Design and Analysis of Experiments, 6th Edition

by Douglas C. Montgomery (Arizona State University)

• ISBN13: 9780471487357
• ISBN10: 047148735X
• Edition: 6th
• Format: Hardcover
• Copyright: 2004-12-01
• Publisher: WILEY

Summary

Now in its 6th edition, this bestselling professional reference has helped over 100,000 engineers and scientists with the success of their experiments. Douglas Montgomery arms readers with the most effective approach for learning how to design, conduct, and analyze experiments that optimize performance in products and processes. He shows how to use statistically designed experiments to obtain information for characterization and optimization of systems, improve manufacturing processes, and design and develop new processes and products. You will also learn how to evaluate material alternatives in product design, improve the field performance, reliability, and manufacturing aspects of products, and conduct experiments effectively and efficiently. Discover how to improve the quality and efficiency of working systems with this highly-acclaimed book. This 6th Edition: Places a strong focus on the use of the computer, providing output from two software products: Minitab and DesignExpert. Presents timely, new examples as well as expanded coverage on adding runs to a fractional factorial to de-alias effects. Includes detailed discussions on how computers are currently used in the analysis and design of experiments. Offers new material on a number of important topics, including follow-up experimentation and split-plot design. Focuses even more sharply on factorial and fractional factorial design.

Author Biography

Douglas C. Montgomery Professor of Engineering and Statistics at Arizona State University, received his B.S., M.S., and Ph.D. degrees from Virginia Polytechnic Institute, all in engineering, from 1969 to 1984 he was a faculty member of the School of Industrial & Systems Engineering at the Georgia Institute of Technology; from 1984 to 1988 he was at the University of Washington, where he held the John M. Fluke Distinguished chair of Manufacturing Engineering, was Professor of Mechanical Engineering, and Director of the Program in industrial Engineering.

Dr. Montgomery has research and teaching interests in industrial statistics including statistical quality control techniques, design of experiments, regression analysis and empirical model building, and the application of operations research methodology to problems in manufacturing systems. He has authored and coauthored many technical papers in these fields and is an author of twelve other books. Dr. Montgomery is a Fellow of the American Society for Quality, a Fellow of the American Statistical Association, a Fellow of the Royal Statistical Society, a Fellow of the Institute of Industrial Engineers, and an Elected member of the International Statistical Institute. He is a Stewart Medallist of the American Society for Quality, and has also received the Brumbaugh Award, the William G. Hunter Award, and the Shewell Award(twice) from the ASQ. He is a recipient of the Ellis R. Ott Award. He is a former editor of the Journal of Quality Technology, the current editor of Quality and Reliability Engineering International, and serves on the editorial boards of several journals.

Table of Contents

Chapter 1 Introduction	1	(22)
1-1 Strategy of Experimentation	1	(7)
1-2 Some Typical Applications of Experimental Design	8	(4)
1-3 Basic Principles	12	(2)
1-4 Guidelines for Designing Experiments	14	(5)
1-5 A Brief History of Statistical Design	19	(2)
1-6 Summary: Using Statistical Techniques in Experimentation	21	(1)
1-7 Problems	22	(1)
Chapter 2 Simple Comparative Experiments	23	(37)
2-1 Introduction	23	(1)
2-2 Basic Statistical Concepts	24	(4)
2-3 Sampling and Sampling Distributions	28	(6)
2-4 Inferences about the Differences in Means, Randomized Designs	34	(14)
2-4.1 Hypothesis Testing	34	(7)
2-4.2 Choice of Sample Size	41	(2)
2-4.3 Confidence Intervals	43	(2)
2-4.4 The Case Where σ²1 not equal σ²2	45	(1)
2-4.5 The Case Where σ²1 and σ²2 Are Known	45	(1)
2-4.6 Comparing a Single Mean to a Specified Value	46	(1)
2-4.7 Summary	47	(1)
2-5 Inferences about the Differences in Means, Paired Comparison Designs	48	(4)
2-5.1 The Paired Comparison Problem	48	(3)
2-5.2 Advantages of the Paired Comparison Design	51	(1)
2-6 Inferences about the Variances of Normal Distributions	52	(2)
2-7 Problems	54	(6)
Chapter 3 Experiments with a Single Factor: The Analysis of Variance	60	(59)
3-1 An Example	61	(2)
3-2 The Analysis of Variance	63	(2)
3-3 Analysis of the Fixed Effects Model	65	(10)
3-3.1 Decomposition of the Total Sum of Squares	66	(2)
3-3.2 Statistical Analysis	68	(5)
3-3.3 Estimation of the Model Parameters	73	(2)
3-3.4 Unbalanced Data	75	(1)
3-4 Model Adequacy Checking	75	(10)
3-4.1 The Normality Assumption	76	(2)
3-4.2 Plot of Residuals in Time Sequence	78	(1)
3-4.3 Plot of Residuals Versus Fitted Values	79	(5)
3-4.4 Plots of Residuals Versus Other Variables	84	(1)
3-5 Practical Interpretation of Results	85	(13)
3-5.1 A Regression Model	85	(2)
3-5.2 Comparisons Among Treatment Means	87	(1)
3-5.3 Graphical Comparisons of Means	87	(1)
3-5.4 Contrasts	88	(3)
3-5.5 Orthogonal Contrasts	91	(2)
3-5.6 Scheffe's Method for Comparing All Contrasts	93	(1)
3-5.7 Comparing Pairs of Treatment Means	94	(3)
3-5.8 Comparing Treatment Means with a Control	97	(1)
3-6 Sample Computer Output	98	(3)
3-7 Determining Sample Size	101	(4)
3-7.1 Operating Characteristic Curves	101	(3)
3-7.2 Specifying a Standard Deviation Increase	104	(1)
3-7.3 Confidence Interval Estimation Method	104	(1)
3-8 Discovering Dispersion Effects	105	(2)
3-9 The Regression Approach to the Analysis of Variance	107	(3)
3-9.1 Least Squares Estimation of the Model Parameters	107	(1)
3-9.2 The General Regression Significance Test	108	(2)
3-10 Nonparametric Methods in the Analysis of Variance	110	(2)
3-10.1 The Kruskal-Wallis Test	110	(2)
3-10.2 General Comments on the Rank Transformation	112	(1)
3-11 Problems	112	(7)
Chapter 4 Randomized Blocks, Latin Squares, and Related Designs	119	(41)
4-1 The Randomized Complete Block Design	119	(17)
4-1.1 Statistical Analysis of the RCBD	121	(7)
4-1.2 Model Adequacy Checking	128	(2)
4-1.3 Some Other Aspects of the Randomized Complete Block Design	130	(3)
4-1.4 Estimating Model Parameters and the General Regression Significance Test	133	(3)
4-2 The Latin Square Design	136	(6)
4-3 The Graeco-Latin Square Design	142	(3)
4-4 Balanced Incomplete Block Designs	145	(9)
4-4.1 Statistical Analysis of the BIBD	146	(4)
4-4.2 Least Squares Estimation of the Parameters	150	(2)
4-4.3 Recovery of Interblock Information in the BIBD	152	(2)
4-5 Problems	154	(6)
Chapter 5 Introduction to Factorial Designs	160	(43)
5-1 Basic Definitions and Principles	160	(3)
5-2 The Advantage of Factorials	163	(1)
5-3 The Two-Factor Factorial Design	164	(18)
5-3.1 An Example	164	(3)
5-3.2 Statistical Analysis of the Fixed Effects Model	167	(5)
5-3.3 Model Adequacy Checking	172	(3)
5-3.4 Estimating the Model Parameters	175	(2)
5-3.5 Choice of Sample Size	177	(1)
5-3.6 The Assumption of No Interaction in a Two-Factor Model	178	(1)
5-3.7 One Observation per Cell	179	(3)
5-4 The General Factorial Design	182	(6)
5-5 Fitting Response Curves and Surfaces	188	(5)
5-6 Blocking in a Factorial Design	193	(4)
5-7 Problems	197	(6)
Chapter 6 The 2kappa Factorial Design	203	(62)
6-1 Introduction	203	(1)
6-2 The 2² Design	204	(7)
6-3 The 2³ Design	211	(13)
6-4 The General 2kappa Design	224	(2)
6-5 A Single Replicate of the 2kappa Design	226	(21)
6-6 The Addition of Center Points to the 2kappa Design	247	(4)
6-7 Why We Work with Coded Design Variables	251	(3)
6-8 Problems	254	(11)
Chapter 7 Blocking and Confounding in the 2kappa Factorial Design	265	(17)
7-1 Introduction	265	(1)
7-2 Blocking a Replicated 2kappa Factorial Design	266	(1)
7-3 Confounding in the 2kappa Factorial Design	266	(1)
7-4 Confounding the 2kappa Factorial Design in Two Blocks	267	(6)
7-5 Another Illustration of Why Blocking Is Important	273	(2)
7-6 Confounding the 2kappa Factorial Design in Four Blocks	275	(1)
7-7 Confounding the 2kappa Factorial Design in 2ρ Blocks	276	(2)
7-8 Partial Confounding	278	(2)
7-9 Problems	280	(2)
Chapter 8 Two-Level Fractional Factorial Designs	282	(65)
8-1 Introduction	282	(1)
8-2 The One-Half Fraction of the 2kappa Design	283	(13)
8-2.1 Definitions and Basic Principles	283	(2)
8-2.2 Design Resolution	285	(1)
8-2.3 Construct ion and Analysis of the One-Half Fraction	286	(10)
8-3 The One-Quarter Fraction of the 2kappa Design	296	(7)
8-4 The General 2kappa-ρ Fractional Factorial Design	303	(9)
8-4.1 Choosing a Design	303	(3)
8-4.2 Analysis of 2kappa-ρ Fractional Factorials	306	(1)
8-4.3 Blocking Fractional Factorials	307	(5)
8-5 Resolution III Designs	312	(10)
8-5.1 Constructing Resolution III Designs	312	(2)
8-5.2 Fold Over of Resolution III Fractions to Separate Aliased Effects	314	(5)
8-5.3 Plackett-Burman Designs	319	(3)
8-6 Resolution IV and V Designs	322	(11)
8-6.1 Resolution IV Designs	322	(3)
8-6.2 Sequential Experimentation with Resolution IV Designs	325	(6)
8-6.3 Resolution V Designs	331	(2)
8-7 Supersaturated Designs	333	(2)
8-8 Summary	335	(1)
8-9 Problems	335	(12)
Chapter 9 Three-Level and Mixed-Level Factorial and Fractional Factorial Designs	347	(26)
9-1 The 3kappa Factorial Design	347	(9)
9-1.1 Notation and Motivation for the 3kappa Design	347	(2)
9-1.2 The 3² Design	349	(2)
9-1.3 The 3² Design	351	(4)
9-1.4 The General 3kappa Design	355	(1)
9-2 Confounding in the 3kappa Factorial Design	356	(5)
9-2.1 The 3k Factorial Design in Three Blocks	356	(4)
9-2.2 The 3k Factorial Design in Nine Blocks	360	(1)
9-2.3 The 3k Factorial Design in 3ρ Blocks	360	(1)
9-3 Fractional Replication of the 3kappa Factorial Design	361	(4)
9-3.1 The One-Third Fraction of the 3kappa Factorial Design	361	(3)
9-3.2 Other 3kappa-ρ Fractional Factorial Designs	364	(1)
9-4 Factorials with Mixed Levels	365	(4)
9-4.1 Factors at Two and Three Levels	366	(1)
9-4.2 Factors at Two and Four Levels	367	(2)
9-5 Problems	369	(4)
Chapter 10 Fitting Regression Models	373	(32)
10-1 Introduction	373	(1)
10-2 Linear Regression Models	374	(1)
10-3 Estimation of the Parameters in Linear Regression Models	375	(13)
10-4 Hypothesis Testing in Multiple Regression	388	(5)
10-4.1 Test for Significance of Regression	388	(2)
10-4.2 Tests on Individual Regression Coefficients and Groups of Coefficients	390	(3)
10-5 Confidence Intervals in Multiple Regression	393	(1)
10-5.1 Confidence Intervals on the Individual Regression Coefficients	393	(1)
10-5.2 Confidence Interval on the Mean Response	394	(1)
10-6 Prediction of New Response Observations	394	(2)
10-7 Regression Model Diagnostics	396	(4)
10-7.1 Scaled Residuals and PRESS	396	(3)
10-7.2 Influence Diagnostics	399	(1)
10-8 Testing for Lack of Fit	400	(1)
10-9 Problems	401	(4)
Chapter 11 Response Surface Methods and Designs	405	(59)
11-1 Introduction to Response Surface Methodology	405	(2)
11-2 The Method of Steepest Ascent	407	(6)
11-3 Analysis of a Second-Order Response Surface	413	(14)
11-3.1 Location of the Stationary Point	413	(2)
11-3.2 Characterizing the Response Surface	415	(7)
11-3.3 Ridge Systems	422	(1)
11-3.4 Multiple Responses	423	(4)
11-4 Experimental Designs for Fitting Response Surfaces	427	(17)
11-4.1 Designs for Fitting the First-Order Model	428	(1)
11-4.2 Designs for Fitting the Second-Order Model	428	(8)
11-4.3 Blocking in Response Surface Designs	436	(3)
11-4.4 Computer-Generated (Optimal) Designs	439	(5)
11-5 Mixture Experiments	444	(8)
11-6 Evolutionary Operation	452	(6)
11-7 Problems	458	(6)
Chapter 12 Robust Parameter Design and Process Robustness Studies	464	(20)
12-1 Introduction	464	(2)
12-2 Crossed Array Designs	466	(2)
12-3 Analysis of the Crossed Array Design	468	(3)
12-4 Combined Array Designs and the Response Model Approach	471	(6)
12-5 Choice of Designs	477	(3)
12-6 Problems	480	(4)
Chapter 13 Experiments with Random Factors	484	(41)
13-1 The Random Effects Model	485	(5)
13-2 The Two-Factor Factorial with Random Factors	490	(5)
13-3 The Two-Factor Mixed Model	495	(5)
13-4 Sample Size Determination with Random Effects	500	(1)
13-5 Rules for Expected Mean Squares	501	(4)
13-6 Approximate F Tests	505	(6)
13-7 Some Additional Topics on Estimation of Variance Components	511	(10)
13-7.1 Approximate Confidence Intervals on Variance Components	511	(3)
13-7.2 The Modified Large-Sample Method	514	(2)
13-7.3 Maximum Likelihood Estimation of Variance Components	516	(5)
13-8 Problems	521	(4)
Chapter 14 Nested and Split-Plot Designs	525	(34)
14-1 The Two-Stage Nested Design	525	(9)
14-1.1 Statistical Analysis	526	(5)
14-1.2 Diagnostic Checking	531	(1)
14-1.3 Variance Components	532	(1)
14-1.4 Staggered Nested Designs	533	(1)
14-2 The General m-Stage Nested Design	534	(2)
14-3 Designs with Both Nested and Factorial Factors	536	(4)
14-4 The Split-Plot Design	540	(5)
14-5 Other Variations of the Split-Plot Design	545	(9)
14-5.1 Split-Plot Designs with More Than Two Factors	545	(5)
14-5.2 The Split-Split-Plot Design	550	(2)
14-5.3 The Strip-Split-Plot Design	552	(2)
14-6 Problems	554	(5)
Chapter 15 Other Design and Analysis Topics	559	(36)
15-1 Nonnormal Responses and Transformations	560	(10)
15-1.1 Selecting a Transformation: The Box-Cox Method	560	(3)
15-1.2 The Generalized Linear Model	563	(7)
15-2 Unbalanced Data in a Factorial Design	570	(4)
15-2.1 Proportional Data: An Easy Case	571	(1)
15-2.2 Approximate Methods	572	(2)
15-2.3 The Exact Method	574	(1)
15-3 The Analysis of Covariance	574	(16)
15-3.1 Description of the Procedure	576	(7)
15-3.2 Computer Solution	583	(1)
15-3.3 Development by the General Regression Significance Test	584	(2)
15-3.4 Factorial Experiments with Covariates	586	(4)
15-4 Repeated Measures	590	(2)
15-5 Problems	592	(3)
Bibliography	595	(8)
Appendix	603	(35)
Table I. Cumulative Standard Normal Distribution	604	(2)
Table II. Percentage Points of the τ Distribution	606	(1)
Table III. Percentage Points of the χ² Distribution	607	(1)
Table IV Percentage Points of the F Distribution	608	(5)
Table V. Operating Characteristic Curves for the Fixed Effects Model Analysis of Variance	613	(4)
Table VI. Operating Characteristic Curves for the Random Effects Model Analysis of Variance	617	(4)
Table VII. Percentage Points of the Studentized Range Statistic	621	(2)
Table VIII. Critical Values for Dunnett's Test for Comparing Treatments with a Control	623	(2)
Table IX. Coefficients of Orthogonal Polynomials	625	(13)
Table X. Alias Relationships for 2kappa-ρ Fractional Factorial Designs with k less than equal to 15 and n less than equal to 64 626
Index	638