试验设计与分析(第6版)(英文影印版)

.2-5　inferences about the differences in means, paired comparison designs　48
2-5.1　the paired comparison problem　48
2-5.2　advantages of the paired comparison design　51
2-6　inferences about the variances of normal distributions　52
2-7　problems　54
chapter 3　experiments with a single factor: the analysis of variance　60
3-1　an example　61
3-2　the analysis of variance　63
3-3　analysis of the fixed effects model　65
3-3.1　decomposition of the total sum of squares　66
3-3.2　statistical analysis　68
3-3.3　estimation of the model parameters　73
3-3.4　unbalanced data　75
3-4　model adequacy checking　75
3-4.1　the normality assumption　76
3-4.2　plot of residuals in time sequence　78
3-4.3　plot of residuals versus fitted values　79
3-4.4　plots of residuals versus other variables　84
3-5　practical interpretation of results　85
3-5.1　a regression model　85
3-5.2　comparisons among treatment means　87
3-5.3　graphical comparisons of means　87
3-5.4　contrasts　88
3-5.5　orthogonal contrasts　91
3-5.6　scheff??s method for comparing all contrasts　93
3-5.7　comparing pairs of treatment means　94
3-5.8　comparing treatment means with a control　97
3-6　sample computer output　98
3-7　determining sample size　101
3-7.1　operating characteristic curves　101
3-7.2　specifying a standard deviation increase　104
3-7.3　confidence interval estimation method　104
3-8　discovering dispersion effects　105
3-9　the regression approach to the analysis of variance　107
3-9.1　least squares estimation of the model parameters　107
3-9.2　the general regression significance test　108
3-10　nonparametric methods in the analysis of variance　110
3-10.1　the kruskaldwallis test　110
3-10.2　general comments on the rank transformation　112
3-11　problems　112
chapter 4　randomized blocks, latin squares, and related designs　119
4-1　the randomized complete block design　119
4-1.1　statistical analysis of the rcbd　121
4-1.2　model adequacy checking　128
4-1.3　some other aspects of the randomized complete block design　130
4-1.4　estimating model parameters and the general regression significance test　133
4-2　the latin square design　136
4-3　the graeco-latin square design　142
4-4　balanced incomplete block designs　145
4-4.1　statistical analysis of the bibd　146
4-4.2　least squares estimation of the parameters　150
4-4.3　recovery of interblock information in the bibd　152
4-5　problems　154
chapter 5　introduction to factorial designs　160
5-1　basic definitions and principles　160
5-2　the advantage of factorials　163
5-3　the two-factor factorial design　164
5-3.1　an example　164
5-3.2　statistical analysis of the fixed effects model　167
5-3.3　model adequacy checking　172
5-3.4　estimating the model parameters　175
5-3.5　choice of sample size　177
5-3.6　the assumption of no interaction in a two-factor model　178
5-3.7　one observation per cell　179
5-4　the general factorial design　182
5-5　fitting response curves and surfaces　188
5-6　blocking in a factorial design　193
5-7　problems　197
chapter 6　the 2k factorial design　203
6-1　introduction　203
6-2　the 22 design　204
6-3　the 23 design　211
6-4　the general 2k design　224
6-5　a single replicate of the 2k design　226
6-6　the addition of center points to the 2k design　247
6-7　why we work with coded design variables　251
6-8　problems　254
chapter 7　blocking and confounding in the 2k factorial design　265
7-1　introduction　265
7-2　blocking a replicated 2k factorial design　266
7-3　confounding in the 2k factorial design　266
7-4　confounding the 2k factorial design in two blocks　267
7-5　another illustration of why blocking is important　273
7-6　confounding the 2k factorial design in four blocks　275
7-7　confounding the 2k factorial design in 2p blocks　276
7-8　partial confounding　278
7-9　problems　280
chapter 8　two-level fractional factorial designs　282
8-1　introduction　282
8-2　the one-half fraction of the 2k design　283
8-2.1　definitions and basic principles　283
8-2.2　design resolution　285
8-2.3　construction and analysis of the one-half fraction　286
8-3　the one-quarter fraction of the 2k design　296
8-4　the general 2k2p fractional factorial design　303
8-4.1　choosing a design　303
8-4.2　analysis of 2k2p fractional factorials　306
8-4.3　blocking fractional factorials　307
8-5　resolution iii designs　312
8-5.1　constructing resolution iii designs　312
8-5.2　fold over of resolution iii fractions to separate aliased effects　314
8-5.3　plackettdburman designs　319
8-6　resolution iv and v designs　322
8-6.1　resolution iv designs　322
8-6.2　sequential experimentation with resolution iv designs　325
8-6.3　resolution v designs　331
8-7　supersaturated designs　333
8-8　summary　335
8-9　problems..　335
chapter 9　three-level and mixed-level factorial and fractional factorial designs　347
9-1　the 3k factorial design　347
9-1.1　notation and motivation for the 3k design　347
9-1.2　the 32 design　349
9-1.3　the 33 design　351
9-1.4　the general 3k design　355
9-2　confounding in the 3k factorial design　356
9-2.1　the 3k factorial design in three blocks　356
9-2.2　the 3k factorial design in nine blocks　360
9-2.3　the 3k factorial design in 3p blocks　360
9-3　fractional replication of the 3k factorial design　361
9-3.1　the one-third fraction of the 3k factorial design　361
9-3.2　other 3k2p fractional factorial designs　364
9-4　factorials with mixed levels　365
9-4.1　factors at two and three levels　366
9-4.2　factors at two and four levels　367
9-5　problems　369
chapter 10　fitting regression models　373
10-1　introduction 　373
10-2　linear regression models　374
10-3　estimation of the parameters in linear regression models　375
10-4　hypothesis testing in multiple regression　388
10-4.1　test for significance of regression　388
10-4.2　tests on individual regression coefficients and groups of coefficients　390
10-5　confidence intervals in multiple regression　393
10-5.1　confidence intervals on the individual regression coefficients　393
10-5.2　confidence interval on the mean response　394
10-6　prediction of new response observations　394
10-7　regression model diagnostics　396
10-7.1　scaled residuals and press　396
10-7.2　influence diagnostics　399
10-8　testing for lack of fit　400
10-9　problems　401
chapter 11　response surface methods and designs　405
11-1　introduction to response surface methodology　405
11-2　the method of steepest ascent　407
11-3　analysis of a second-order response surface　413
11-3.1　location of the stationary point　413
11-3.2　characterizing the response surface　415
11-3.3　ridge systems　422
11-3.4　multiple responses　423
11-4　experimental designs for fitting response surfaces　427
11-4.1　designs for fitting the first-order model　428
11-4.2　designs for fitting the second-order model　428
11-4.3　blocking in response surface designs　436
11-4.4　computer-generated (optimal) designs　439
11-5　mixture experiments　444
11-6　evolutionary operation　452
11-7　problems　458
chapter 12　robust parameter design and process robustness studies　464
12-1　introduction　464
12-2　crossed array designs　466
12-3　analysis of the crossed array design　468
12-4　combined array designs and the response model approach　471
12-5　choice of designs　477
12-6　problems　480
chapter 13　experiments with random factors　484
13-1　the random effects model　485
13-2　the two-factor factorial with random factors　490
13-3　the two-factor mixed model　495
13-4　sample size determination with random effects　500
13-5　rules for expected mean squares　501
13-6　approximate f tests　505
13-7　some additional topics on estimation of variance components　511
13-7.1　approximate confidence intervals on variance components　511
13-7.2　the modified large-sample method　514
13-7.3　maximum likelihood estimation of variance components　516
13-8　problems　521
chapter 14　nested and split-plot designs　525
14-1　the two-stage nested design　525
14-1.1　statistical analysis　526
14-1.2　diagnostic checking　531
14-1.3　variance components　532
14-1.4　staggered nested designs　533
14-2　the general m-stage nested design　534
14-3　designs with both nested and factorial factors　536
14-4　the split-plot design　540
14-5　other variations of the split-plot design　545
14-5.1　split-plot designs with more than two factors　545
14-5.2　the split-split-plot design　550
14-5.3　the strip-split-plot design　552
14-6　problems　554
chapter 15　other design and analysis topics　559
15-1　nonnormal responses and transformations　560
15-1.1　selecting a transformation: the boxdcox method　560
15-1.2　the generalized linear model　563
15-2　unbalanced data in a factorial design　570
15-2.1　proportional data: an easy case　571
15-2.2　approximate methods　572
15-2.3　the exact method　574
15-3　the analysis of covariance　574
15-3.1　description of the procedure　576
15-3.2　computer solution　583
15-3.3　development by the general regression significance test　584
15-3.4　factorial experiments with covariates　586
15d4　repeated measures　590
15-5　problems　592
bibliography　595
appendix　603
table i.　cumulative standard normal distribution　604
table ii.　percentage points of the t distribution　606
table iii.　percentage points of the x2 distribution　607
table iv.　percentage points of the f distribution　608
table v.　operating characteristic curves for the fixed effects model analysis of variance　613
table vi.　operating characteristic curves for the random effects model analysis of variance　617
table vii.　percentage points of the studentized range statistic　621
table viii.　critical values for dunnett's test for comparing treatments with a control　623
table ix.　coefficients of orthogonal polynomials　625
table x.　alias relationships for 2k-p fractional factorial designs with k≤15 and n≤64　626
index　...638

.　　For the sixth edition I have prepared supplemental text material for each chapter of the book. Often, this supplemental material elaborates on topics that could not be discussed in greater detail in the book. I have also presented some subjects that do not appear directly in the book, but an introduction to them could prove useful to some students and professional practitioners. Some of this material is at a higher mathematical level than the text. I realize that instructors use this book with a wide array of audiences, and some more advanced design courses could possibly benefit from including several of the supplemental text material topics. This material is in electronic form on the World Wide Website for this book, located at www. wiley.com/college/montgomery.
　　WEBSITE
　　Current supporting material for instructors and students is available at the website www. wiley.com/college/montgomery. This site will be used to communicate information about innovations and recommendations for effectively using this text. The supplemental text material described above is available at the site, along with electronic versions of data sets used for examples and homework problems, a course syllabus, and some representative student term projects from the course at Arizona State University.
　　Student Companion Site
　　The student's section of the textbook website contains the following:
　　1. The supplemental text material described above
　　2. Data sets from the book examples and homework problems, in electronic form
　　3. Sample Student Projects
　　Instructor Companion Site
　　The instructor's section of the textbook website contains the following:
　　4. Solutions to the text problems
　　5. The supplemental text material described above
　　6. PowerPoint lecture slides
　　7. Figures from the text in electronic format, for easy inclusion in lecture slides
　　8. Data sets from the book examples and homework problems, in electronic form
　　9. Sample Syllabus
　　10. Sample Student Projects
　　The instructor's section is for instructor use only, and is password-protected. Visit the Instructor Companion Site portion of the website, located at www. wiley, com/college/montgomery, to register for a password.
　　Student Solutions Manual
　　The purpose of the Student Solutions Manual is to provide the student with an in-depth understanding of how to apply the concepts presented in the Design and Analysis of Experiments, 6th Edition, by Douglas C. Montgomery. Along with detailed instructions on how to solve the selected chapter exercises, insights from practical applications are also shared.
　　Solutions have been provided for problems selected by the author of the text, Douglas C. Montgomery. Occasionally a group of "continued exercises" is presented and provides the student with a full solution for a specific data set. Problems that are included in the Student Solutions Manual are indicated by an icon appearing in the text margin next to the problem statement.
　　This is an excellent study aid that many text users will find extremely helpful. The Student Solutions Manual may be ordered in a set with the text, or purchased separately. Contact your local Wiley representative to request the set for your bookstore, or purchase the Student Solutions Manual from the Wiley website.
　　ACKNOWLEDGMENTS
　　I express my appreciation to the many students, instructors, and colleagues who have used the four earlier editions of this book and who have made helpful suggestions for its revision. The contributions of Dr. Raymond H. Myers, Dr. G. Geoffrey Vining, Dr. Dennis Lin, Dr. John Ramberg, Dr. Joseph Pignatiello, Dr. Lloyd S. Nelson, Dr. Andre Khuri, Dr. Peter Nelson, Dr. John A. Cornell, Dr. George C. Runger, Dr. Bert Keats, Dr. Dwayne Rollier, Dr. Norma Hubele, Dr. Murat Kulahci, Dr. Cynthia Lowry, Dr. Russell G. Heikes, Dr. Harrison M, Wadsworth, Dr. William W. Hines, Dr. Arvind Shah, Dr. Jane Ammons, Dr. Diane Schaub, Mr. Mark Anderson, Mr. Pat Whitcomb, Dr. Pat Spagon, and Dr. William DuMouche were particularly valuable. My Department Chair, Dr. Gary Hogg, has provided an intellectually stimulating environment in which to work.
　　The contributions of the professional practitioners with whom I have worked have been invaluable. It is impossible to mention everyone, but some of the major contributors include Dr. Dan McCarville of Mindspeed Corporation, Dr. Lisa Custer of the George Group; Dr. Richard Post of Intel; Mr. Tom Bingham, Mr. Dick Vaughn, Dr. Julian Anderson, Mr. Richard Alkire, and Mr. Chase Neilson of the Boeing Company; Mr. Mike Goza, Mr. Don Walton, Ms. Karen Madison, Mr. Jeff Stevens, and Mr. Bob Kohm of Alcoa; Dr. Jay Gardiner, Mr. John Butora, Mr. Dana Lesher, Mr. Lolly Marwah, Mr. Leon Mason of IBM; Dr. Paul Tobias of Somatech; Ms. Elizabeth A. Peck of The Coca-Cola Company; Dr. Sadri Khalessi and Mr. Franz Wagner of Signetics; Mr. Robert V. Baxley of Monsanto Chemicals; Mr. Harry Peterson-Nedry and Dr. Russell Boyles of Precision Castparts Corporation; Mr. Bill New and Mr. Randy Schmid of Allied-Signal Aerospace; Mr. John M. Fluke, Jr, of the John Fluke Manufacturing Company; Mr. Larry Newton and Mr. Kip Howlett of Georgia-Pacific; and Dr. Ernesto Ramos of BBN Software Products Corporation.
　　I am indebted to Professor E. S. Pearson and the Biometrika Trustees, John Wiley & Sons, Prentice Hall, The American Statistical Association, The Institute of Mathematical Statistics, and the editors of Biometrics for permission to use copyrighted material. Dr. Lisa Custer did an excellent job of preparing the solutions that appear in the Instructor's Solutions Manual, and Dr. Cheryl Jennings and Dr. Sarah Streett provided effective and very helpful proofreading assistance. I am grateful to the Office of Naval Research, the National Science Foundation, the member companies of the NSF/Industry/University Cooperative Research Center in Quality and Reliability Engineering at Arizona State University, and the IBM Corporation for supporting much of my research in engineering statistics and experimental design. ...
　　Douglas C. Montgomery
　　Tempe, Arizona