اسم المؤلف
Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke
التاريخ
24 أكتوبر 2020
المشاهدات
52
التقييم
(لا توجد تقييمات)

Statistics in Engineering With Examples in MATLAB and R
Second Edition
Andrew Metcalfe
David Green
Tony Greenfield
Mahayaudin Mansor
Andrew Smith
Jonathan Tuke
Contents
Preface xvii
1 Why understand statistics? 1
1.1 Introduction . 1
1.2 Using the book 2
1.3 Software . 2
2 Probability and making decisions 3
2.1 Introduction . 3
2.2 Random digits 4
2.2.1 Concepts and uses 4
2.2.2 Generating random digits 5
2.2.3 Pseudo random digits 6
2.3 Defining probabilities 7
2.3.1 Defining probabilities { Equally likely outcomes 8
2.3.2 Defining probabilities { Relative frequencies 11
2.3.3 Defining probabilities { Subjective probability and expected monetary
value . 13
2.4 Axioms of probability . 15
2.5 The addition rule of probability 15
2.5.1 Complement . 16
2.6 Conditional probability . 18
2.6.1 Conditioning on information 18
2.6.2 Conditional probability and the multiplicative rule 18
2.6.3 Independence . 20
2.6.4 Tree diagrams . 23
2.7 Bayes’ theorem . 25
2.7.1 Law of total probability . 26
2.7.2 Bayes’ theorem for two events 27
2.7.3 Bayes’ theorem for any number of events . 28
2.8 Decision trees 29
2.9 Permutations and combinations 31
2.10 Simple random sample . 33
2.11 Summary . 35
2.11.1 Notation 35
2.11.2 Summary of main results 36
2.11.3 MATLAB R and R commands . 36
2.12 Exercises . 37
vvi Contents
3 Graphical displays of data and descriptive statistics 55
3.1 Types of variables 55
3.2 Samples and populations 58
3.3 Displaying data . 61
3.3.1 Stem-and-leaf plot 61
3.3.2 Time series plot . 62
3.3.3 Pictogram . 65
3.3.4 Pie chart . 68
3.3.5 Bar chart . 68
3.3.6 Rose plot . 70
3.3.7 Line chart for discrete variables . 70
3.3.8 Histogram and cumulative frequency polygon for continuous variables 73
3.3.9 Pareto chart . 77
3.4 Numerical summaries of data . 79
3.4.1 Population and sample . 79
3.4.2 Measures of location . 81
3.4.3 Measures of spread 90
3.5 Box-plots 95
3.6 Outlying values and robust statistics . 97
3.6.1 Outlying values 97
3.6.2 Robust statistics . 98
3.7 Grouped data 99
3.7.1 Calculation of the mean and standard deviation for discrete data . 99
3.7.2 Grouped continuous data [Mean and standard deviation for grouped
continuous data] . 100
3.7.3 Mean as center of gravity 101
3.7.4 Case study of wave stress on offshore structure . 103
3.8 Shape of distributions . 103
3.8.1 Skewness . 103
3.8.2 Kurtosis 104
3.8.3 Some contrasting histograms 105
3.9 Multivariate data 108
3.9.1 Scatter plot . 108
3.9.2 Histogram for bivariate data 110
3.9.3 Parallel coordinates plot . 111
3.10 Descriptive time series . 113
3.10.1 Definition of time series . 113
3.10.2 Missing values in time series . 114
3.10.3 Decomposition of time series 114
3.10.3.1 Trend – Centered moving average 114
3.10.3.2 Seasonal component – Additive monthly model . 115
3.10.3.3 Seasonal component – Multiplicative monthly model 115
3.10.3.4 Seasonal adjustment 116
3.10.3.5 Forecasting . 116
3.10.4 Index numbers 119
3.11 Summary . 121
3.11.1 Notation 121
3.11.2 Summary of main results 121
3.11.3 MATLAB and R commands . 122
3.12 Exercises . 123Contents vii
4 Discrete probability distributions 137
4.1 Discrete random variables . 137
4.1.1 Definition of a discrete probability distribution 138
4.1.2 Expected value 139
4.2 Bernoulli trial 140
4.2.1 Introduction . 140
4.2.2 Defining the Bernoulli distribution . 141
4.2.3 Mean and variance of the Bernoulli distribution 141
4.3 Binomial distribution 142
4.3.1 Introduction . 142
4.3.2 Defining the Binomial distribution . 142
4.3.3 A model for conductivity 147
4.3.4 Mean and variance of the binomial distribution 148
4.3.5 Random deviates from binomial distribution . 149
4.3.6 Fitting a binomial distribution . 149
4.4 Hypergeometric distribution 150
4.4.1 Defining the hypergeometric distribution 151
4.4.2 Random deviates from the hypergeometric distribution . 152
4.4.3 Fitting the hypergeometric distribution 152
4.5 Negative binomial distribution . 153
4.5.1 The geometric distribution . 153
4.5.2 Defining the negative binomial distribution 154
4.5.3 Applications of negative binomial distribution . 155
4.5.4 Fitting a negative binomial distribution 157
4.5.5 Random numbers from a negative binomial distribution . 157
4.6 Poisson process . 158
4.6.1 Defining a Poisson process in time . 158
4.6.2 Superimposing Poisson processes 158
4.6.3 Spatial Poisson process . 158
4.6.4 Modifications to Poisson processes . 159
4.6.5 Poisson distribution . 159
4.6.6 Fitting a Poisson distribution 160
4.6.7 Times between events 161
4.7 Summary . 162
4.7.1 Notation 162
4.7.2 Summary of main results 162
4.7.3 MATLAB and R commands . 163
4.8 Exercises . 164
5 Continuous probability distributions 175
5.1 Continuous random variables . 175
5.1.1 Definition of a continuous random variable 175
5.1.2 Definition of a continuous probability distribution 176
5.1.3 Moments of a continuous probability distribution . 177
5.1.4 Median and mode of a continuous probability distribution 181
5.1.5 Parameters of probability distributions . 181
5.2 Uniform distribution 181
5.2.1 Definition of a uniform distribution . 182
5.2.2 Applications of the uniform distribution 183
5.2.3 Random deviates from a uniform distribution . 183
5.2.4 Distribution of F (X) is uniform 183viii Contents
5.2.5 Fitting a uniform distribution 184
5.3 Exponential distribution 184
5.3.1 Definition of an exponential distribution 184
5.3.2 Markov property . 186
5.3.2.1 Poisson process . 186
5.3.2.2 Lifetime distribution 186
5.3.3 Applications of the exponential distribution 187
5.3.4 Random deviates from an exponential distribution 189
5.3.5 Fitting an exponential distribution . 190
5.4 Normal (Gaussian) distribution 194
5.4.1 Definition of a normal distribution . 194
5.4.2 The standard normal distribution Z ∼ N(0; 1) 195
5.4.3 Applications of the normal distribution 199
5.4.4 Random numbers from a normal distribution . 203
5.4.5 Fitting a normal distribution 203
5.5 Probability plots 203
5.5.1 Quantile-quantile plots 204
5.5.2 Probability plot 204
5.6 Lognormal distribution . 205
5.6.1 Definition of a lognormal distribution . 205
5.6.2 Applications of the lognormal distribution . 208
5.6.3 Random numbers from lognormal distribution . 209
5.6.4 Fitting a lognormal distribution . 209
5.7 Gamma distribution 209
5.7.1 Definition of a gamma distribution . 210
5.7.2 Applications of the gamma distribution 212
5.7.3 Random deviates from gamma distribution 212
5.7.4 Fitting a gamma distribution 212
5.8 Gumbel distribution 213
5.8.1 Definition of a Gumbel distribution . 213
5.8.2 Applications of the Gumbel distribution 215
5.8.3 Random deviates from a Gumbel distribution . 215
5.8.4 Fitting a Gumbel distribution 216
5.9 Summary . 218
5.9.1 Notation 218
5.9.2 Summary of main results 218
5.9.3 MATLAB and R commands . 219
5.10 Exercises . 220
6 Correlation and functions of random variables 233
6.1 Introduction . 233
6.2 Sample covariance and correlation coefficient . 236
6.2.1 Defining sample covariance . 236
6.3 Bivariate distributions, population covariance and correlation coefficient . 244
6.3.1 Population covariance and correlation coefficient . 245
6.3.2 Bivariate distributions – Discrete case . 246
6.3.3 Bivariate distributions – Continuous case . 248
6.3.3.1 Marginal distributions . 248
6.3.3.2 Bivariate histogram 249
6.3.3.3 Covariate and correlation . 250
6.3.3.4 Bivariate probability distributions 251Contents ix
6.3.4 Copulas 256
6.4 Linear combination of random variables (propagation of error) . 256
6.4.1 Mean and variance of a linear combination of random variables . 257
6.4.1.1 Bounds for correlation coefficient 259
6.4.2 Linear combination of normal random variables 260
6.4.3 Central Limit Theorem and distribution of the sample mean 262
6.5 Non-linear functions of random variables (propagation of error) 265
6.6 Summary . 267
6.6.1 Notation 267
6.6.2 Summary of main results 267
6.6.3 MATLAB and R commands . 268
6.7 Exercises . 268
7 Estimation and inference 279
7.1 Introduction . 279
7.2 Statistics as estimators . 279
7.2.1 Population parameters . 280
7.2.2 Sample statistics and sampling distributions 280
7.2.3 Bias and MSE 282
7.3 Accuracy and precision . 285
7.4 Precision of estimate of population mean . 285
7.4.1 Confidence interval for population mean when σ known . 285
7.4.2 Confidence interval for mean when σ unknown 288
7.4.2.1 Construction of confidence interval and rationale for the
t-distribution 288
7.4.2.2 The t-distribution . 289
7.4.3 Robustness 291
7.4.4 Bootstrap methods 292
7.4.4.1 Bootstrap resampling . 292
7.4.4.2 Basic bootstrap confidence intervals . 293
7.4.4.3 Percentile bootstrap confidence intervals 293
7.4.5 Parametric bootstrap 296
7.5 Hypothesis testing . 299
7.5.1 Hypothesis test for population mean when σ known . 300
7.5.2 Hypothesis test for population mean when σ unknown 302
7.5.3 Relation between a hypothesis test and the confidence interval . 303
7.5.4 p-value . 304
7.5.5 One-sided confidence intervals and one-sided tests 304
7.6 Sample size . 305
7.7 Confidence interval for a population variance and standard deviation . 307
7.8 Comparison of means 309
7.8.1 Independent samples 309
7.8.1.1 Population standard deviations differ 309
7.8.1.2 Population standard deviations assumed equal . 312
7.8.2 Matched pairs 315
7.9 Comparing variances 317
7.10 Inference about proportions 318
7.10.1 Single sample 318
7.10.2 Comparing two proportions . 320
7.10.3 McNemar’s test 323
7.11 Prediction intervals and statistical tolerance intervals 325x Contents
7.11.1 Prediction interval 325
7.11.2 Statistical tolerance interval . 326
7.12 Goodness of fit tests 327
7.12.1 Chi-square test 328
7.12.2 Empirical distribution function tests 330
7.13 Summary . 332
7.13.1 Notation 332
7.13.2 Summary of main results 333
7.13.3 MATLAB and R commands . 335
7.14 Exercises . 335
8 Linear regression and linear relationships 357
8.1 Linear regression 357
8.1.1 Introduction . 357
8.1.2 The model 359
8.1.3 Fitting the model . 361
8.1.3.1 Fitting the regression line . 361
8.1.3.2 Identical forms for the least squares estimate of the slope . 363
8.1.3.3 Relation to correlation 363
8.1.3.4 Alternative form for the fitted regression line 364
8.1.3.5 Residuals 365
8.1.3.6 Identities satisfied by the residuals 366
8.1.3.7 Estimating the standard deviation of the errors . 367
8.1.3.8 Checking assumptions A3, A4 and A5 368
8.1.4 Properties of the estimators . 368
8.1.4.1 Estimator of the slope . 369
8.1.4.2 Estimator of the intercept . 371
8.1.5 Predictions 371
8.1.5.1 Confidence interval for mean value of Y given x 371
8.1.5.2 Limits of prediction 373
8.1.5.3 Plotting confidence intervals and prediction limits . 374
8.1.6 Summarizing the algebra 375
8.1.7 Coefficient of determination R2 . 376
8.2 Regression for a bivariate normal distribution 376
8.2.1 The bivariate normal distribution 377
8.3 Regression towards the mean . 378
8.4 Relationship between correlation and regression . 380
8.4.1 Values of x are assumed to be measured without error and can be
preselected 381
8.4.2 The data pairs are assumed to be a random sample from a bivariate
normal distribution 381
8.5 Fitting a linear relationship when both variables are measured with error . 383
8.6 Calibration lines . 386
8.7 Intrinsically linear models 389
8.8 Summary . 393
8.8.1 Notation 393
8.8.2 Summary of main results 393
8.8.3 MATLAB and R commands . 394
8.9 Exercises . 395Contents xi
9 Multiple regression 403
9.1 Introduction . 403
9.2 Multivariate data 404
9.3 Multiple regression model . 405
9.3.1 The linear model . 405
9.3.2 Random vectors . 406
9.3.2.1 Linear transformations of a random vector . 406
9.3.2.2 Multivariate normal distribution . 407
9.3.3 Matrix formulation of the linear model . 407
9.3.4 Geometrical interpretation 407
9.4 Fitting the model 408
9.4.1 Principle of least squares 408
9.4.2 Multivariate calculus – Three basic results 409
9.4.3 The least squares estimator of the coefficients . 410
9.4.4 Estimating the coefficients 411
9.4.5 Estimating the standard deviation of the errors 416
9.4.6 Standard errors of the estimators of the coefficients 417
9.5 Assessing the fit . 418
9.5.1 The residuals . 419
9.5.2 R-squared . 420
9.5.3 F-statistic . 421
9.5.4 Cross validation . 422
9.6 Predictions . 422
9.7 Building multiple regression models 424
9.7.1 Interactions . 424
9.7.2 Categorical variables . 428
9.7.3 F-test for an added set of variables . 433
9.7.4 Quadratic terms . 440
9.7.5 Guidelines for fitting regression models . 447
9.8 Time series . 450
9.8.1 Introduction . 450
9.8.2 Aliasing and sampling intervals 450
9.8.3 Fitting a trend and seasonal variation with regression 451
9.8.4 Auto-covariance and auto-correlation 456
9.8.4.1 Defining auto-covariance for a stationary times series model 457
9.8.4.2 Defining sample auto-covariance and the correlogram . 458
9.8.5 Auto-regressive models 459
9.8.5.1 AR(1) and AR(2) models . 460
9.9 Non-linear least squares 465
9.10 Generalized linear model 468
9.10.1 Logistic regression 468
9.10.2 Poisson regression 470
9.11 Summary . 474
9.11.1 Notation 474
9.11.2 Summary of main results 474
9.11.3 MATLAB and R commands . 475
9.12 Exercises . 476xii Contents
10 Statistical quality control 491
10.1 Continuous improvement 491
10.1.1 Defining quality . 491
10.1.2 Taking measurements 492
10.1.3 Avoiding rework . 493
10.1.4 Strategies for quality improvement . 494
10.1.5 Quality management systems 494
10.1.6 Implementing continuous improvement . 495
10.2 Process stability . 496
10.2.1 Runs chart 496
10.2.2 Histograms and box plots 499
10.2.3 Components of variance . 501
10.3 Capability 510
10.3.1 Process capability index . 510
10.3.2 Process performance index . 511
10.3.3 One-sided process capability indices 512
10.4 Reliability 514
10.4.1 Introduction . 514
10.4.1.1 Reliability of components . 514
10.4.1.2 Reliability function and the failure rate . 515
10.4.2 Weibull analysis . 517
10.4.2.1 Definition of the Weibull distribution 517
10.4.2.2 Weibull quantile plot . 518
10.4.2.3 Censored data . 522
10.4.3 Maximum likelihood . 524
10.4.4 Kaplan-Meier estimator of reliability 529
10.5 Acceptance sampling 530
10.6 Statistical quality control charts 533
10.6.1 Shewhart mean and range chart for continuous variables . 533
10.6.1.1 Mean chart . 533
10.6.1.2 Range chart 535
10.6.2 p-charts for proportions . 538
10.6.3 c-charts for counts 539
10.6.4 Cumulative sum charts . 542
10.6.5 Multivariate control charts . 544
10.7 Summary . 548
10.7.1 Notation 548
10.7.2 Summary of main results 548
10.7.3 MATLAB and R commands . 550
10.8 Exercises . 550
11 Design of experiments with regression analysis 559
11.1 Introduction . 559
11.2 Factorial designs with factors at two levels 562
11.2.1 Full factorial designs . 562
11.2.1.1 Setting up a 2k design . 562
11.2.1.2 Analysis of 2k design . 565
11.3 Fractional factorial designs . 580
11.4 Central composite designs . 585
11.5 Evolutionary operation (EVOP) 593
11.6 Summary . 597Contents xiii
11.6.1 Notation 597
11.6.2 Summary of main results 597
11.6.3 MATLAB and R commands . 598
11.7 Exercises . 598
12 Design of experiments and analysis of variance 605
12.1 Introduction . 605
12.2 Comparison of several means with one-way ANOVA 605
12.2.1 Defining the model 606
12.2.2 Limitation of multiple t-tests 606
12.2.3 One-way ANOVA 607
12.2.4 Testing H0O 610
12.2.5 Follow up procedure . 610
12.3 Two factors at multiple levels . 613
12.3.1 Two factors without replication (two-way ANOVA) 614
12.3.2 Two factors with replication (three-way ANOVA) . 618
12.4 Randomized block design . 621
12.5 Split plot design . 626
12.6 Summary . 636
12.6.1 Notation 636
12.6.2 Summary of main results 637
12.6.3 MATLAB and R commands . 637
12.7 Exercises . 638
13 Probability models 649
13.1 System reliability 649
13.1.1 Series system . 649
13.1.2 Parallel system 650
13.1.3 k-out-of-n system . 651
13.1.4 Modules 652
13.1.5 Duality 653
13.1.6 Paths and cut sets 655
13.1.7 Reliability function 656
13.1.8 Redundancy 658
13.1.9 Non-repairable systems . 658
13.1.10 Standby systems . 659
13.1.11 Common cause failures 661
13.1.12 Reliability bounds 661
13.2 Markov chains 662
13.2.1 Discrete Markov chain 663
13.2.2 Equilibrium behavior of irreducible Markov chains 667
13.2.3 Methods for solving equilibrium equations . 670
13.2.4 Absorbing Markov chains 675
13.2.5 Markov chains in continuous time . 681
13.3 Simulation of systems . 684
13.3.1 The simulation procedure 685
13.3.2 Drawing inference from simulation outputs 689
13.3.3 Variance reduction 692
13.4 Summary . 694
13.4.1 Notation 694
13.4.2 Summary of main results 694xiv Contents
13.5 Exercises . 696
14 Sampling strategies 699
14.1 Introduction . 699
14.2 Simple random sampling from a finite population 702
14.2.1 Finite population correction . 702
14.2.2 Randomization theory 703
14.2.2.1 Defining the simple random sample . 703
14.2.2.2 Mean and variance of sample mean . 704
14.2.2.3 Mean and variance of estimator of population total 705
14.2.3 Model based analysis . 707
14.2.4 Sample size 708
14.3 Stratified sampling . 708
14.3.1 Principle of stratified sampling . 709
14.3.2 Estimating the population mean and total . 709
14.3.3 Optimal allocation of the sample over strata 711
14.4 Multi-stage sampling 713
14.5 Quota sampling . 716
14.6 Ratio estimators and regression estimators 716
14.6.1 Introduction . 716
14.6.2 Regression estimators 716
14.6.3 Ratio estimator 716
14.7 Calibration of the unit cost data base . 718
14.7.1 Sources of error in an AMP . 718
14.7.2 Calibration factor 719
14.8 Summary . 721
14.8.1 Notation 721
14.8.2 Summary of main results 721
14.9 Exercises . 722
Appendix A – Notation 727
A.1 General 727
A.2 Probability 727
A.3 Statistics . 728
A.4 Probability distributions 729
Appendix B – Glossary 731
Appendix C – Getting started in R 745
C.1 Installing R 745
C.2 Using R as a calculator . 745
C.3 Setting the path . 747
C.4 R scripts . 747
C.5 Data entry 747
C.5.1 From keyboard 747
C.5.2 From a file 748
C.5.2.1 Single variable . 748
C.5.2.2 Several variables 748
C.6 R vectors . 749
C.7 User defined functions 750
C.8 Matrices . 750Contents xv
C.9 Loops and conditionals . 751
C.10 Basic plotting 752
C.11 Installing packages 753
C.12 Creating time series objects . 753
Appendix D – Getting started in MATLAB 755
D.1 Installing MATLAB . 755
D.2 Using MATLAB as a calculator 755
D.3 Setting the path . 756
D.4 MATLAB scripts (m-files) . 756
D.5 Data entry 757
D.5.1 From keyboard 757
D.5.2 From a file 757
D.5.2.1 Single variable . 757
D.5.2.2 Several variables 758
D.6 MATLAB vectors 758
D.7 User defined functions 761
D.8 Matrices . 761
D.9 Loops and conditionals . 761
D.10 Basic plotting 763
D.11 Creating time series objects . 764
Appendix E – Experiments 765
E.1 How good is your probability assessment? 765
E.1.1 Objectives . 765
E.1.2 Experiment 765
E.1.3 Question sets . 765
E.1.4 Discussion . 767
E.1.5 Follow up questions . 767
E.2 Buffon’s needle . 767
E.2.1 Objectives . 767
E.2.2 Experiment 767
E.2.3 Questions . 768
E.2.4 Computer simulation . 768
E.2.5 Historical note 768
E.3 Robot rabbit 768
E.3.1 Objectives . 768
E.3.2 Experiment 769
E.3.3 Data 770
E.3.4 Discussion . 770
E.3.5 Follow up question 772
E.4 Use your braking brains 772
E.4.1 Objectives . 772
E.4.2 Experiment 772
E.4.3 Discussion . 772
E.5 Predicting descent time from payload . 773
E.5.1 Objectives . 773
E.5.2 Experiment 773
E.5.3 Discussion . 774
E.5.4 Follow up question 774
E.6 Company efficiency, resources and teamwork . 774xvi Contents
E.6.1 Objectives . 774
E.6.2 Experiment 774
E.6.3 Discussion . 776
E.7 Factorial experiment { reaction times by distraction, dexterity and
distinctness 776
E.7.1 Aim 776
E.7.2 Experiment 776
E.7.3 Analysis 776
E.7.4 Discussion . 777
E.7.5 Follow up questions . 777
E.8 Weibull analysis of cycles to failure 778
E.8.1 Aim 778
E.8.2 Experiment 778
E.8.3 Weibull plot 778
E.8.4 Discussion . 779
E.9 Control or tamper? . 779
E.10 Where is the summit? . 781
References 783
Index
Index
2-factor interaction, 565{567, 571, 574, 578,
581, 582, 587, 591, 598{600
3-factor interaction, 565, 580, 582, 585, 601
absorbing states, 675{678
acceptance sampling, 531{533
accuracy, 119, 200, 279, 285, 298, 337, 339,
453, 503
addition rule, 11, 13, 15{17, 36, 40, 41, 645
aliases, 450, 581, 598, 600
AMP, 711, 718{720, 724
analysis of variance, 375, 421, 605, 607, 615,
616, 620
ANOVA, 375, 421, 480, 605, 607, 608, 610,
611, 613, 614, 622, 624, 625, 627,
630, 631, 634, 636, 637, 639{643,
647
AOQL, 531{533, 555
aperiodic, 668, 671
asset management plan, 699, 711
auto-correlation, 419, 457, 463, 499, 691
auto-covariance, 457
auto-regressive, 459
balance, 39, 82, 102, 180, 352, 506, 605, 607,
614, 621, 637, 642, 646, 671, 674,
675, 772, 777
Bayes’ theorem, 25, 27, 28, 45
Bernoulli trial, 137, 140{142, 149, 153, 154,
158, 162, 165, 353, 489
between samples, 607, 609, 610
bias, 5, 282{285, 293, 299, 337{339, 348, 402,
499, 503, 528, 554, 691, 722, 723
bin, 125, 177, 178, 249
binomial distribution, 137, 143{145, 147{
151, 153, 154, 157, 160, 163, 165,
166, 168, 170, 188, 221, 231, 328,
525, 722, 723
bivariate, 108, 233, 245, 246, 249, 251{253,
255, 256, 267, 271, 337, 357, 376{
378, 380{382, 394, 399
block, 37, 38, 53, 86, 110, 236, 249{251, 344,
481, 561, 621{627, 629{634, 637,
642, 643, 646, 654
bootstrap, xvii, 292{299, 337{339, 349, 370,
397, 465, 487, 499, 512, 527, 528
box plot, 95, 97, 122, 131, 217, 226, 311, 313,
339, 498{500, 509, 556, 592, 611
categorical variable, 55{57, 123, 403, 428,
431, 448, 640, 641
censored, 514, 522, 523, 525, 527
central composite design, 559, 585, 586, 594,
595, 597, 598, 603
Central Limit Theorem, 2, 211, 233, 263, 267,
281, 286, 309, 370, 527, 534, 690
Chapman-Kolmogorov equation, 666
Chi-squared distribution, 307, 341, 342
coefficient, 50, 94, 101, 166, 170, 207, 233,
238, 287, 357, 359, 403, 405, 514,
565, 640, 671, 674, 708
coefficient of variation, 166
coefficient of determination, 376, 729
coefficient of variation, 94, 101, 170, 207, 264,
287, 306, 349, 387, 514, 708
cold standby, 659
common cause variation, 491, 495, 496, 499,
509
concomitant variable, 428, 560{562, 564, 571,
590, 591
conditional distribution, 255, 271, 360, 368,
376{378, 381, 407
conditional probability, 18{20, 28, 41, 43,
255, 515, 525
confidence interval, 197, 279, 285, 359, 370,
418, 504, 512, 579, 603, 611, 613,
690, 708
continuity correction, 320{323
continuous, 55, 138, 175, 246, 248, 330, 404,
492, 514, 575, 580, 605, 615, 681,
683, 716
contour plot, 446, 448, 596
correlation coefficient, 236, 238, 239, 245,
246, 259, 268, 393, 397
correlogram, 458, 459
789790 Statistics in Engineering, Second Edition
covariance, 233, 456, 457, 545, 559, 587, 598,
689, 704
covariate, 250, 404, 405, 450
cumulative distribution function, 121, 138,
176, 252, 256, 330, 515
cumulative frequency polygon, 73, 76, 77, 82,
121, 124, 132, 176
cumulative frequency polygon, 77, 83
datum, 62, 73, 92, 108, 130, 202, 366, 404,
422, 478, 482
degrees of freedom, 93, 268, 288, 367, 417,
502, 545, 566, 567, 607, 706
deseasonalized, 116, 456, 458, 459, 462, 463
design generator, 581, 582, 600
design matrix, 565
detrended, 456, 458, 459, 462, 463
deviance, 470, 473, 489
deviate, 149, 152, 175, 182{184, 189, 190,
203, 212, 215, 216, 242, 243, 342,
518, 692
discrete event simulation, 685, 688, 692
empirical (cdf), 330, 332
endogenous, 685
ensemble, 456, 457
equilibrium, 667, 668, 670{672, 674, 675, 683,
694, 695, 697
equilibrium equations, 667, 668, 670, 671,
674, 675
error, 1, 27, 34, 71, 78, 82, 130, 194, 239,
256, 280, 357, 405, 499, 560, 566,
605, 606, 691, 703
estimator, 126, 172, 191, 259, 279, 280, 360,
367, 405, 408, 497, 566, 587, 607,
689, 690, 701, 703
evolutionary operation, 559, 593, 594, 603
exogenous, 685
expected value, 32, 54, 124, 139, 177, 178,
234, 245, 284, 328, 375, 391, 447,
452, 551, 579, 607, 609, 657, 658,
704
explanatory variable, 118, 716
exponential distribution, 162, 184, 242, 263,
280, 292, 402, 486, 514, 515, 658
F-distribution, 317, 332, 421
factor, 114, 143, 208, 214, 242, 255, 282, 363,
391, 503, 560, 605, 702, 703
factorial experiment, 559, 571, 580, 586, 594,
642
fixed effect, 622, 627, 633, 643
frequency, 12, 61, 70, 176, 177, 245, 249, 328,
396, 450, 503, 534, 564, 674, 686
gamma distribution, 209{214, 228, 307, 683
gamma function, 52, 154
generalized linear regression, 468
generalized variance, 545
geometric distribution, 153, 154, 169
goodness of fit test, 327, 328, 330, 347
Gumbel distribution, 213{219, 226, 228, 229,
296, 297, 336, 338, 339, 351
hidden states, 683, 697
histogram, 73, 175, 176, 246, 249, 297, 298,
368, 382, 453
hot standby, 659
hypothesis (null and alternative), 279, 371,
376, 418, 434, 502, 606, 691
ill-conditioned, 442
imaginary infinite population, 58
independent, 16, 20, 143, 184, 186, 242, 281,
282, 357, 359, 405, 419, 495, 499,
559, 606, 607, 656, 657, 707
indicator variable, 164, 428{431, 434, 435,
439, 448, 452, 456, 484, 488, 560,
605, 643, 646, 647
inherent variability, 358
inter-quartile range (IQR), 90{92, 96, 99,
124, 125, 132, 226, 231, 311, 314,
556
interaction, 403, 424, 562, 613, 684, 685
interval estimate, 280, 333
intrinsically linear model, 389, 390, 394
kurtosis, 104{107, 121, 122, 126, 134, 164,
180, 181, 186, 194, 210, 221, 222,
289, 342, 348, 463, 510
lag, 456, 457, 461, 496, 499, 548, 689, 691
Laplace distribution, 181, 230, 231, 283, 352,
360, 397
least significant difference, 605, 610, 637
least squares estimate, 363, 366, 367, 409
level of significance, 300, 303, 332, 340, 341,
345, 353{355, 614, 625, 632
linear model, 357, 359, 365, 389, 390, 394,
403, 411, 444, 465, 468, 469, 482,
487, 566, 595, 597, 606, 614Index 791
linear regression, 357, 361, 371, 377, 381, 386,
395, 400, 401, 468, 475, 646
linear transformation, 298, 406, 427
linear trend, 117, 451, 452, 454, 455
logit, 468, 469, 488, 489
lower confidence bound, 308
m-step transition matrix, 664
main effect, 565{567, 571, 574{576, 578, 581,
582, 584, 585, 587, 590, 591, 598,
599, 613, 618, 620, 636, 637
main-plot factor, 626, 628, 629
marginal distribution, 245, 246, 248, 249,
251, 252, 256, 271, 377, 382, 452
Markov chain, 662{664, 666{668, 671, 675,
676, 679, 681, 694{696
Markov process, 662, 664, 681, 695
matched pairs, 309, 315, 316, 344, 621, 692
maximum likelihood, 384, 468, 519, 524
mean, 81, 139, 177, 233, 279, 359, 403, 405,
492, 559, 560, 605, 685, 688, 699,
700
mean-adjusted/corrected, 237, 363, 375, 393,
425, 483, 609
mean-square error (MSE), 284, 717
measurement error, 358, 385, 394, 399
median, 82, 181, 283, 284, 389, 391, 413, 496,
497, 579, 580
method of moments, 149, 157, 160, 181, 191,
204, 402, 525, 526
minimal cut set, 655, 656, 661
minimal cut vector, 655
minimal path set, 655, 656
minimal path vector, 655
mode, 22, 56, 85{87, 132, 181, 186, 188, 193,
194, 214
Monte-Carlo simulation, 296, 545
multiple regression, xvii, 2, 403{405, 407,
413, 419, 424, 428, 438, 443, 450,
459, 475, 476, 481{483, 559, 560,
605, 643
multiplicative rule, 18, 19, 23, 26, 36
multivariate normal distribution, 407
mutually exclusive, 8, 12{17, 20, 23, 24, 26,
28, 36, 68, 142, 143, 172
non-linear least squares, 465, 487
normal distribution, 181, 194, 260, 279, 280,
407, 492, 497, 613, 639, 707
normal distribution, 233, 357, 361, 683, 720
normalizing factor, 255
null recurrent, 667, 668
orthogonal, 485, 566, 574, 584, 586, 589, 591,
601
over-dispersed, 470
p-value, 304, 371, 418, 421, 599, 607, 610, 694
Paasche price index, 120, 135
parameter, 6, 7, 79, 81, 141, 181, 256, 260,
279, 280, 359, 361, 416, 461, 515,
517, 566, 568, 606, 609, 660, 700
parametric bootstrap, 296, 297
parent distribution, 287, 288, 291, 292, 295{
297
partial balance, 671, 674, 675
periodic, 360, 668, 671
point estimate, 280, 339, 690
Poisson distribution, 137, 158{161, 171, 172,
185, 189, 328, 330, 470, 471, 539,
540, 549
Poisson process, 158, 159, 169{171, 184, 186,
187, 189, 210, 213, 224, 330, 472,
660
positive recurrent, 667, 668
power, 1, 20, 56, 104, 118, 119, 330, 341, 389,
419, 471, 513, 523, 529, 643, 651,
661
precision, 105, 132, 161, 202, 279, 285, 359,
423, 426, 495, 503, 564, 630, 690,
699
prediction interval, 279, 325, 360, 423, 706,
707
predictor variable, 357, 403, 559, 604, 699,
716
probability, xvii, 1{3, 58, 59, 137, 138, 175,
176, 246, 279, 280, 370, 371, 470,
488, 492, 498, 607, 649, 658, 701
probability density function, 121, 175, 176,
246, 251, 554
probability mass function, 121, 138, 162, 246,
270, 666, 667
process capability index, 510
process performance index, 511
pseudo-3D plot, 413
pseudo-random numbers, xvii, 203, 256, 486,
551
quantile, 83, 90, 181, 182, 402, 438, 443, 518,
519, 571, 578, 610, 640
quantile-quantile plot, 190, 203, 204, 297,
298, 402, 443, 518, 571, 574, 616,
621792 Statistics in Engineering, Second Edition
quartile, 90, 231, 556
quota sample, 716, 723
random digits, 3, 5, 6
random effect, 621, 622, 627
random numbers, xvii, 6, 34, 149, 163, 203,
209, 212, 242, 256, 486, 551, 691,
692
random variable, 126, 137, 175, 233, 245, 280,
281, 359, 368, 406, 525, 606, 656,
657, 703, 704
range, xviii, 1, 2, 4, 5, 73, 78, 175, 201, 236,
239, 280, 300, 357, 364, 403, 415,
496, 510, 564, 585, 611, 617, 649,
665, 706, 716
rate matrix, 682, 683
realization, 419, 452, 662, 691
regression, xvii, 2, 361, 403, 404, 559, 560,
605, 610, 699, 715
regression line, 361, 363, 724
regression sum of squares, 375
regression towards the mean, 378
relative frequency, 74
relative frequency density, 74
reliability function, 185, 515, 657, 661
repeatability, 503, 504
replication, 562, 570, 614, 618, 691, 692
residual sum of squares, 375, 376, 639
response surface, 594
response variable, 357, 359, 421, 443, 561,
570, 716
robust, 97, 98
run, 37, 58, 183, 202, 261, 378, 446, 484, 492,
504, 562, 563, 613, 614, 619, 652,
670, 711
sample, 3, 4, 55, 58, 137, 142, 175, 176, 233,
234, 357, 370, 404, 497, 559, 605,
606, 662, 663, 699
sample path, 662
sample space, 7, 9, 137, 142, 175, 662
sampling distribution, xvii, 397, 458, 545,
551, 639, 706, 720
scatterplot, 244, 365, 368, 413
seasonal term/effect/component, 55, 114,
116, 452, 454, 455
simple random sample, 33, 34, 151, 213, 233,
263, 703, 721
simulation, xvii, xviii, 4, 5, 105, 157, 170,
175, 191, 276, 397, 447, 450, 452,
453, 492, 684, 685, 723
skewness, 102, 103, 165, 180, 181, 265, 517,
518
spurious correlation, 240, 242
standard error, 263, 360, 371, 417, 418, 521,
574, 575, 629, 705, 706
standard deviation, 93, 140, 194, 234, 359,
360, 416, 492, 496, 566, 567, 610,
625, 700, 706
standard error, 521
standard normal distribution, 195, 197
standard order, 563
state space, 663, 665
stationarity, 452, 457
statistic, 205, 420, 471, 545, 549, 639, 691,
692
statistically significant, 433, 439, 499, 561,
575, 606, 610
strata, 709, 710
stratification, 714, 716
stratified sampling, 35, 708, 710, 721, 723
Student’s t-distribution, 288
sub-plot factor, 626, 628
survey population, 700, 714
systematic sample, 701, 710, 715
t-ratio, 599
target population, 284, 699, 700
test statistic, 300, 301
time homogeneous, 663
tolerance interval, 201, 279, 325, 326
training data, 422
transition matrix, 663, 669
transition probability, 663, 664
trend, 54, 55, 63, 297, 323, 451, 452, 497, 551
unbiased estimator, 282, 283, 367, 376, 433,
497, 507, 607, 610, 689, 690, 701,
716
uniform distribution, 139, 140, 181{183, 280,
351, 550
variance, 92{94, 140, 141, 179, 181, 183, 281,
360, 367, 405, 406, 502, 578, 598,
605, 606, 674, 690, 702, 704
variance-covariance matrix, 406, 407, 481,
545, 549, 598
Weibull distribution, 231, 517, 518
weighted mean, 89
within samples estimator, 607
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