




S. No. 
Chapter 
Title of the Chapters 
Page 
Size (KB) 





1 
0 
Contents/ Abstract 

201.46 KB 





2 
1 
Introduction 
1 
477.47 KB 

1.1 
Response surface methodology 
1 

1.2 
First order design 
8 

1.3 
Second order design 
10 

1.4 
Central composite design 
11 

1.5 
Orthogonal design 
29 

1.6 
The Box Behnken design 
31 

1.7 
Centre points 
33 

1.8 
Optimal design 
34 

1.9 
Robustness of design 
37 





3 
2 
Designs with Missing observations 
51 
304.61 KB 

2.1 
Designs with missing observations 
51 

2.2 
Compound matrices of R matrix 
54 

2.3 
The losses due to one missing observation 
57 

2.4 
Twofactor CCD with single replication of factorial and axial parts 
58 

2.5 
Threefactor CCD with single replication of factorial and axial parts 
59 

2.6 
Fourfactor CCD with single replication of factorial and axial parts 
60 

2.7 
Fivefactor CCD with single replication of factorial and axial parts 
61 

2.8 
Fivefactor CCD with half replication of factorial part and complete replication of axial part 
62 

2.9 
Sixfactor CCD with single replication of factorial and axial parts 
63 

2.10 
Sixfactor CCD with half replication of factorial part and complete Replication of axial part 
65 

2.11 
Losses due to a pair of missing observations 
66 

2.12 
Twofactor CCD with single replication of factorial and axial parts 
67 

2.13 
Threefactor CCD with single replication of factorial and axial parts 
69 

2.14 
Fourfactor CCD with single replication of factorial and axial parts 
70 

2.15 
Fivefactor CCD with single replication of factorial and axial parts 
71 

2.16 
Fivefactor CCD with half replication of factorial and complete replication of axial parts 
73 

2.17 
Sixfactor CCD with single replication of factorial and axial parts 
74 

2.18 
Six factor CCD with half replication of factorial and complete replication of axial parts. 
76 





4 
3 
Designs robust to three missing observations 
78 
629.4 KB 

3.1 
The losses due to three missing design points 
78 

3.2 
Twofactor central composite design with single replication of factorial and axial points. 
80 

3.3 
Threefactor design with single replication of factorial and axial points 
89 

3.4 
Fourfactor CCD with single replication of factorial and axial points 
99 

3.5 
Fivefactor CCD with single replication of factorial and axial points 
105 

3.6 
Fivefactor CCD with half replication of factorial and complete replication of axial points 
112 

3.7 
Sixfactor CCD with complete replication of factorial and axial parts 
121 

3.8 
Sixfactor CCD with half replication of factorial and complete replication of axial parts. 
129 





5 
4 
Structure of losssensitive combinations of three missing observations 
138 
345.68 KB 

4.1 
Formation of the combinations of three missing observations 
138 

4.2 
The Combinations of three missing observations with high losses 
148 

4.3 
The Comparison of the losses due to different combinations of the same configuration. 
149 

4.4 
A combination of three missing factorial points for high losses when k ≥3 
150 

4.5 
Combinations of three missing observations with two factorial and one axial points 
151 

4.6 
Combinations of three missing observations with one factorial and two axial points for 3≤k≤6 
153 

4.7 
Combinations of three missing axial points for k≥3 
154 

4.8 
Combinations of three missing observations with two coaxial and one centre points 
155 

4.9 
Design with half replication of factorial parts and complete replication of axial part. 
156 

4.10 
The combinations of three missing observations with high losses in five factors design with halfreplicate of factorial and complete replicate of axial part 
158 

4.11 
Combinations of three missing observations with high losses in sixfactor design with halfreplicate of factorial and complete replicate of axial part 
160 





6 
5 
Comparison of different central composite designs 
165 
405.94 KB 

5.1 
Structure of R matrix 
165 

5.2 
Comparison of the minimaxloss design with different central composite designs of the same configuration. 
174 

5.3 
The Variance of the parameter estimates for the response surface design 
188 





7 
6 
The trace criterion for efficiency of the central composite Design 
203 
170.17 KB 

6.1 
Effect of missing observations on trace of information Matrix 
203 

6.2 
Replication of influential points to the design 
209 





8 
7 
Conclusions 
220 
56.62 KB 

7.1 
Losses due to three missing observations 
220 

7.2 
Central composite designs robust to three missing observations 
221 

7.3 
The effect of the missing observations on the variances of the estimates 
222 

7.4 
Breakdown of design and solution there of 
222 

7.5 
Future extension to the work 
223 





9 
8 
References 
225 
73.01 KB 





10 
9 
Appendix 
230 
25.31 KB 




