Understanding the Features of Non-Orthogonality in Quadratic Response Surface Designs
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Authors
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Nripes Kumar Mandal
Retd. Professor, University of Calcutta, Kolkata
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Bikas Kumar Sinha
Retd. Professor, Indian Statistical Institute, Kolkata
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Manisha Pal
Adjunct Professor, St. Xavier’s University, Kolkata
Keywords:
Response surface design; Orthogonal design; Non-orthogonality measures; D-optimal design; Rotatable design.Abstract
Orthogonality is an important concept in design of experiment. Though orthogonal designs exist for multivariate first-degree regression model, such
designs do not exist for second- and higher-degree models. In this paper, an attempt has been made to first introduce some measures or indices to
non-orthogonality, and then to identify designs with minimum non-orthogonality indices. It is observed that such designs are neither D-optimal nor
rotatable. Some examples are given for second degree model with two and three factors.
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References
Bose, R.C., and Draper, N.R. (1959). Second order rotatable designs in
three dimensions. Ann. Math. Stat., 30, 1097-1107.
Box, G.E.P. and Draper, N.R. (1975). Robust designs. Biometrika,
62(2), 347-352.
Box,G.E.P.and Hunter, J.S. (1957). Multifactor experimental designs
for exploring response surfaces. Ann. Math. Stat. 28, 195-241.
Das, M.N. and Narasimham, V.L. (1962). Construction of rotatable
designs through BIB designs.Ann. Math. Stat. 33, 1421-1439.
Das M. N., Parsad R. and Manocha V. P. (1999). Response surface
designs, symmetrical and asymmetrical, rotatable and modified,
Statistics and Applications, 1, 17–34.
Herzberg, A. M. (1967). A method for the construction of second order
rotatable designs in k-dimensions. Ann. Math. Stat. 38, 177-180.
Kiefer, J. (1959). Optimum experimental designs (with discussion). J.
Roy. Statist. Soc. B21, 272-319.
Liski, E. P., Mandal N.K., Shah, K.R. and Sinha, Bikas K. (2002).
Topics in Optimal Design. Springer.
Mandal, N.K. (2017). Measures of non-orthogonality in block designs.
Comm. in Stat.- Theory and Methods.46, 5, 2364-2369.
Nigam, A.K. and Das M.N.(1966). On a method of construction of
rotatable designs with smaller number of points controlling the
number of levels. Calcutta Stat. Assoc. Bull., 15, 147-157.
Pukelsheim, F. (1993). Optimal Design of Experiments. Wiley, New
York
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