Index
22 factorial design, 594
23 factorial design example, 603
23 factorial design, 601
2k−1 fractional factorial design, 626
2k − p fractional factorial designs, 632
2k factorial designs, 594
A
Abuses of regression, 431
Actual process capability, 691
Addition rules of probabilities, 35
Adjusted R2 statistic, 499
Agresti-Coull confidence interval on a binomial proportion, 294
Aliases in a fractional factorial design, 628
All possible regressions, 523
Alternate fraction, 628
Alternative hypothesis, 307
Analysis of a second-order response surface, 647
Analysis of variance (ANOVA), 539, 542, 544, 545
Analysis of variance for factorials, 583
Analysis of variance method of estimating variance components, 560
Analysis of variance tests in linear regression, 443, 497
ANOVA with unequal sample sizes, 548
Approximating the P-value, 333
Assignable causes of variability, 667
Assumptions in simple linear regression, 452
Attributes control chart, 669, 695, 697
Axioms of probability, 33
B
Backward elimination of predictors in linear regression, 527
Bayes' theorem, 54
Bayesian estimation of parameters, 264
Bernoulli trials, 80
Beta distribution, 148
Bias of an estimator, 249
Binomial expansion, 82
Bins in a histogram, 213
Bivariate normal distribution, 181
Blocking in a 2k design, 619
Blocking in a designed experiment, 562, 563, 566
Bootstrap confidence intervals, 296
Bootstrap sample, 253
Bootstrap standard error, 252
Box plots, 217
C
C chart, 698
Categorical variables as predictors in linear regression, 520
Cause-and-effect diagram, 716
Census, 4
Center line on a control chart, 9, 667
Center points in a 2k design, 611, 631
Central composite design, 647, 649
Central limit theorem, 243
Chance causes of variability, 666
Chi-square goodness-of-fit-test, 350
Chi-square(d) distribution, 142, 287
Choice of sample size for a confidence interval on a mean, 276
Coefficient of determination; see R2
Combinations, 25
Combining P-values, 367
Comparative experiment, 6, 306, 374
Complement of an event, 21
Completely randomized design, 375, 541
Conditional probability distribution, 161, 169, 182
Conditional probability, 40, 42, 54
Confidence coefficient, 273
Confidence interval on a proportion, 291, 294
Confidence interval on the difference in two proportions, 417
Confidence interval on the mean response in multiple linear regression, 507
Confidence interval on the mean response in simple linear regression, 448
Confidence interval on the variance and standard deviation of a normal distribution, 287
Confidence interval on treatment means in ANOVA, 547, 548
Confidence intervals on individual regression coefficients, 506
Confidence intervals on means, 273, 279, 282, 284, 379, 390, 392
Confidence intervals on the ratio of variances of two normal distributions, 407
Confidence intervals on the slope and intercept in simple linear regression, 447
Confounding, 619
Connection between hypothesis tests and confidence intervals, 316
Continuous probability distribution, 108
Continuous random variable, 58, 107, 110
Continuous sample space, 18
Continuous uniform distribution, 116
Contour plot, 577
Contrasts, 595
Control chart for defects per unit (U chart), 697
Control chart for proportions (P chart), 695, 696
Control chart performance, 700
Control charts for 
, R and S, 674, 675, 676
Control charts for individual measurements, 684
Control charts, 9, 667, 669, 674
Cook's distance, 514
Correlation and regression, 457
Correlation coefficient, 458
Counting techniques, 22, 23, 24
Covariance matrix, 488
Cp statistic in regression, 523
Critical region, 308
Critical values of a test statistic, 308
Cumulative binomial probabilities, 83
Cumulative distribution function, 71, 112
Cumulative frequency plot, 215
Cumulative sum control charts, 703, 705
Cumulative Weibull distribution, 143
Cycles in data, 219
D
Data versus information, 5
Decision interval on a CUSUM, 706
Decision theory, 717
Defining contrast, 620
Degree of belief interpretation of probability, 30
Degrees of freedom, 204, 283, 287
Deming, W. Edwards, 8, 664, 721
Deming's bead experiment, 664
DeMorgan's laws, 22
Descriptive statistics, 199
Design generator, 627
Design matrix, 600
Design of a control chart, 670
Design resolution, 621
Designed experiment, 6, 431, 539, 575, 576, 591, 626, 632, 643
Digidot plot, 220
Discrete probability distribution; see probability mass function
Discrete random variable, 58, 65, 66, 74
Discrete uniform distribution, 78
Dot diagram, 3
Dummy variables, 520
E
Empirical model, 11, 12, 428, 429
Engineering method, 2
Engineering sciences, 2
Equivalence testing, 365
Erlang distribution, 139
Error propagation, 285
Estimated standard error, 252
Estimating variance components, 560
Estimating σ2 in regression, 435, 487
Expected cost decision criterion, 719
Expected mean squares in a random effects model, 559
Expected value of a function of a continuous random variable, 115
Expected value of a function of a discrete random variable, 76
Expected value of a function of two random variables, 174
Expected values of mean squares in a factorial, 584
Expected values of sums of squares in ANOVA, 544
Experimentation, 2
Exponential distribution, 133
Exponentially weighted moving average (EWMA) control chart, 709
Extra sum of squares method, 501
Extrapolation in regression, 509
F
Factorial experiment, 6, 576, 578, 582, 591, 594, 600, 611
False alarms on control charts, 686, 701
F-distribution, 407
First-order model, 643
Fisher's LSD method, 549
Fixed factors in an experiment, 543, 582
Fixed significance level test, 314
Forward selection of predictors in linear regression, 527
Fraction defective control chart; see control chart for proportions
Fractional factorial experiment, 7, 626
Frequency distribution, 213
F-test, ANOVA, 545
Full model, 502
G
Gamma function, 140
General factorial experiments, 591
General function of a continuous random variable, 189
General function of a discrete random variable, 189
General functions of random variables, 188
General method for deriving a confidence interval, 277
Generalized interaction, 622
Geometric distribution, 86, 87
Graphical comparison of means following ANOVA, 550
H
Hat matrix in regression, 513
Hidden extrapolation in regression, 509
Histogram, 213
Hypergeometric distribution, 93
Hypothesis testing, 6, 305, 307, 312, 316, 318, 322, 329, 331, 340, 344, 346
Hypothesis tests in linear regression, 441, 443, 497
Hypothesis tests on a proportion, 344, 346
Hypothesis tests on the difference in means of two normal distributions, 376, 383
Hypothesis tests on the mean of a normal distribution, 322, 329, 331
Hypothesis tests on the ratio of variances of two normal distributions, 407
Hypothesis tests on the variance and standard deviation of a normal distribution, 340
I
Importance of blocking, 566
Independence, 49, 50, 51, 165, 182
Independent random variables, 166
Indicator variables, 520
Influential observations in regression, 514
Interaction of factors, 579, 581
Interaction terms in a regression model, 479
Interpreting a confidence interval, 274
Interquartile range, 210
Intersection of events, 21
Intrinsically linear model, 463
J
Joint probability distribution, 156, 157, 158, 167, 179, 181
L
Lack of memory property of the exponential distribution, 135
Lack of memory property of the geometric distribution, 88
Large-sample confidence interval on a mean, 279
Large-sample test on the difference in two proportions, 414
Large-sample tests on means, 329
Large-sample tests on proportions, 344
Least squares normal equations, 432, 481, 484
Likelihood function, 258
Linear function of random variables, 184
Location or central tendency of data, 3
Logistic regression model, 467
Logit response function, 468
Lognormal distribution, 146
M
Main effect of a factor, 579
Marginal probability distribution, 159, 168, 182
Matrix of scatter diagrams, 226, 525
Mean and variance of a continuous random variable, 114
Mean and variance of a discrete uniform distribution, 78
Mean and variance of an average, 186
Mean and variance of the beta distribution, 149
Mean and variance of the binomial distribution, 84
Mean and variance of the continuous uniform distribution, 117
Mean and variance of the exponential distribution, 134
Mean and variance of the gamma distribution, 141
Mean and variance of the geometric distribution, 88
Mean and variance of the hypergeometric distribution, 95
Mean and variance of the lognormal distribution, 146
Mean and variance of the negative binomial distribution, 90
Mean and variance of the normal distribution, 119
Mean and variance of the Poisson distribution, 101
Mean and variance of the Weibull distribution, 143
Mean of a discrete random variable, 74
Mean of a linear function of random variables, 185
Mean squared error of an estimator, 254
Mean squares, 545
Mechanistic model, 11
Median, 209
Method of least squares, 431, 440, 481
Method of maximum likelihood, 258, 262, 469
Method of moments, 256
Method of steepest ascent, 644
Minimax decision criterion, 718
Minimin decision criterion, 718
Minimum variance unbiased estimator, 251
Model adequacy checking in ANOVA, 551, 568, 587
Model adequacy checking in regression, 452, 511
Model matrix in regression, 484
Moment generating functions, 191
Moments, 257
Most probable decision criterion, 719
Moving range, 684
Multicollinearity, 529
Multinomial distribution, 179
Multiple comparisons following ANOVA, 549, 550
Multiple comparisons in a randomized complete block design, 567
Multiple linear regression model, 478
Multiplication rule (counting technique), 23
Multiplication rule for probabilities, 45
Mutually exclusive events, 22, 38
N
Natural tolerance limits of a process, 789
Negative binomial distribution, 89
Nonparametric tests, 357, 368, 362, 396
Normal approximation to the binomial distribution, 128, 129
Normal approximation to the Poisson distribution, 128, 130
Normal distribution, 119
Normal probability plot, 231, 551
Normal probability plot of effects in a 2k design, 608, 630
Normality and the t-test, 334
Nuisance factor and blocking, 563
Null hypothesis, 307
Observational study, 5
Odds ratio, 469
Ohm's law as a mechanistic model, 11
One observation per cell in a factorial experiment; unreplicated design, 588, 607
One-factor-at-a-time (OFAT) experiments, 581
One-sided alternative hypothesis, 307, 313
Operating characteristic curves, 327
Optimization experiment, 577
Ordered stem-and-leaf diagram, 209
Orthogonal X matrix in regression, 529
Overcontrol of a process, 9
P
Parameter estimation, 239, 249
Partial F-test, 502
Partial regression coefficients, 489
Patterns on control charts, 672
Pearson correlation coefficient, 227
Percentile, 209
Permutations, 23
Permutations of similar objects, 24
Permutations of subsets, 23
Point estimate of a parameter, 239, 240, 241
Point estimator, 241
Polynomial regression model, 479, 517
Pooled estimator of variance, 383
Pooled t-test, 383
Population, 4
Posterior distribution, 265
Potential process capability 691
Power of a statistical test, 313
Prediction interval, 273, 297, 449
Prediction interval on future observations in simple linear regression, 449
PRESS statistic in regression, 523
Principal block, 621
Principal fraction, 628
Prior distribution, 265
Probability density function, 108
Probability distribution, 67, 107
Probability mass function, 67, 68
Probability model, 13
Probability of a union, 36
Probability plots, 230
Probability, 13, 15, 30, 32, 35, 40
Process capability ratio PCRk, 691
Process capability ratio, PCR, 689
Process characterization experiment, 576
Process design experiment, 578
Process improvement, 10
Process monitoring, control, 10
Projection of fractional factorials, 621
Properties of maximum likelihood estimators, 262
Properties of moment generating functions, 193
Properties of the least squares estimators in linear regression, 440, 488
P-values, 314, 315, 316, 333, 367
Q
Quality improvement, 664
Quality of conformance, 664
Quality of design, 664
Quartiles, 209
R
R2 in regression models, 454, 455, 499
Random experiment, 16
Random factors in an experiment, 543, 558
Random samples and conditional probability 42
Random variable, 57
Randomized complete block design, 562, 564
Rational subgroups and control charts, 671
Reduced model, 502
Reference distribution, 323, 332
Reference value on a CUSUM, 706
Regression model building, 522, 529
Regression model for a factorial experiment, 597, 606
Regression model, 11, 428, 429, 478
Relative efficiency of estimators, 254
Relative frequency interpretation of probability, 30
Reproductive property of the normal distribution, 186
Residual analysis, 453, 511, 551
Residual plots in a 22 factorial design, 599
Residual plots, 453
Residuals in a 22 factorial design, 599
Response surface methodology, 643
Response surface plot, 580
Retrospective study, 5
Ridge regression, 530
Rotatable central composite design, 650
Runs rules on control charts, 674
S
Sample, 4
Sample correlation coefficient, 459
Sample mean, 200
Sample range, 204
Sample size for a confidence interval on a binomial proportion, 293
Sample size in hypothesis testing on means, 325, 336
Sample size in hypothesis testing on proportions, 347
Sample size in single-factor experiments, 552
Sample variance and standard deviation, 201
Sampling distribution of the mean, 242
Sampling distribution, 240, 242
Sampling with replacement, 49
Sampling without replacement, 25, 72, 93
Saturated fractional factorial, 639
Scatter in data, 3
Science of data, 3
Scientific method, 2
Screening experiment, 540, 577
Second-order model, 64
Sequential experimentation, 644
Shewhart control chart, 668, 674, 684
Significance level of a statistical test, 309
Simple linear regression model, 429
Single-factor experiment, 541
Single replicate of a 2k design, 607
Six-sigma process, 692
Size of a test, see significance level
Small-sample tests on a proportion, 346
Sources of variability, 3
SPC problem-solving tools, 715
Standard error of a point estimator, 251
Standard normal random variable, 120
Standardized residuals, 512
Standardizing a normal random variable, 122
Statistic, 240
Statistical inference, 4
Statistical intervals, 271
Statistical process control (SPC), 10, 666, 715, 720
Statistical quality control, 665
Statistical significance versus practical significance, 319
Stem-and-leaf diagram, 206
Stepwise regression, 526
Strong versus weak conclusions in hypothesis testing, 312
Studentized residuals, 513
T
Tabular CUSUM, 705
Tampering, 9
t-distribution, 283
Testing for curvature in a 2k design, 611
Testing homogeneity in a contingency table, 356
Testing independence in a contingency table, 355
Testing significance of regression, 442, 444, 497
Tests for goodness of fit, 350
Tests on individual means in a factorial experiment 587
Tests on subsets of parameters in linear regression, 501
Three-factor factorial experiment, 591
Time series, 219
Total probability rule, 46
Transformations to correct model inadequacy, 453
Tree diagrams, 19
Trends, 219
t-tests in linear regression, 441, 500
Two-factor factorial experiments, 582, 588
Two-sample t-test, 386
Two-sided alternative hypothesis, 307, 313
Type I error, 308
Type II error, 308
U
Unbalanced experiments, 548
Unbiased estimators, 249
V
Variability, 3
Variables control chart, 669, 674
Variance components, 559
Variance components, 559
Variance inflation factors, 529
Variance of a discrete random variable, 74
Variance of a linear function of random variables, 185
Variance of a point estimator, 251
W
Warning limits on control charts, 674
Weibull distribution, 143
Wilcoxon rank-sum test, 396
Wilcoxon signed-rank test, 362
X
X matrix in regression, 484
X′X matrix in regression 484
Z