Preface ...................................................... xvii
Chapter 1 Introduction
1.1 Designed Experiment ........................................ 2
1.1.1 Motivation for the Study ............................ 2
1.1.2 Investigation ....................................... 2
1.1.3 Changing Criteria ................................... 2
1.1.4 A Summary of the Various Phases of the
Investigation ....................................... 3
1.2 A Survey ................................................... 5
1.3 An Observational Study ..................................... 6
1.4 A Set of Historical Data ................................... 6
1.5 A Brief Description of What is Covered in This Book ........ 6
Chapter 2 Describing Data Graphically and Numerically ......... 11
2.1 Getting Started with Statistics ........................... 12
2.1.1 What Is Statistics? ................................ 12
2.1.2 Population and Sample in a Statistical Study ....... 12
2.2 Classification of Various Types of Data ................... 15
2.2.1 Nominal Data ....................................... 15
2.2.2 Ordinal Data ....................................... 16
2.2.3 Interval Data ...................................... 16
2.2.4 Ratio Data ......................................... 16
2.3 Frequency Distribution Tables for Qualitative and
Quantitative Data ......................................... 17
2.3.1 Qualitative Data ................................... 17
2.3.2 Quantitative Data .................................. 20
2.4 Graphical Description of Qualitative and Quantitative
Data ...................................................... 25
2.4.1 Dot Plot ........................................... 25
2.4.2 Pie Chart .......................................... 25
2.4.3 Bar Chart .......................................... 27
2.4.4 Histograms ......................................... 30
2.4.5 Line Graph ......................................... 35
2.4.6 Stem-and-Leaf Plot ................................. 37
2.5 Numerical Measures of Quantitative Data ................... 41
2.5.1 Measures of Centrality ............................. 42
2.5.2 Measures of Dispersion ............................. 46
2.6 Numerical Measures of Grouped Data ........................ 55
2.6.1 Mean of a Grouped Data ............................. 56
2.6.2 Median of a Grouped Data ........................... 56
2.6.3 Mode of a Grouped Data ............................. 57
2.6.4 Variance of a Grouped Data ......................... 57
2.7 Measures of Relative Position ............................. 59
2.7.1 Percentiles ........................................ 59
2.7.2 Quartiles .......................................... 60
2.7.3 Interquartile Range ................................ 60
2.7.4 Coefficient of Variation ........................... 61
2.8 Box-Whisker Plot .......................................... 62
2.8.1 Construction of a Box Plot ......................... 62
2.8.2 How to Use the Box Plot ............................ 63
2.9 Measures of Association ................................... 68
2.10 Case Studies .............................................. 71
2.11 Using JMP® ................................................ 73
Review Practice Problems .................................. 73
Chapter 3 Elements of Probability ............................. 83
3.1 Introduction .............................................. 84
3.2 Random Experiments, Sample Spaces, and Events ............. 84
3.2.1 Random Experiments and Sample Spaces ............... 84
3.2.2 Events ............................................. 85
3.3 Concepts of Probability ................................... 88
3.4 Techniques of Counting Sample Points ...................... 93
3.4.1 Tree Diagram ....................................... 93
3.4.2 Permutations ....................................... 94
3.4.3 Combinations ....................................... 95
3.4.4 Arrangements of n Objects Involving Several Kinds
of Objects ......................................... 96
3.5 Conditional Probability ................................... 98
3.6 Bayes's Theorem .......................................... 100
3.7 Introducing Random Variables ............................. 104
Review Practice Problems ................................. 105
Chapter 4 Discrete Random Variables and Some Important
Discrete Probability Distributions ............................ 111
4.1 Graphical Descriptions of Discrete Distributions ......... 112
4.2 Mean and Variance of a Discrete Random Variable .......... 113
4.2.1 Expected Value of Discrete Random Variables and
Their Functions ................................... 113
4.2.2 The Moment-Generating Function-Expected Value of
a Special Function of X ........................... 115
4.3 The Discrete Uniform Distribution ........................ 117
4.4 The Hypergeometric Distribution .......................... 119
4.5 The Bernoulli Distribution ............................... 122
4.6 The Binomial Distribution ................................ 123
4.7 The Multinomial Distribution ............................. 126
4.8 The Poisson Distribution ................................. 128
4.8.1 Definition and Properties of the Poisson
Distribution ...................................... 128
4.8.2 Poisson Process ................................... 128
4.8.3 Poisson Distribution as a Limiting Form of the
Binomial .......................................... 128
4.9 The Negative Binomial Distribution ....................... 132
4.10 Some Derivations and Proofs (Optional) ................... 135
4.11 A Case Study ............................................. 135
4.12 Using JMP 135 Review Practice Problems ................... 136
Chapter 5 Continuous Random Variables and Some Important
Continuous Probability Distributions .......................... 143
5.1 Continuous Random Variables .............................. 144
5.2 Mean and Variance of Continuous Random Variables ......... 146
5.2.1 Expected Value of Continuous Random Variables
and Their Function ................................ 146
5.2.2 The Moment-Generating Function-Expected Value of
a Special Function of X ........................... 149
5.3 Chebychev's Inequality ................................... 151
5.4 The Uniform Distribution ................................. 152
5.4.1 Definition and Properties ......................... 152
5.4.2 Mean and Standard Deviation of the Uniform
Distribution ...................................... 155
5.5 The Normal Distribution .................................. 157
5.5.1 Definition and Properties ......................... 157
5.5.2 The Standard Normal Distribution .................. 158
5.5.3 The Moment-Generating Function of the Normal
Distribution ...................................... 164
5.6 Distribution of Linear Combination of Independent
Normal Variables ......................................... 165
5.7 Approximation of the Binomial and Poisson Distribution
by the Normal Distribution ............................... 169
5.7.1 Approximation of the Binomial Distribution by
the Normal Distribution ........................... 169
5.7.2 Approximation of the Poisson Distribution by
the Normal Distribution ........................... 171
5.8 A Test of Normality ...................................... 171
5.9 Probability Models Commonly Used in Reliability Theory ... 175
5.9.1 The Lognormal Distribution ........................ 176
5.9.2 The Exponential Distribution ...................... 180
5.9.3 The Gamma Distribution ............................ 184
5.9.4 The Weibull Distribution .......................... 187
5.10 A Case Study ............................................. 191
5.11 Using JMP ................................................ 192
Review Practice Problems ...................................... 192
Chapter 6 I Distribution of Functions of Random Variables .... 199
6.1 Introduction ............................................. 200
6.2 Distribution Functions of Two Random Variables ........... 200
6.2.1 Case of Two Discrete Random Variables ............. 200
6.2.2 Case of Two Continuous Random Variables ........... 202
6.2.3 The Mean Value and Variance of Functions of Two
Random Variables .................................. 204
6.2.4 Conditional Distributions ......................... 206
6.2.5 Correlation between Two Random Variables .......... 208
6.2.6 Bivariate Normal Distribution ..................... 211
6.3 Extension to Several Random Variables .................... 214
6.4 The Moment-Generating Function Revisited ................. 214
Review Practice Problems ................................. 218
Chapter 7 Sampling Distributions ............................. 223
7.1 Random Sampling ........................................... 224
7.1.1 Random Sampling from an Infinite Population ....... 224
7.1.2 Random Sampling from a Finite Population .......... 225
7.2 The Sampling Distribution of the Mean .................... 228
7.2.1 Normal Sampled Population ......................... 228
7.2.2 Nonnormal Sampled Population ...................... 228
7.2.3 The Central Limit Theorem ......................... 228
7.3 Sampling from a Normal Population ........................ 234
7.3.1 The Chi-Square Distribution ....................... 234
7.3.2 The Student ^-Distribution ........................ 240
7.3.3 Snedecor's F-Distribution ......................... 244
7.4 Order Statistics ......................................... 247
7.5 Using JMP 247 Review Practice Problems ................... 247
Chapter 8 I Estimation of Population Parameters .............. 251
8.1 Introduction ............................................. 252
8.2 Point Estimators for the Population Mean and Variance .... 252
8.2.1 Properties of Point Estimators .................... 253
8.2.2 Methods of Finding Point Estimators ............... 256
8.3 Interval Estimators for the Mean д of a Normal
Population ............................................... 262
8.3.1 σ2 Known .......................................... 262
8.3.2 σ2 Unknown ........................................ 264
8.3.3 Sample Size Is Large .............................. 266
8.4 Interval Estimators for the Difference of Means of Two
Normal Populations ....................................... 272
8.4.1 Variances Are Known ............................... 272
8.4.2 Variances Are Unknown ............................. 273
8.5 Interval Estimators for the Variance of a Normal
Population ............................................... 280
8.6 Interval Estimator for the Ratio of Variances of Two
Normal Populations ....................................... 284
8.7 Point and Interval Estimators for the Parameters of
Binomial Populations ..................................... 288
8.7.1 One Binomial Population ........................... 288
8.7.2 Two Binomial Populations........................... 290
8.8 Determination of Sample Size.............................. 294
8.8.1 One Population Mean ............................... 294
8.8.2 Difference of Two Population Means ................ 295
8.8.3 One Population Proportion ......................... 296
8.8.4 Difference of Two Population Proportions .......... 296
8.9 Some Supplemental Information ............................ 298
8.10 A Case Study ............................................. 298
8.11 Using JMP ................................................ 299
Review Practice Problems ................................. 299
A Case Study Review Practice Problems ................... 299
Chapter 9 Hypothesis Testing ................................. 307
9.1 Introduction ............................................. 308
9.2 Basic Concepts of Testing a Statistical Hypothesis ....... 308
9.2.1 Hypothesis Formulation ............................ 308
9.2.2 Risk Assessment ................................... 310
9.3 Tests Concerning the Mean of a Normal Population Having
Known Variance ........................................... 312
9.3.1 Case of a One-Tail (Left-Sided) Test .............. 312
9.3.2 Case of a One-Tail (Right-Sided) Test ............. 316
9.3.3 Case of a Two-Tail Test ........................... 317
9.4 Tests Concerning the Mean of a Normal Population Having
Unknown Variance ......................................... 324
9.4.1 Case of a Left-Tail Test .......................... 324
9.4.2 Case of a Right-Tail Test ......................... 326
9.4.3 The Two-Tail Case ................................. 326
9.5 Large Sample Theory ...................................... 330
9.6 Tests Concerning the Difference of Means of Two
Populations Having Distributions with Known Variances .... 332
9.6.1 The Left-Tail Test ................................ 332
9.6.2 The Right-Tail Test ............................... 333
9.6.3 The Two-Tail Test ................................. 334
9.7 Tests Concerning the Difference of Means of Two
Populations Having Normal Distributions with Unknown
Variances ................................................ 339
9.7.1 Two Population Variances Are Equal ................ 339
9.7.2 Two Population Variances Are Unequal .............. 342
9.7.3 The Paired t-Test ................................. 344
9.8 Testing Population Proportions ........................... 349
9.8.1 Test Concerning One Population Proportion ......... 349
9.8.2 Test Concerning the Difference between Two
Population Proportions ............................ 351
9.9 Tests Concerning the Variance of a Normal Population ..... 355
9.10 Tests Concerning the Ratio of Variances of Two Normal
Populations .............................................. 358
9.11 Testing of Statistical Hypotheses Using Confidence
Intervals ................................................ 362
9.12 Sequential Tests of Hypotheses ........................... 367
9.12.1 A One-Tail Sequential Testing Procedure ........... 367
9.12.2 A Two-Tail Sequential Testing Procedure ........... 371
9.13 Case Studies ............................................. 374
9.14 Using JMP ................................................ 375
Review Practice Problems ................................. 375
PART II
Chapter 10 Elements of Reliability Theory .................... 389
10.1 The Reliability Function ................................. 390
10.1.1 The Hazard Rate Function .......................... 391
10.1.2 Employing the Hazard Function ..................... 398
10.2 Estimation: Exponential Distribution ..................... 399
10.3 Hypothesis Testing: Exponential Distribution ............. 406
10.4 Estimation: Weibull Distribution ......................... 407
10.5 Case Studies ............................................. 414
10.6 Using JMP 416 Review Practice Problems ................... 416
Chapter 11 Statistical Quality Control—Phase I Control
Charts ........................................................ 419
11.1 Basic Concepts of Quality and Its Benefits ............... 420
11.2 What a Process Is and Some Valuable Tools ................ 420
11.2.1 Check Sheet ....................................... 422
11.2.2 Pareto Chart ...................................... 422
11.2.3 Cause-and-Effect (Fishbone or Ishikawa) Diagram ... 425
11.2.4 Defect Concentration Diagram ...................... 427
11.3 Common and Assignable Causes ............................. 427
11.3.1 Process Evaluation ................................ 427
11.3.2 Action on the Process ............................. 428
11.3.3 Action on Output .................................. 428
11.3.4 Variation ......................................... 428
11.4 Control Charts ........................................... 429
11.4.1 Preparation for Use of Control Charts ............. 430
11.4.2 Benefits of a Control Chart ....................... 431
11.4.3 Control Limits Versus Specification Limits ........ 433
11.5 Control Charts for Variables ............................. 434
11.5.1 Shewhart X and R Control Charts ................... 434
11.5.2 Shewhart X and R Control Charts When Process
Mean д and Process Standard Deviation a Are
Known ............................................. 440
11.5.3 Shewhart X and S Control Charts ................... 441
11.6 Control Charts for Attributes ............................ 448
11.6.1 The p Chart: Control Chart for the Fraction of
Nonconforming Units ............................... 449
11.6.2 The p Chart: Control Chart for the Fraction
Nonconforming with Variable Sample Sizes .......... 454
11.6.3 The np Control Chart: Control Chart for the
Number of Nonconforming Units ..................... 456
11.6.4 The с Control Chart ............................... 458
11.6.5 The u Control Chart ............................... 461
11.7 Process Capability ....................................... 468
11.8 Case Studies ............................................. 470
11.9 Using JMP ................................................ 472
Review Practice Problems ................................. 472
Chapter 12 Statistical Quality Control—Phase II Control
Charts ........................................................ 479
12.1 Introduction ............................................. 480
12.2 Basic Concepts of CUSUM Control Chart .................... 480
12.3 Designing a CUSUM Control Chart .......................... 483
12.3.1 Two-Sided CUSUM Control Chart Using a Numerical
Procedure ......................................... 484
12.3.2 The Fast Initial Response (FIR) Feature for
CUSUM Control Chart ............................... 489
12.3.3 The Combined Shewhart-CUSUM Control Chart ......... 492
12.3.4 The CUSUM Control Chart for Controlling Process
Variability ....................................... 493
12.4 The Moving Average (MA) Control Chart .................... 495
12.5 The Exponentially Weighted Moving Average (EWMA)
Control Chart ............................................ 499
12.6 Case Studies ............................................. 504
12.7 Using JMP ................................................ 505
Review Practice Problems ...................................... 506
Chapter 13 Analysis of Categorical Data ...................... 509
13.1 Introduction ............................................. 509
13.2 The Chi-Square Goodness-of-Fit Test ...................... 510
13.3 Contingency Tables ....................................... 517
13.3.1 The 2x2 Case Parameters Known ..................... 517
13.3.2 The 2x2 Case with Unknown Parameters .............. 519
13.3.3 The r x s Contingency Table ....................... 521
13.4 Chi-Square Test for Homogeneity .......................... 525
13.5 Comments on the Distribution of the Lack-of-Fit
Statistics ................................................
13.6 Case Studies ............................................. 529
Review Practice Problems ...................................... 531
Chapter 14 Nonparametric Tests ............................... 537
14.1 Introduction ............................................. 537
14.2 The Sign Test ............................................ 538
14.2.1 One-Sample Test ................................... 538
14.2.2 The Wilcoxon Signed-Rank Test ..................... 541
14.2.3 Two-Sample Test ................................... 543
14.3 Mann-Whitney (Wilcoxon) W Test for Two Samples ........... 548
14.4 Runs Test ................................................ 551
14.4.1 Runs Above and Below the Median ................... 551
14.4.2 The Wald-Wolfowitz Run Test ....................... 553
14.5 Spearman Rank Correlation ................................ 556
14.6 Using JMP ................................................ 559
Review Practice Problems ................................. 559
Chapter 15 Simple Linear Regression Analysis .................. 566
15.1 Introduction ............................................. 566
15.2 Fitting the Simple Linear Regression Model ............... 567
15.2.1 Simple Linear Regression Model .................... 567
15.2.2 Fitting a Straight Line by Least Squares .......... 569
15.2.3 Sampling Distribution of the Estimators of
Regression Coefficients ........................... 573
15.3 Unbiased Estimator of σ2 ................................. 578
15.4 Further Inferences Concerning Regression Coefficients
(β0, β0, E(Y), and Y ..................................... 580
15.4.1 Confidence Interval for Д with Confidence
Coefficient (1 - α) ............................... 580
15.4.2 Confidence Interval for β0 with Confidence
Coefficient (1 - α) ............................... 581
15.4.3 Confidence Interval for E(Y|X) with Confidence
Coefficient (1 - α) ............................... 582
15.4.4 Prediction Interval for a Future Observation Y
with Confidence Coefficient (1 - α) ............... 585
15.5 Tests of Hypotheses for β0 and β1 ........................ 590
15.5.1 Test of Hypotheses for βx ......................... 590
15.5.2 Test of Hypotheses for β0 ......................... 590
15.6 Analysis of Variance Approach to Simple Linear
Regression Analysis ...................................... 596
15.7 Residual Analysis ........................................ 601
15.8 Transformations .......................................... 609
15.9 Inference About ρ ........................................ 615
15.10 A Case Study ............................................ 618
15.11 Using JMP ............................................... 619
Review Practice Problems ...................................... 619
Chapter 16 I Multiple Linear Regression Analysis ............. 628
16.1 Introduction ............................................. 628
16.2 Multiple Linear Regression Models ........................ 628
16.3 Estimation of Regression Coefficients .................... 632
16.3.1 Estimation of Regression Coefficients Using
Matrix Notation ................................... 633
16.3.2 Properties of the Least-Squares Estimators ........ 635
16.3.3 The Analysis of Variance Table .................... 636
16.3.4 More Inferences about Regression Coefficients ..... 639
16.4 Multiple Linear Regression Model Using Quantitative and
Qualitative Predictor Variables .......................... 646
16.4.1 Single Qualitative Variable with Two Categories ... 646
16.4.2 Single Qualitative Variable with Three or More
Categories ........................................ 647
16.5 Standardized Regression Coefficients ..................... 658
16.5.1 Multicollinearity ................................. 660
16.5.2 Consequences of Multicollinearity ................. 661
16.6 Building Regression Type Prediction Models ............... 662
16.6.1 First Variable to Enter into the Model ............ 662
16.7 Residual Analysis and Certain Criteria for Model
Selection ................................................ 665
16.7.1 Residual Analysis ................................. 665
16.7.2 Certain Criteria for Model Selection .............. 667
16.8 Logistic Regression ...................................... 672
16.9 Case Studies ............................................. 676
16.10 Using JMP ............................................... 677
Review Practice Problems ................................. 678
Chapter 17 Analysis of Variance .............................. 685
17.1 Introduction ............................................. 686
17.2 The Design Models ........................................ 686
17.2.1 Estimable Parameters .............................. 686
17.2.2 Estimable Functions ............................... 688
17.3 One-Way Experimental Layouts ............................. 689
17.3.1 The Model and Its Analysis ........................ 689
17.3.2 Confidence Intervals for Treatment Means .......... 695
17.3.3 Multiple Comparisons .............................. 700
17.3.4 Determination of Sample Size ...................... 706
17.3.5 The Kruskal-Wallis Test for One-Way Layouts
(Nonparametric Method) ............................ 707
17.4 Randomized Complete Block Designs ........................ 710
17.4.1 The Friedman Fr-Test for Randomized Complete
Block Design (Nonparametric Method) ............... 718
17.4.2 Experiments with One Missing Observation in an
RCB-Design Experiment ............................. 719
17.4.3 Experiments with Several Missing Observations in
an RCB-Design Experiment .......................... 719
17.5 Two-Way Experimental Layouts ............................. 722
17.5.1 Two-Way Experimental Layouts with One
Observation per Cell .............................. 724
17.5.2 Two-Way Experimental Layouts with r > 1
Observations per Cell ............................. 725
17.5.3 Blocking in Two-Way Experimental Layouts .......... 734
17.5.4 Extending Two-Way Experimental Designs to n-Way
Experimental Layouts .............................. 734
17.6 Latin Square Designs ..................................... 736
17.7 Random-Effects and Mixed-Effects Models .................. 742
17.7.1 Random-Effects Model .............................. 742
17.7.2 Mixed-Effects Model ............................... 744
17.7.3 Nested (Hierarchical) Designs ..................... 746
17.8 A Case Study ............................................. 752
17.9 Using JMP ................................................ 753
Review Practice Problems ...................................... 753
Chapter 18 The 2k Factorial Designs .......................... 765
18.1 Introduction ............................................. 766
18.2 The Factorial Designs .................................... 766
18.3 The 2k Factorial Design .................................. 768
18.4 Unreplicated 2k Factorial Designs ........................ 776
18.5 Blocking in the 2k Factorial Design ...................... 782
18.5.1 Confounding in the 2k Factorial Design ............ 783
18.5.2 Yates's Algorithm for the 2k Factorial Designs .... 788
18.6 The 2k Fractional Factorial Designs ...................... 790
18.6.1 One-half Replicate of a 2k Factorial Design ....... 790
18.6.2 One-quarter Replicate of a 2k Factorial Design .... 795
18.7 Case Studies ............................................. 799
18.8 Using JMP 801 Review Practice Problems ................... 801
Chapter 19 Response Surfaces This chapter is not included
in text, but is available for download via the book's website:
www.wiley.com/go/statsforengineers
Appendices .................................................... 807
Appendix A Statistical Tables ........................... 809
Appendix В Answers to Selected Problems ................. 845
Appendix С Bibliography ................................. 863
Index ......................................................... 867
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