Construction of Second Order Slope Rotatable Designs under Tri-Diagonal Correlated Structure of Errors Using Balanced Incomplete Block Designs
Keywords:
Second order slope rotatable designs (SOSRD), tri-diagonal correlated errorsAbstract
In this paper, second order slope rotatable design (SOSRD) under tri-diagonal correlated structure of errors using balanced incomplete block designs (BIBD) is suggested by following the works of Das (2003a, 2003b). Further, the variance of the estimated slopes for different values of the tri-diagonal correlated coefficient (-0.9 to 0.9) for “
factors 3 to 8” using BIBD is studied and observed that for some factors SOSRD under correlated structure of errors using BIBD has less number of design points than the corresponding SOSRD under tri-diagonal correlated structure of errors using central composite designs (CCD).
References
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Das MN, Narasimham VL. Construction of rotatable designs through balanced incomplete block designs. Ann Math Stat. 1962; 33: 1421-1439.
Das RN. Robust second order rotatable designs: part I. Calcutta Stat Assoc Bull. 1997; 47: 199-214.
Das RN. Robust second order rotatable designs: part II (RSORD). Calcutta Stat Assoc Bull. 1999; 49: 65-78.
Das RN. Robust second order rotatable designs: part-III. J Ind Soc Agr Stat. 2003a; 56: 117-130.
Das RN. Slope rotatability with correlated errors. Calcutta Stat Assoc Bull. 2003b; 54: 57-70.
Das RN, Park SH. A measure of robust slope-rotatability for second-order response surface experimental designs. J Appl Stat. 2009; 36: 755-767.
Das RN, Park SH, Aggarwal M. On D-optimal robust second order slope-rotatable designs. J Stat Plan Inference. 2010; 140: 1269-1279.
Hader RJ, Park SH. Slope-rotatable central composite designs. Technometrics. 1978; 20: 413-417.
Panda RN, Das RN. First order rotatable designs with correlated errors (FORDWCE). Calcutta Stat Assoc Bull. 1994; 44: 83-102.
Park SH. A class of multifactor designs for estimating the slope of response surfaces. Technometrics. 1987; 29: 449-453.
Raghavarao D. Constructions and combinatorial problems in design of experiments. New York: Wiley; 1971.
Rajyalakshmi K, Victorbabu B Re. Construction of second order slope rotatable designs under tri-diagonal correlated structure of errors using central composite designs. Int J Adv Stat Prob. 2014; 2: 70-76.
Rajyalakshmi K, Victorbabu B Re. Construction of second order slope rotatable designs under tri-diagonal correlated structure of errors using pairwise balanced designs. Int J Agric Stat Sci 2015; 11: 1-7.
Rajyalakshmi K, Victorbabu B Re. An empirical study of second order rotatable designs under tri-diagonal correlated structure of errors using incomplete block designs. Srilankan J Appl Stat. 2016; 17: 1-17.
Rajyalakshmi K, Victorbabu B Re. Construction of second order slope rotatable designs under tri-diagonal correlated structure of errors using symmetrical unequal block arrangements with two unequal block sizes. J Stat Mana Sys. 2018; 21: 201-215.
Victorbabu B Re, Narasimham VL. Construction of second order slope rotatable designs through balanced incomplete block designs. Comm Stat.-Theory and Methods. 1991; 20: 2467-2478.
Das MN, Narasimham VL. Construction of rotatable designs through balanced incomplete block designs. Ann Math Stat. 1962; 33: 1421-1439.
Das RN. Robust second order rotatable designs: part I. Calcutta Stat Assoc Bull. 1997; 47: 199-214.
Das RN. Robust second order rotatable designs: part II (RSORD). Calcutta Stat Assoc Bull. 1999; 49: 65-78.
Das RN. Robust second order rotatable designs: part-III. J Ind Soc Agr Stat. 2003a; 56: 117-130.
Das RN. Slope rotatability with correlated errors. Calcutta Stat Assoc Bull. 2003b; 54: 57-70.
Das RN, Park SH. A measure of robust slope-rotatability for second-order response surface experimental designs. J Appl Stat. 2009; 36: 755-767.
Das RN, Park SH, Aggarwal M. On D-optimal robust second order slope-rotatable designs. J Stat Plan Inference. 2010; 140: 1269-1279.
Hader RJ, Park SH. Slope-rotatable central composite designs. Technometrics. 1978; 20: 413-417.
Panda RN, Das RN. First order rotatable designs with correlated errors (FORDWCE). Calcutta Stat Assoc Bull. 1994; 44: 83-102.
Park SH. A class of multifactor designs for estimating the slope of response surfaces. Technometrics. 1987; 29: 449-453.
Raghavarao D. Constructions and combinatorial problems in design of experiments. New York: Wiley; 1971.
Rajyalakshmi K, Victorbabu B Re. Construction of second order slope rotatable designs under tri-diagonal correlated structure of errors using central composite designs. Int J Adv Stat Prob. 2014; 2: 70-76.
Rajyalakshmi K, Victorbabu B Re. Construction of second order slope rotatable designs under tri-diagonal correlated structure of errors using pairwise balanced designs. Int J Agric Stat Sci 2015; 11: 1-7.
Rajyalakshmi K, Victorbabu B Re. An empirical study of second order rotatable designs under tri-diagonal correlated structure of errors using incomplete block designs. Srilankan J Appl Stat. 2016; 17: 1-17.
Rajyalakshmi K, Victorbabu B Re. Construction of second order slope rotatable designs under tri-diagonal correlated structure of errors using symmetrical unequal block arrangements with two unequal block sizes. J Stat Mana Sys. 2018; 21: 201-215.
Victorbabu B Re, Narasimham VL. Construction of second order slope rotatable designs through balanced incomplete block designs. Comm Stat.-Theory and Methods. 1991; 20: 2467-2478.
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Published
2018-12-27
How to Cite
Rajyalakshmi, K., & Victorbabu, B. R. (2018). Construction of Second Order Slope Rotatable Designs under Tri-Diagonal Correlated Structure of Errors Using Balanced Incomplete Block Designs. Thailand Statistician, 17(1), 104–117. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/163220
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