Applied Statistics and Probability for Engineers

Applied Statistics and Probability for Engineers

Applied Statistics and Probability for Engineers Third Edition (822 Pages)
By Douglas. C. Montgomery, George. C. Runger

Applied Statistics and Probability for Engineers

Contents of Applied Statistics and Probability for Engineers
CHAPTER 1 The Role of
Statistics in Engineering 1
1-1 The Engineering Method and
Statistical Thinking 2
1-2 Collecting Engineering Data 5
1-2.1 Basic Principles 5
1-2.2 Retrospective Study 5
1-2.3 Observational Study 6
1-2.4 Designed Experiments 6
1-2.5 A Factorial Experiment for
the Connector Pull-Off Force
Problem (CD Only) 8
1-2.6 Observing Processes Over Time 8
1-3 Mechanistic and Empirical Models 11
1-4 Probability and Probability Models 14
CHAPTER 2 Probability 16
2-1 Sample Spaces and Events 17
2-1.1 Random Experiments 17
2-1.2 Sample Spaces 18
2-1.3 Events 22
2-1.4 Counting Techniques
(CD Only) 25
2-2 Interpretations of Probability 27
2-2.1 Introduction 27
2-2.2 Axioms of Probability 30
2-3 Addition Rules 33
2-4 Conditional Probability 37
2-5 Multiplication and Total Probability
Rules 42
2-5.1 Multiplication Rule 42
2-5.2 Total Probability Rule 43
2-6 Independence 46
2-7 Bayes’ Theorem 51
2-8 Random Variables 53
CHAPTER 3 Discrete Random
Variables and Probability
Distributions 59
3-1 Discrete Random Variables 60
3-2 Probability Distributions and
Probability Mass Functions 61
3-3 Cumulative Distribution
Functions 63
3-4 Mean and Variance of a Discrete
Random Variable 66
3-5 Discrete Uniform Distribution 70
3-6 Binomial Distribution 72
3-7 Geometric and Negative Binomial
Distributions 78
3-7.1 Geometric Distribution 78
3-7.2 Negative Binomial
Distribution 80
3-8 Hypergeometric Distribution 84
3-9 Poisson Distribution 89
CHAPTER 4 Continuous Random
Variables and Probability
Distributions 97
4-1 Continuous Random
Variables 98
4-2 Probability Distributions
and Probability Density
Functions 98
4-3 Cumulative Distribution
Functions 102
4-4 Mean and Variance of a
Continuous Random Variable 105
4-5 Continuous Uniform
Distribution 107
4-6 Normal Distribution 109
4-7 Normal Approximation to the
Binomial and Poisson
Distributions 118
4-8 Continuity Corrections to
Improve the Approximation
(CD Only) 122
4-9 Exponential Distribution 122
4-10 Erlang and Gamma
Distribution 128
4-10.1 Erlang Distribution 128
4-10.2 Gamma Distribution 130
4-11 Weibull Distribution 133
4-12 Lognormal Distribution 135
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CHAPTER 5 Joint Probability
Distributions 141
5-1 Two Discrete Random Variables 142
5-1.1 Joint Probability
Distributions 142
5-1.2 Marginal Probability
Distributions 144
5-1.3 Conditional Probability
Distributions 146
5-1.4 Independence 148
5-2 Multiple Discrete Random
Variables 151
5-2.1 Joint Probability
Distributions 151
5-2.2 Multinomial Probability
Distribution 154
5-3 Two Continuous Random
Variables 157
5-3.1 Joint Probability
Distributions 157
5-3.2 Marginal Probability
Distributions 159
5-3.3 Conditional Probability
Distributions 162
5-3.4 Independence 164
5-4 Multiple Continuous Random
Variables 167
5-5 Covariance and Correlation 171
5-6 Bivariate Normal Distribution 177
5-7 Linear Combinations of Random
Variables 180
5-8 Functions of Random Variables
(CD Only) 185
5-9 Moment Generating Functions
(CD Only) 185
5-10 Chebyshev’s Inequality
(CD Only) 185
CHAPTER 6 Random Sampling
and Data Description 189
6-1 Data Summary and Display 190
6-2 Random Sampling 195
6-3 Stem-and-Leaf Diagrams 197
6-4 Frequency Distributions and
Histograms 203
6-5 Box Plots 207
6-6 Time Sequence Plots 209
6-7 Probability Plots 212
6-8 More About Probability Plotting
(CD Only) 216
CHAPTER 7 Point Estimation of
Parameters 220
7-1 Introduction 221
7-2 General Concepts of Point
Estimation 222
7-2.1 Unbiased Estimators 222
7-2.2 Proof that S is a Biased Estimator
of (CD Only) 224
7-2.3 Variance of a Point Estimator 224
7-2.4 Standard Error: Reporting a Point
Estimator 225
7-2.5 Bootstrap Estimate of the Standard
Error (CD Only) 226
7-2.6 Mean Square Error of an
Estimator 226
7-3 Methods of Point Estimation 229
7-3.1 Method of Moments 229
7-3.2 Method of Maximum
Likelihood 230
7-3.3 Bayesian Estimation of Parameters
(CD Only) 237
7-4 Sampling Distributions 238
7-5 Sampling Distribution of
Means 239
CHAPTER 8 Statistical Intervals
for a Single Sample 247
8-1 Introduction 248
8-2 Confidence Interval on the Mean of
a Normal Distribution, Variance
Known 249
8-2.1 Development of the Confidence
Interval and Its Basic
Properties 249
8-2.2 Choice of Sample Size 252
8-2.3 One-sided Confidence
Bounds 253
8-2.4 General method to Derive a
Confidence Interval 253
8-2.5 A Large-Sample Confidence
Interval for 254
8-2.6 Bootstrap Confidence Intervals
(CD Only) 256
8-3 Confidence Interval on the Mean of a
Normal Distribution, Variance
Unknown 257
8-3.1 The t Distribution 258
8-3.2 Development of the t Distribution
(CD Only) 259
8-3.3 The t Confidence Interval
on 259
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8-4 Confidence Interval on the Variance
and Standard Deviation of a Normal
Distribution 261
8-5 A Large-Sample Confidence Interval
for a Population Proportion 265
8-6 A Prediction Interval for a Future
Observation 268
8-7 Tolerance Intervals for a Normal
Distribution 270
CHAPTER 9 Tests of Hypotheses
for a Single Sample 277
9-1 Hypothesis Testing 278
9-1.1 Statistical Hypotheses 278
9-1.2 Tests of Statistical
Hypotheses 280
9-1.3 One-Sided and Two-Sided
Hypotheses 286
9-1.4 General Procedure for Hypothesis
Testing 287
9-2 Tests on the Mean of a
Normal Distribution, Variance
Known 289
9-2.1 Hypothesis Tests on the Mean 289
9-2.2 P-Values in Hypothesis
Tests 292
9-2.3 Connection Between Hypothesis
Tests and Confidence
Intervals 293
9-2.4 Type II Error and Choice of Sample
Size 293
9-2.5 Large Sample Test 297
9-2.6 Some Practical Comments on
Hypothesis Tests 298
9-3 Tests on the Mean of a Normal
Distribution, Variance
Unknown 300
9-3.1 Hypothesis Tests on the
Mean 300
9-3.2 P-Value for a t-Test 303
9-3.3 Choice of Sample Size 304
9-3.4 Likelihood Ratio Approach to
Development of Test Procedures
(CD Only) 305
9-4 Tests on the Variance and
Standard Deviation of a Normal
Distribution 307
9-4.1 The Hypothesis Testing
Procedures 307
9-4.2 -Error and Choice of
Sample Size 309
9-5 Tests on a Population
Proportion 310
9-5.1 Large-Sample Tests on a
Proportion 310
9-5.2 Small-Sample Tests on a
Proportion (CD Only) 312
9-5.3 Type II Error and Choice of Sample
Size 312
9-6 Summary of Inference Procedures for
a Single Sample 315
9-7 Testing for Goodness of Fit 315
9-8 Contingency Table Tests 320
CHAPTER 10 Statistical Inference
for Two Samples 327
10-1 Introduction 328
10-2 Inference For a Difference in Means
of Two Normal Distributions,
Variances Known 328
10-2.1 Hypothesis Tests for a
Difference in Means, Variances
Known 329
10-2.2 Choice of Sample Size 331
10-2.3 Identifying Cause and Effect 333
10-2.4 Confidence Interval on a
Difference in Means, Variances
Known 334
10-3 Inference For a Difference in Means
of Two Normal Distributions,
Variances Unknown 337
10-3.1 Hypothesis Tests for a
Difference in Means, Variances
Unknown 337
10-3.2 More About the Equal Variance
Assumption (CD Only) 344
10-3.3 Choice of Sample Size 344
10-3.4 Confidence Interval on a
Difference in Means, Variances
Unknown 345
10-4 Paired t-Test 349
10-5 Inference on the Variances of Two
Normal Distributions 355
10-5.1 The F Distribution 355
10-5.2 Development of the F
Distribution (CD Only) 357
10-5.3 Hypothesis Tests on the Ratio of
Two Variances 357
10-5.4 -Error and Choice of Sample
Size 359
10-5.5 Confidence Interval on the Ratio
of Two Variances 359
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10-6 Inference on Two Population
Proportions 361
10-6.1 Large-Sample Test for
H0 : p1  p2 361
10-6.2 Small Sample Test for
H0 : p1 p2 (CD Only) 364
10-6.3 -Error and Choice of
Sample Size 364
10-6.4 Confidence Interval for
P1  P2 365
10-7 Summary Table for Inference
Procedures for Two Samples 367
CHAPTER 11 Simple Linear
Regression and Correlation 372
11-1 Empirical Models 373
11-2 Simple Linear Regression 375
11-3 Properties of the Least Squares
Estimators 383
11-4 Some Comments on Uses of
Regression (CD Only) 384
11-5 Hypothesis Tests in Simple Linear
Regression 384
11-5.1 Use of t-Tests 384
11-5.2 Analysis of Variance Approach
to Test Significance of
Regression 387
11-6 Confidence Intervals 389
11-6.1 Confidence Intervals on the
Slope and Intercept 389
11-6.2 Confidence Interval on the
Mean Response 390
11-7 Prediction of New Observations 392
11-8 Adequacy of the Regression
Model 395
11-8.1 Residual Analysis 395
11-8.2 Coefficient of Determination
(R2
) 397
11-8.3 Lack-of-Fit Test
(CD Only) 398
11-9 Transformations to a Straight
Line 400
11-10 More About Transformations
(CD Only) 400
11-11 Correlation 400
CHAPTER 12 Multiple Linear
Regression 410
12-1 Multiple Linear Regression
Model 411
12-1.1 Introduction 411
12-1.2 Least Squares Estimation of the
Parameters 414
12-1.3 Matrix Approach to Multiple
Linear Regression 417
12-1.4 Properties of the Least Squares
Estimators 421
12-2 Hypothesis Tests in Multiple Linear
Regression 428
12-2.1 Test for Significance of
Regression 428
12-2.2 Tests on Individual Regression
Coefficients and Subsets of
Coefficients 432
12-2.3 More About the Extra Sum of
Squares Method (CD Only) 435
12-3 Confidence Intervals in Multiple
Linear Regression 437
12-3.1 Confidence Intervals on Individual
Regression Coefficients 437
12-3.2 Confidence Interval on the Mean
Response 438
12-4 Prediction of New Observations 439
12-5 Model Adequacy Checking 441
12-5.1 Residual Analysis 441
12-5.2 Influential Observations 444
12-6 Aspects of Multiple Regression
Modeling 447
12-6.1 Polynomial Regression
Models 447
12-6.2 Categorical Regressors and
Indicator Variables 450
12-6.3 Selection of Variables and Model
Building 452
12-6.4 Multicollinearity 460
12-6.5 Ridge Regression
(CD Only) 461
12-6.6 Nonlinear Regression Models
(CD Only) 461
CHAPTER 13 Design and
Analysis of Single-Factor
Experiments: The Analysis
of Variance 468
13-1 Designing Engineering
Experiments 469
13-2 The Completely Randomized
Single-Factor Experiment 470
13-2.1 An Example 470
13-2.2 The Analysis of Variance 472
13-2.3 Multiple Comparisons Following
the ANOVA 479
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13-2.4 More About Multiple
Comparisons (CD Only) 481
13-2.5 Residual Analysis and Model
Checking 481
13-2.6 Determining Sample Size 482
13-2.7 Technical Details about the
Analysis of Variance
(CD Only) 485
13-3 The Random Effects Model 487
13-3.1 Fixed Versus Random
Factors 487
13-3.2 ANOVA and Variance
Components 487
13-3.3 Determining Sample Size in
the Random Model
(CD Only) 490
13-4 Randomized Complete Block
Design 491
13-4.1 Design and Statistical
Analysis 491
13-4.2 Multiple Comparisons 497
13-4.3 Residual Analysis and Model
Checking 498
13-4.4 Randomized Complete Block
Design with Random Factors
(CD Only) 498
CHAPTER 14 Design of
Experiments with Several
Factors 505
14-1 Introduction 506
14-2 Some Applications of Designed
Experiments (CD Only) 506
14-3 Factorial Experiments 506
14-4 Two-Factor Factorial
Experiments 510
14-4.1 Statistical Analysis of the FixedEffects
Model 511
14-4.2 Model Adequacy Checking 517
14-4.3 One Observation Per Cell 517
14-4.4 Factorial Experiments with
Random Factors: Overview 518
14-5 General Factorial Experiments 520
14-6 Factorial Experiments with Random
Factors (CD Only) 523
14-7 2k Factorial Designs 523
14-7.1 22 Design 524
14-7.2 2k Design for k  3 Factors 529
14-7.3 Single Replicate of the 2k
Design 537
14-7.4 Addition of Center Points to a 2k
Design (CD Only) 541
14-8 Blocking and Confounding in the 2k
Design 543
14-9 Fractional Replication of the 2k
Design 549
14-9.1 One Half Fraction of the
2k Design 549
14-9.2 Smaller Fractions: The 2kp
Fractional Factorial 555
14-10 Response Surface Methods and
Designs (CD Only) 564
CHAPTER 15 Nonparametric
Statistics 571
15-1 Introduction 572
15-2 Sign Test 572
15-2.1 Description of the Test 572
15-2.2 Sign Test for Paired Samples 576
15-2.3 Type II Error for the Sign
Test 578
15-2.4 Comparison to the t-Test 579
15-3 Wilcoxon Signed-Rank Test 581
15-3.1 Description of the Test 581
15-3.2 Large-Sample
Approximation 583
15-3.3 Paired Observations 583
15-3.4 Comparison to the t-Test 584
15-4 Wilcoxon Rank-Sum Test 585
15-4.1 Description of the Test 585
15-4.2 Large-Sample
Approximation 587
15-4.3 Comparison to the t-Test 588
15-5 Nonparametric Methods in the
Analysis of Variance 589
15-5.1 Kruskal-Wallis Test 589
15-5.2 Rank Transformation 591
CHAPTER 16 Statistical Quality
Control 595
16-1 Quality Improvement and
Statistics 596
16-2 Statistical Quality Control 597
16-3 Statistical Process Control 597
16-4 Introduction to Control Charts 598
16-4.1 Basic Principles 598
16-4.2 Design of a Control Chart 602
16-4.3 Rational Subgroups 603
16-4.4 Analysis of Patterns on Control
Charts 604
16-5 and R or S Control Chart 607
16-6 Control Charts for Individual
Measurements 615
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16-7 Process Capability 619
16-8 Attribute Control Charts 625
16-8.1 P Chart (Control Chart for
Proportion) 625
16-8.2 U Chart (Control Chart for
Defects per Unit) 627
16-9 Control Chart Performance 630
16-10 Cumulative Sum Control
Chart 632
16-11 Other SPC Problem-Solving
Tools 639
16-12 Implementing SPC 641
APPENDICES 649
APPENDIX A: Statistical Tables
and Charts 651
Table I Summary of Common Probability
Distributions 652
Table II Cumulative Standard Normal
Distribution 653
Table III Percentage Points 2
,
of the ChiSquared
Distribution 655
Table IV Percentage Points t ,
of the
t-distribution 656
Table V Percentage Points f ,v1,v2 of the
F-distribution 657
Chart VI Operating Characteristic
Curves 662
Table VII Critical Values for the Sign
Test 671
Table VIII Critical Values for the Wilcoxon
Signed-Rank Test 671
Table IX Critical Values for the Wilcoxon
Rank-Sum Test 672
Table X Factors for Constructing Variables
Control Charts 673
Table XI Factors for Tolerance
Intervals 674
APPENDIX B: Bibliography 677
APPENDIX C: Answers to
Selected Exercises
679
GLOSSARY 689
INDEX 703
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