Design and Analysis of Experiments, Volume 2 Advanced Experimental Design

by Hinkelmann, Klaus; Kempthorne, Oscar

• ISBN13: 9780471551775
• ISBN10: 0471551775
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-04-28
• Publisher: Wiley-Interscience

Summary

The development and introduction of new experimental designs in the last fifty years has been quite staggering, brought about largely by an ever-widening field of applications. Design and Analysis of Experiments, Volume 2: Advanced Experimental Design is the second of a two-volume body of work that builds upon the philosophical foundations of experimental design set forth by Oscar Kempthorne half a century ago and updates it with the latest developments in the field. Designed for advanced-level graduate students and industry professionals, this text includes coverage of incomplete block and row-column designs; symmetrical, asymmetrical, and fractional factorial designs; main effect plans and their construction; supersaturated designs; robust design, or Taguchi experiments; lattice designs; and cross-over designs.

Author Biography

KLAUS HINKELMANN, PHD, is Emeritus Professor of Statistics at Virginia Polytechnic Institute and State University Department of Statistics, where he also served as both graduate administrator and department head. In addition to being a Fellow of both the American Statistical Association and the American Association for the Advancement of Science, Professor Hinkelmann is a member of the International Statistical Institute, and has served as a council member of the International Biometric Society. He was editor of Biometrics and the Current Index to Statistics.

OSCAR KEMPTHORNE, SCD, was Emeritus Professor of Statistics and Emeritus Distinguished Professor of Liberal Arts and Sciences at Iowa State University. He was a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the American Association for the Advancement of Science, as well as an Honorary Fellow of the Royal Statistical Society and a member of the International Statistical Institute. In addition, Dr. Kempthorne was a past president of the Eastern North American Region (ENAR) of the International Biometric Society, a former chairman of statistics within the American Association for the Advancement of Science, and a past president of the Institute of Mathematical Statistics.

Table of Contents

Preface	xix
1 General Incomplete Block Design	1	(70)
1.1 Introduction and Examples,	1	(2)
1.2 General Remarks on the Analysis of Incomplete Block Designs,	3	(1)
1.3 The Intrablock Analysis,	4	(9)
1.3.1 Notation and Model,	4	(1)
1.3.2 Normal and Reduced Normal Equations,	5	(2)
1.3.3 The C Matrix and Estimable Functions,	7	(1)
1.3.4 Solving the Reduced Normal Equations,	8	(2)
1.3.5 Estimable Functions of Treatment Effects,	10	(2)
1.3.6 Analyses of Variance,	12	(1)
1.4 Incomplete Designs with Variable Block Size,	13	(1)
1.5 Disconnected Incomplete Block Designs,	14	(2)
1.6 Randomization Analysis,	16	(7)
1.6.1 Derived Linear Model,	16	(2)
1.6.2 Randomization Analysis of ANOVA Tables,	18	(5)
1.7 Interblock Information in an Incomplete Block Design,	23	(4)
1.7.1 Introduction and Rationale,	23	(1)
1.7.2 Interblock Normal Equations,	23	(4)
1.7.3 Nonavailability of Interblock Information,	27	(1)
1.8 Combined Intra- and Interblock Analysis,	27	(4)
1.8.1 Combining Intra- and Interblock Information,	27	(1)
1.8.2 Linear Model,	27	(1)
1.8.3 Normal Equations,	28	(3)
1.8.4 Some Special Cases,	31	(1)
1.9 Relationships Among Intrablock, Interblock, and Combined Estimation,	31	(5)
1.9.1 General Case,	32	(2)
1.9.2 Case of Proper, Equireplicate Designs,	34	(2)
1.10 Estimation of Weights for the Combined Analysis,	36	(3)
1.10.1 Yates Procedure,	37	(1)
1.10.2 Properties of Combined Estimators,	38	(1)
1.11 Maximum-Likelihood Type Estimation,	39	(4)
1.11.1 Maximum-Likelihood Estimation,	39	(1)
1.11.2 Restricted Maximum-Likelihood Estimation,	40	(3)
1.12 Efficiency Factor of an Incomplete Block Design,	43	(5)
1.12.1 Average Variance for Treatment Comparisons for an IBD,	43	(2)
1.12.2 Definition of Efficiency Factor,	45	(2)
1.12.3 Upper Bound for the Efficiency Factor,	47	(1)
1.13 Optimal Designs,	48	(4)
1.13.1 Information Function,	48	(1)
1.13.2 Optimality Criteria,	49	(1)
1.13.3 Optimal Symmetric Designs,	50	(1)
1.13.4 Optimality and Research,	50	(2)
1.14 Computational Procedures,	52	(19)
1.14.1 Intrablock Analysis Using SAS PROC GLM,	52	(6)
1.14.2 Intrablock Analysis Using the Absorb Option in SAS PROC GLM,	58	(3)
1.14.3 Combined Intra- and Interblock Analysis Using the Yates Procedure,	61	(2)
1.14.4 Combined Intra- and Interblock Analysis Using SAS PROC MIXED,	63	(1)
1.14.5 Comparison of Estimation Procedures,	63	(3)
1.14.6 Testing of Hypotheses,	66	(5)
2 Balanced Incomplete Block Designs	71	(33)
2.1 Introduction,	71	(1)
2.2 Definition of the BIB Design,	71	(1)
2.3 Properties of BIB Designs,	72	(2)
2.4 Analysis of BIB Designs,	74	(3)
2.4.1 Intrablock Analysis,	74	(2)
2.4.2 Combined Analysis,	76	(1)
2.5 Estimation of ρ,	77	(2)
2.6 Significance Tests,	79	(10)
2.7 Some Special Arrangements,	89	(9)
2.7.1 Replication Groups Across Blocks,	89	(2)
2.7.2 Grouped Blocks,	91	(5)
2.7.3 α-Resolvable BIB Designs with Replication Groups Across Blocks,	96	(2)
2.8 Resistant and Susceptible BIB Designs,	98	(6)
2.8.1 Variance-Balanced Designs,	98	(1)
2.8.2 Definition of Resistant Designs,	99	(1)
2.8.3 Characterization of Resistant Designs,	100	(3)
2.8.4 Robustness and Connectedness,	103	(1)
3 Construction of Balanced Incomplete Block Designs	104	(15)
3.1 Introduction,	104	(1)
3.2 Difference Methods,	104	(9)
3.2.1 Cyclic Development of Difference Sets,	104	(3)
3.2.2 Method of Symmetrically Repeated Differences,	107	(5)
3.2.3 Formulation in Terms of Galois Field Theory,	112	(1)
3.3 Other Methods,	113	(2)
3.3.1 Irreducible BIB Designs,	113	(1)
3.3.2 Complement of BIB Designs,	113	(1)
3.3.3 Residual BIB Designs,	114	(1)
3.3.4 Orthogonal Series,	114	(1)
3.4 Listing of Existing BIB Designs,	115	(4)
4 Partially Balanced Incomplete Block Designs	119	(39)
4.1 Introduction,	119	(1)
4.2 Preliminaries,	119	(4)
4.2.1 Association Scheme,	120	(1)
4.2.2 Association Matrices,	120	(1)
4.2.3 Solving the RNE,	121	(1)
4.2.4 Parameters of the Second Kind,	122	(1)
4.3 Definition and Properties of PBIB Designs,	123	(4)
4.3.1 Definition of PBIB Designs,	123	(2)
4.3.2 Relationships Among Parameters of a PBIB Design,	125	(2)
4.4 Association Schemes and Linear Associative Algebras,	127	(4)
4.4.1 Linear Associative Algebra of Association Matrices,	127	(1)
4.4.2 Linear Associative Algebra of P Matrices,	128	(1)
4.4.3 Applications of the Algebras,	129	(2)
4.5 Analysis of PBIB Designs,	131	(6)
4.5.1 Intrablock Analysis,	131	(3)
4.5.2 Combined Analysis,	134	(3)
4.6 Classification of PBIB Designs,	137	(18)
4.6.1 Group-Divisible (GD) PBIB(2) Designs,	137	(2)
4.6.2 Triangular PBIB(2) Designs,	139	(1)
4.6.3 Latin Square Type PBIB(2) Designs,	140	(1)
4.6.4 Cyclic PBIB(2) Designs,	141	(1)
4.6.5 Rectangular PBIB(3) Designs,	142	(1)
4.6.6 Generalized Group-Divisible (GGD) PBIB(3) Designs,	143	(1)
4.6.7 Generalized Triangular PBIB(3) Designs,	144	(2)
4.6.8 Cubic PBIB(3) Designs,	146	(1)
4.6.9 Extended Group-Divisible (EGD) PBIB Designs,	147	(2)
4.6.10 Hypercubic PBIB Designs,	149	(2)
4.6.11 Right-Angular PBIB(4) Designs,	151	(2)
4.6.12 Cyclic PBIB Designs,	153	(1)
4.6.13 Some Remarks,	154	(1)
4.7 Estimation of ρ for PBIB(2) Designs,	155	(3)
4.7.1 Shah Estimator,	155	(1)
4.7.2 Application to PBIB(2) Designs,	156	(2)
5 Construction of Partially Balanced Incomplete Block Designs	158	(31)
5.1 Group-Divisible PBIB(2) Designs,	158	(7)
5.1.1 Duals of BIB Designs,	158	(2)
5.1.2 Method of Differences,	160	(2)
5.1.3 Finite Geometries,	162	(2)
5.1.4 Orthogonal Arrays,	164	(1)
5.2 Construction of Other PBIB(2) Designs,	165	(2)
5.2.1 Triangular PBIB(2) Designs,	165	(1)
5.2.2 Latin Square PBIB(2) Designs,	166	(1)
5.3 Cyclic PBIB Designs,	167	(5)
5.3.1 Construction of Cyclic Designs,	167	(2)
5.3.2 Analysis of Cyclic Designs,	169	(3)
5.4 Kronecker Product Designs,	172	(6)
5.4.1 Definition of Kronecker Product Designs,	172	(1)
5.4.2 Properties of Kronecker Product Designs,	172	(5)
5.4.3 Usefulness of Kronecker Product Designs,	177	(1)
5.5 Extended Group-Divisible PBIB Designs,	178	(9)
5.5.1 EGD-PBIB Designs as Kronecker Product Designs,	178	(1)
5.5.2 Method of Balanced Arrays,	178	(2)
5.5.3 Direct Method,	180	(5)
5.5.4 Generalization of the Direct Method,	185	(2)
5.6 Hypercubic PBIB Designs,	187	(2)
6 More Block Designs and Blocking Structures	189	(52)
6.1 Introduction,	189	(1)
6.2 Alpha Designs,	190	(3)
6.2.1 Construction Method,	190	(2)
6.2.2 Available Software,	192	(1)
6.2.3 Alpha Designs with Unequal Block Sizes,	192	(1)
6.3 Generalized Cyclic Incomplete Block Designs,	193	(1)
6.4 Designs Based on the Successive Diagonalizing Method,	194	(1)
6.4.1 Designs for t = Kk,	194	(1)
6.4.2 Designs with t = n²,	194	(1)
6.5 Comparing Treatments with a Control,	195	(18)
6.5.1 Supplemented Balance,	196	(1)
6.5.2 Efficiencies and Optimality Criteria,	197	(2)
6.5.3 Balanced Treatment Incomplete Block Designs,	199	(6)
6.5.4 Partially Balanced Treatment Incomplete Block Designs,	205	(6)
6.5.5 Optimal Designs,	211	(2)
6.6 Row-Column Designs,	213	(28)
6.6.1 Introduction,	213	(1)
6.6.2 Model and Normal Equations,	213	(2)
6.6.3 Analysis of Variance,	215	(1)
6.6.4 An Example,	216	(14)
6.6.5 Regular Row-Column Designs,	230	(1)
6.6.6 Doubly Incomplete Row-Column Designs,	230	(2)
6.6.7 Properties of Row-Column Designs,	232	(5)
6.6.8 Construction,	237	(1)
6.6.9 Resolvable Row-Column Designs,	238	(3)
7 Two-Level Factorial Designs	241	(38)
7.1 Introduction,	241	(1)
7.2 Case of Two Factors,	241	(7)
7.2.1 Definition of Main Effects and Interaction,	241	(2)
7.2.2 Orthogonal Contrasts,	243	(1)
7.2.3 Parameterizations of Treatment Responses,	244	(3)
7.2.4 Alternative Representation of Treatment Combinations, Main Effects, and Interaction,	247	(1)
7.3 Case of Three Factors,	248	(5)
7.3.1 Definition of Main Effects and Interactions,	249	(3)
7.3.2 Parameterization of Treatment Responses,	252	(1)
7.3.3 The x-Representation,	252	(1)
7.4 General Case,	253	(7)
7.4.1 Definition of Main Effects and Interactions,	254	(2)
7.4.2 Parameterization of Treatment Responses,	256	(2)
7.4.3 Generalized Interactions,	258	(2)
7.5 Interpretation of Effects and Interactions,	260	(2)
7.6 Analysis of Factorial Experiments,	262	(17)
7.6.1 Linear Models,	262	(1)
7.6.2 Yates Algorithm,	263	(2)
7.6.3 Variances of Estimators,	265	(1)
7.6.4 Analysis of Variance,	265	(2)
7.6.5 Numerical Examples,	267	(11)
7.6.6 Use of Only One Replicate,	278	(1)
8 Confounding in 2n Factorial Designs	279	(33)
8.1 Introduction,	279	(4)
8.1.1 A Simple Example,	279	(1)
8.1.2 Comparison of Information,	280	(1)
8.1.3 Basic Analysis,	280	(3)
8.2 Systems of Confounding,	283	(6)
8.2.1 Blocks of Size 2n-¹,	283	(1)
8.2.2 Blocks of Size 2n-²,	283	(2)
8.2.3 General Case,	285	(4)
8.3 Composition of Blocks for a Particular System of Confounding,	289	(2)
8.3.1 Intrablock Subgroup,	289	(1)
8.3.2 Remaining Blocks,	290	(1)
8.4 Detecting a System of Confounding,	291	(2)
8.5 Using SAS for Constructing Systems of Confounding,	293	(1)
8.6 Analysis of Experiments with Confounding,	293	(10)
8.6.1 Estimation of Effects and Interactions,	293	(4)
8.6.2 Parameterization of Treatment Responses,	297	(1)
8.6.3 ANOVA Tables,	298	(5)
8.7 Interblock Information in Confounded Experiments,	303	(8)
8.8 Numerical Example Using SAS,	311	(1)
9 Partial Confounding in 2n Factorial Designs	312	(47)
9.1 Introduction,	312	(1)
9.2 Simple Case of Partial Confounding,	312	(6)
9.2.1 Basic Plan,	312	(1)
9.2.2 Analysis,	313	(2)
9.2.3 Use of Intra- and Interblock Information,	315	(3)
9.3 Partial Confounding as an Incomplete Block Design,	318	(5)
9.3.1 Two Models,	318	(2)
9.3.2 Normal Equations,	320	(2)
9.3.3 Block Contrasts,	322	(1)
9.4 Efficiency of Partial Confounding,	323	(1)
9.5 Partial Confounding in a 2³ Experiment,	324	(3)
9.5.1 Blocks of Size 2,	324	(1)
9.5.2 Blocks of Size 4,	325	(2)
9.6 Partial Confounding in a 24 Experiment,	327	(2)
9.6.1 Blocks of Size 2,	327	(1)
9.6.2 Blocks of Size 4,	328	(1)
9.6.3 Blocks of Size 8,	328	(1)
9.7 General Case,	329	(6)
9.7.1 Intrablock Information,	330	(1)
9.7.2 The ANOVAs,	330	(2)
9.7.3 Interblock Information,	332	(1)
9.7.4 Combined Intra- and Interblock Information,	333	(1)
9.7.5 Estimation of Weights,	333	(1)
9.7.6 Efficiencies,	334	(1)
9.8 Double Confounding,	335	(1)
9.9 Confounding in Squares,	336	(2)
9.9.1 2³ Factorial in Two 4x4 Squares,	337	(1)
9.9.2 24 Factorial in 8x8 Squares,	338	(1)
9.10 Numerical Examples Using SAS,	338	(21)
9.10.1 2³ Factorial in Blocks of Size 2,	338	(12)
9.10.2 24 Factorial in Blocks of Size 4,	350	(9)
10 Designs with Factors at Three Levels	359	(34)
10.1 Introduction,	359	(1)
10.2 Definition of Main Effects and Interactions,	359	(6)
10.2.1 The 3² Case,	359	(4)
10.2.2 General Case,	363	(2)
10.3 Parameterization in Terms of Main Effects and Interactions,	365	(1)
10.4 Analysis of 3n Experiments,	366	(2)
10.5 Confounding in a 3" Factorial,	368	(6)
10.5.1 The 3³ Experiment in Blocks of Size 3,	369	(1)
10.5.2 Using SAS PROC FACTEX,	370	(4)
10.5.3 General Case,	374	(1)
10.6 Useful Systems of Confounding,	374	(6)
10.6.1 Two Factors,	376	(1)
10.6.2 Three Factors,	376	(1)
10.6.3 Treatment Comparisons,	376	(3)
10.6.4 Four Factors,	379	(1)
10.6.5 Five Factors,	379	(1)
10.6.6 Double Confounding,	379	(1)
10.7 Analysis of Confounded 3n Factorials,	380	(7)
10.7.1 Intrablock Information,	381	(1)
10.7.2 The ANOVAs,	381	(3)
10.7.3 Tests of Hypotheses,	384	(1)
10.7.4 Interblock Information,	385	(1)
10.7.5 Combined Intra- and Interblock Information,	386	(1)
10.7.6 Estimation of Weights,	386	(1)
10.8 Numerical Example,	387	(6)
10.8.1 Intrablock Analysis,	387	(1)
10.8.2 Combined Analysis,	387	(6)
11 General Symmetrical Factorial Design	393	(73)
11.1 Introduction,	393	(2)
11.2 Representation of Effects and Interactions,	395	(1)
11.3 Generalized Interactions,	396	(2)
11.4 Systems of Confounding,	398	(2)
11.5 Intrablock Subgroup,	400	(2)
11.6 Enumerating Systems of Confounding,	402	(1)
11.7 Fisher Plans,	403	(6)
11.7.1 Existence and Construction,	403	(3)
11.7.2 Identifying System of Confounding,	406	(1)
11.7.3 Application to Fisher Plans,	407	(2)
11.8 Symmetrical Factorials and Finite Geometries,	409	(1)
11.9 Parameterization of Treatment Responses,	410	(2)
11.10 Analysis of ρn Factorial Experiments,	412	(9)
11.10.1 Intrablock Analysis,	413	(4)
11.10.2 Disconnected Resolved Incomplete Block Designs,	417	(3)
11.10.3 Analysis of Variance Tables,	420	(1)
11.11 Interblock Analysis,	421	(5)
11.11.1 Combining Interblock Information,	422	(3)
11.11.2 Estimating Confounded Interactions,	425	(1)
11.12 Combined Intra- and Interblock Information,	426	(5)
11.12.1 Combined Estimators,	427	(3)
11.12.2 Variance of Treatment Comparisons,	430	(1)
11.13 The sn Factorial,	431	(16)
11.13.1 Method of Galois Field Theory,	431	(2)
11.13.2 Systems of Confounding,	433	(2)
11.13.3 Method of Pseudofactors,	435	(8)
11.13.4 The (ρ1 x ρ2 x···x ρm)n Factorial,	443	(4)
11.14 General Method of Confounding for the Symmetrical Factorial Experiment,	447	(16)
11.14.1 Factorial Calculus,	448	(4)
11.14.2 Orthogonal Factorial Structure (OFS),	452	(1)
11.14.3 Systems of Confounding with OFS,	453	(4)
11.14.4 Constructing Systems of Confounding,	457	(2)
11.14.5 Verifying Orthogonal Factorial Structure,	459	(3)
11.14.6 Identifying Confounded Interactions,	462	(1)
11.15 Choice of Initial Block,	463	(3)
12 Confounding in Asymmetrical Factorial Designs	466	(41)
12.1 Introduction,	466	(1)
12.2 Combining Symmetrical Systems of Confounding,	467	(10)
12.2.1 Construction of Blocks,	467	(2)
12.2.2 Properties of Kronecker Product Method,	469	(5)
12.2.3 Use of Pseudofactors,	474	(3)
12.3 The GC/n Method,	477	(3)
12.3.1 Description of the Method,	478	(1)
12.3.2 Choice of Generators,	479	(1)
12.3.3 Loss of Degrees of Freedom,	479	(1)
12.4 Method of Finite Rings,	480	(11)
12.4.1 Mathematics of Ideals and Rings,	481	(2)
12.4.2 Treatment Representations,	483	(1)
12.4.3 Representation of Main Effects and Interactions,	483	(2)
12.4.4 Parameterization of Treatment Responses,	485	(3)
12.4.5 Characterization and Properties of the Parameterization,	488	(3)
12.4.6 Other Methods for Constructing Systems of Confounding,	491	(1)
12.5 Balanced Factorial Designs (BFD),	491	(16)
12.5.1 Definitions and Properties of BFDs,	493	(6)
12.5.2 EGD-PBIBs and BFDs,	499	(3)
12.5.3 Construction of BFDs,	502	(5)
13 Fractional Factorial Designs	507	(57)
13.1 Introduction,	507	(2)
13.2 Simple Example of Fractional Replication,	509	(4)
13.3 Fractional Replicates for 2n Factorial Designs,	513	(11)
13.3.1 The ½e Fraction,	513	(3)
13.3.2 Resolution of Fractional Factorials,	516	(2)
13.3.3 Word Length Pattern,	518	(1)
13.3.4 Criteria for Design Selection,	518	(6)
13.4 Fractional Replicates for 3n Factorial Designs,	524	(5)
13.5 General Case of Fractional Replication,	529	(7)
13.5.1 Symmetrical Factorials,	529	(1)
13.5.2 Asymmetrical Factorials,	529	(2)
13.5.3 General Considerations,	531	(3)
13.5.4 Maximum Resolution Design,	534	(2)
13.6 Characterization of Fractional Factorial Designs of Resolution III, IV, and V,	536	(11)
13.6.1 General Formulation,	536	(2)
13.6.2 Resolution III Designs,	538	(1)
13.6.3 Resolution IV Designs,	539	(4)
13.6.4 Foldover Designs,	543	(3)
13.6.5 Resolution V Designs,	546	(1)
13.7 Fractional Factorials and Combinatorial Arrays,	547	(2)
13.7.1 Orthogonal Arrays,	547	(2)
13.7.2 Balanced Arrays,	549	(1)
13.8 Blocking in Fractional Factorials,	549	(9)
13.8.1 General Idea,	549	(1)
13.8.2 Blocking in 2n- Designs,	550	(1)
13.8.3 Optimal Blocking,	551	(7)
13.9 Analysis of Unreplicated Factorials,	558	(6)
13.9.1 Half-Normal Plots,	558	(4)
13.9.2 Bar Chart,	562	(1)
13.9.3 Extension to Nonorthogonal Design,	563	(1)
14 Main Effect Plans	564	(32)
14.1 Introduction,	564	(1)
14.2 Orthogonal Resolution III Designs for Symmetrical Factorials,	564	(18)
14.2.1 Fisher Plans,	564	(3)
14.2.2 Collapsing Factor Levels,	567	(1)
14.2.3 Alias Structure,	567	(8)
14.2.4 Plackett-Burman Designs,	575	(2)
14.2.5 Other Methods,	577	(5)
14.3 Orthogonal Resolution III Designs for Asymmetrical Factorials,	582	(12)
14.3.1 Kronecker Product Design,	583	(1)
14.3.2 Orthogonality Condition,	583	(3)
14.3.3 Addelman-Kempthorne Methods,	586	(8)
14.4 Nonorthogonal Resolution III Designs,	594	(2)
15 Supersaturated Designs	596	(12)
15.1 Introduction and Rationale,	596	(1)
15.2 Random Balance Designs,	596	(1)
15.3 Definition and Properties of Supersaturated Designs,	597	(1)
15.4 Construction of Two-Level Supersaturated Designs,	598	(5)
15.4.1 Computer Search Designs,	598	(1)
15.4.2 Hadamard-Type Designs,	599	(2)
15.4.3 BIBD-Based Supersaturated Designs,	601	(2)
15.5 Three-Level Supersaturated Designs,	603	(1)
15.6 Analysis of Supersaturated Experiments,	604	(4)
16 Search Designs	608	(25)
16.1 Introduction and Rationale,	608	(1)
16.2 Definition of Search Design,	608	(1)
16.3 Properties of Search Designs,	609	(6)
16.3.1 General Case,	609	(2)
16.3.2 Main Effect Plus One Plans,	611	(3)
16.3.3 Resolution V Plus One Plans,	614	(1)
16.3.4 Other Search Designs,	614	(1)
16.4 Listing of Search Designs,	615	(2)
16.4.1 Resolution III.1 Designs,	615	(1)
16.4.2 Resolution V.1 Designs,	616	(1)
16.5 Analysis of Search Experiments,	617	(13)
16.5.1 General Setup,	617	(1)
16.5.2 Noiseless Case,	618	(7)
16.5.3 Noisy Case,	625	(5)
16.6 Search Probabilities,	630	(3)
17 Robust-Design Experiments	633	(16)
17.1 Off-Line Quality Control,	633	(1)
17.2 Design and Noise Factors,	634	(1)
17.3 Measuring Loss,	635	(1)
17.4 Robust-Design Experiments,	636	(2)
17.4.1 Kronecker Product Arrays,	636	(1)
17.4.2 Single Arrays,	636	(2)
17.5 Modeling of Data,	638	(11)
17.5.1 Location and Dispersion Modeling,	638	(3)
17.5.2 Dual-Response Modeling,	641	(8)
18 Lattice Designs	649	(35)
18.1 Definition of Quasi-Factorial Designs,	649	(4)
18.1.1 An Example: The Design,	649	(1)
18.1.2 Analysis,	650	(3)
18.1.3 General Definition,	653	(1)
18.2 Types of Lattice Designs,	653	(2)
18.3 Construction of One-Restrictional Lattice Designs,	655	(2)
18.3.1 Two-Dimensional Lattices,	655	(1)
18.3.2 Three-Dimensional Lattices,	656	(1)
18.3.3 Higher-Dimensional Lattices,	657	(1)
18.4 General Method of Analysis for One-Restrictional Lattice Designs,	657	(4)
18.5 Effects of Inaccuracies in the Weights,	661	(5)
18.6 Analysis of Lattice Designs as Randomized Complete Block Designs,	666	(3)
18.7 Lattice Designs as Partially Balanced Incomplete Block Designs,	669	(1)
18.8 Lattice Designs with Blocks of Size K,	670	(1)
18.9 Two-Restrictional Lattices,	671	(7)
18.9.1 Lattice Squares with K Prime,	671	(4)
18.9.2 Lattice Squares for General K,	675	(3)
18.10 Lattice Rectangles,	678	(1)
18.11 Rectangular Lattices,	679	(3)
18.11.1 Simple Rectangular Lattices,	680	(1)
18.11.2 Triple Rectangular Lattices,	681	(1)
18.12 Efficiency Factors,	682	(2)
19 Crossover Designs	684	(32)
19.1 Introduction,	684	(1)
19.2 Residual Effects, 685 19.3 The Model,	685	(2)
19.4 Properties of Crossover Designs,	687	(1)
19.5 Construction of Crossover Designs,	688	(7)
19.5.1 Balanced Designs for ρ = t,	688	(3)
19.5.2 Balanced Designs for ρ less than t, 688
19.5.3 Partially Balanced Designs,	691	(1)
19.5.4 Strongly Balanced Designs for ρ = t + 1,	691	(2)
19.5.5 Strongly Balanced Designs for ρ less than t, 692
19.5.6 Balanced Uniform Designs,	693	(1)
19.5.7 Strongly Balanced Uniform Designs,	693	(1)
19.5.8 Designs with Two Treatments,	693	(2)
19.6 Optimal Designs,	695	(4)
19.6.1 Information Matrices,	695	(2)
19.6.2 Optimality Results,	697	(2)
19.7 Analysis of Crossover Designs,	699	(7)
19.8 Comments on Other Models,	706	(10)
19.8.1 No Residual Effects,	706	(1)
19.8.2 No Period Effects,	707	(1)
19.8.3 Random Subject Effects,	707	(1)
19.8.4 Autocorrelation Error Structure,	707	(1)
19.8.5 Second-Order Residual Effects,	708	(2)
19.8.6 Self and Mixed Carryover Effects,	710	(3)
19.8.7 Factorial Treatment Structure,	713	(3)
Appendix A Fields and Galois Fields	716	(5)
Appendix B Finite Geometries	721	(3)
Appendix C Orthogonal and Balanced Arrays	724	(4)
Appendix D Selected Asymmetrical Balanced Factorial Designs	728	(8)
Appendix E Exercises	736	(13)
References	749	(18)
Author Index	767	(4)
Subject Index	771