methods 518
11.7.1 Principal Components 518
11.7.2 Partial Least Squares 523
12
ENGINEERING PROCESS
CONTROL AND SPC 527
Chapter Overview and Learning Objectives 527
12.1 Process Monitoring and Process
Regulation 528
12.2 Process Control by Feedback Adjustment 529
12.2.1 A Simple Adjustment Scheme:
Integral Control 529
12.2.2 The Adjustment Chart 534
12.2.3 Variations of the Adjustment
Chart 536
Contents xiii
12.2.4 Other Types of Feedback
Controllers 539
12.3 Combining SPC and EPC 540
PART 5
PROCESS DESIGN AND
IMPROVEMENT WITH DESIGNED
EXPERIMENTS 547
13
FACTORIAL AND FRACTIONAL
FACTORIAL EXPERIMENTS FOR
PROCESS DESIGN AND
IMPROVEMENT 549
Chapter Overview and Learning Objectives 550
13.1 What is Experimental Design? 550
13.2 Examples of Designed Experiments
In Process and Product Improvement 552
13.3 Guidelines for Designing Experiments 554
13.4 Factorial Experiments 556
13.4.1 An Example 558
13.4.2 Statistical Analysis 558
13.4.3 Residual Analysis 563
13.5 The 2k Factorial Design 564
13.5.1 The 22 Design 564
13.5.2 The 2k Design for k ? 3 Factors 569
13.5.3 A Single Replicate of the 2k
Design 579
13.5.4 Addition of Center Points to
the 2k Design 582
13.5.5 Blocking and Confounding in
the 2k Design 585
13.6 Fractional Replication of the 2k Design 587
13.6.1 The One-Half Fraction of the
2k Design 587
13.6.2 Smaller Fractions: The 2k–p
Fractional Factorial Design 592
14
PROCESS OPTIMIZATION WITH
DESIGNED EXPERIMENTS 602
Chapter Overview and Learning Objectives 602
14.1 Response Surface Methods and Designs 603
14.1.1 The Method of Steepest
Ascent 60514.1.2 Analysis of a Second-Order
Response Surface 607
14.2 Process Robustness Studies 611
14.2.1 Background 611
14.2.2 The Response Surface
Approach to Process
Robustness Studies 613
14.3 Evolutionary Operation 619
PART 6
ACCEPTANCE SAMPLING 629
15
LOT-BY-LOT ACCEPTANCE
SAMPLING FOR ATTRIBUTES 631
Chapter Overview and Learning Objectives 631
15.1 The Acceptance-Sampling Problem 632
15.1.1 Advantages and Disadvantages
of Sampling 633
15.1.2 Types of Sampling Plans 634
15.1.3 Lot Formation 635
15.1.4 Random Sampling 635
15.1.5 Guidelines for Using Acceptance
Sampling 636
15.2 Single-Sampling Plans for Attributes 637
15.2.1 Definition of a Single-Sampling
Plan 637
15.2.2 The OC Curve 637
15.2.3 Designing a Single-Sampling
Plan with a Specified OC
Curve 642
15.2.4 Rectifying Inspection 643
15.3 Double, Multiple, and Sequential
Sampling 646
15.3.1 Double-Sampling Plans 647
15.3.2 Multiple-Sampling Plans 651
15.3.3 Sequential-Sampling Plans 652
15.4 Military Standard 105E (ANSI/
ASQC Z1.4, ISO 2859) 655
15.4.1 Description of the Standard 655
15.4.2 Procedure 657
15.4.3 Discussion 661
15.5 The Dodge–Romig Sampling Plans 663
15.5.1 AOQL Plans 664
15.5.2 LTPD Plans 667
15.5.3 Estimation of Process
Average 667
xiv Contents
16
OTHER ACCEPTANCE-SAMPLING
TECHNIQUES 670
Chapter Overview and Learning Objectives 670
16.1 Acceptance Sampling by Variables 671
16.1.1 Advantages and Disadvantages of
Variables Sampling 671
16.1.2 Types of Sampling Plans Available 672
16.1.3 Caution in the Use of Variables
Sampling 673
16.2 Designing a Variables Sampling Plan
with a Specified OC Curve 673
16.3 MIL STD 414 (ANSI/ASQC Z1.9) 676
16.3.1 General Description of the Standard 676
16.3.2 Use of the Tables 677
16.3.3 Discussion of MIL STD 414 and
ANSI/ASQC Z1.9 679
16.4 Other Variables Sampling Procedures 680
16.4.1 Sampling by Variables to Give
Assurance Regarding the Lot or
Process Mean 680
16.4.2 Sequential Sampling by Variables 681
16.5 Chain Sampling 681
16.6 Continuous Sampling 683
16.6.1 CSP-1 683
16.6.2 Other Continuous-Sampling Plans 686
16.7 Skip-Lot Sampling Plans 686
APPENDIX 691
I. Summary of Common Probability
Distributions Often Used in Statistical
Quality Control 692
II. Cumulative Standard Normal Distribution 693
III. Percentage Points of the ?2 Distribution 695
IV. Percentage Points of the t Distribution 696
V. Percentage Points of the F Distribution 697
VI. Factors for Constructing Variables
Control Charts 702
VII. Factors for Two-Sided Normal
Tolerance Limits 703
VIII. Factors for One-Sided Normal
Tolerance Limits 704
BIBLIOGRAPHY 7

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