A Note on the Construction of TORDs Using t-Designs
Tóm tắt
The family of t-designs is one the most important family of statistical designs. These designs can be used to construct other significant designs. In this paper, an attempt has been made to construct Third Order Rotatable Designs (TORDs) in both symmetric and asymmetric levels using t-designs of unequal set sizes, i.e. UE-t designs. In most cases, the obtained design has lesser run size than third-order designs already in existence. A list of proposed classes of designs has been presented along with their G-efficiency.
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Tài liệu tham khảo
Adhikary B, Panda R (1984) Group divisible third order rotatable designs (GDTORD). Sankhyā: The Ind J Stat 1:135–46
Calvin LD (1954) Doubly balanced incomplete block designs for experiments in which the treatment effects are correlated. Biometrics 10(1):61–88
Das MN, Narasimham VL (1962) Construction of rotatable designs through balanced incomplete block designs. Ann Math Stat 33(4):1421–1439
Ding C, Tang C (2020) Combinatorial t-designs from special functions. Cryptogr Commun 12(5):1011–1033
Draper NR (1960a) Third order rotatable designs in three dimensions. Ann Math Stat 865–874
Draper NR (1960b) A third order rotatable design in four dimensions. Ann Math Stat 31(4):875–877
Draper NR (1962) Third order rotatable designs in three factors: analysis’. Technometrics 4(2):219–234
Draper NR, Herzberg AM (1985) Fourth order rotatability. Commun Stat Simul Comput 14(3):515–28
Draper NR, Pukelsheim F (1994) On third order rotatability. Metrika 41(1):137–161
Gardiner DA, Grandage AHE, Hader RJ (1959) Third order rotatable designs for exploring response surfaces. Ann Math Stat 30(4):1082–1096
Giovannitti-Jensen A, Myers RH (1989) Graphical assessment of the prediction capability of response surface designs. Technometrics 31(2):159–171
Hedayat A, John PWM (1974) Resistant and susceptible BIB designs. Ann Stat 2(1):148–158
Hedayat A, Kageyama S (1980) The family of t-designs—Part I. J Stat Plan Inference 4(2):173–212
Hemavathi M, Varghese E, Shekhar S, Jaggi S (2022a) Sequential asymmetric third order rotatable designs (SATORDs). J Appl Stat 49(6):1364–1381
Hemavathi M, Shekhar S, Varghese E, Jaggi S, Sinha B, Mandal NK (2022b) Theoretical developments in response surface designs: an informative review and further thoughts. Commun Stat Theory Methods 51(7):2009–2033
Herzberg AM (1964) Two third order rotatable designs in four dimensions. Ann Math Stat 35(1):445–446
Huda S (1982) Some third-order rotatable designs. Biom J 24(3):257–263
Huda S (1983) Two third-order rotatable designs in four dimensions. J Stat Plan Inference 8(2):241–243
Hughes DR (1965) On t-designs and groups. Am J Math 87(4):761–778
Kageyama S, Hedayat A (1983) The family of t-designs-Part II. J Stat Plan Inference 7(3):257–287
Kimaiyo JP, Mutiso J, Kosgey M (2019) Construction of a five-level v-dimensional modified third order rotatable designs using a pair of pairwise balanced designs. Afr J Educ Sci Tech 5:190–200
Kosgei MK, Koske JK, Mutiso JM (2014) Construction of three level third order rotatable design using a pair of balanced incomplete block design. East Afr J Stat 7:145–154
Koske JK, Mutiso JM, Mutai CK (2011a) Construction of third order rotatable design through balanced incomplete block design. Far East J Appl Math 58(1):39–47
Koske JK, Kosgei MK, Mutiso JM (2011b) A new third order rotatable design in five dimensions through balanced incomplete block designs. J Agric Sci Technol 13(1):157–163
Mutai CK, Koske JK, Mutiso JM (2012) Construction of a four dimensional third order rotatable design through balanced incomplete block design. Adv Appl Stat 27:47–53
Mutai CK, Koske JK, Mutiso JM (2013) A new method of constructing third order rotatable design. Far East J Theor Stat 42:151–157
Mutiso JM (2005) Some third order rotatable designs in five dimensions. East Afr J Stat 1(1):117–122
Mutiso JM, Koske JK (2007) Some third order rotatable designs in six dimensions. J Agric Sci Technol 9(1):78–87
Nigam AK (1967) On third-order rotatable designs with smaller numbers of levels. J Ind Soc Agric Stat 19:36–41
Njui F, Patel MS (1988) Fifth order rotatability. Commun Stat Theory and Methods 17(3):833–48
Patel MS, Arap Koske JK (1985) Conditions for fourth order rotatability in k dimensions. Commun Stat Theory and Methods 14(6):1343–1351
Raghavarao D, Zhou B (1998) Universal optimality of UE 3-designs for a competing effects model. Commun Stat Theory Methods 27(1):153–164
Tyagi BN (1964) On construction of second and third order rotatable designs through pairwise balanced and doubly balanced designs. Calcutta Stat Assoc Bull 13(3–4):150–162
Varghese E, Hemavati M, Dalal A, Bhowmik A, Jaggi S (2022) SAS Macro for checking the rotatability of Response Surface Design. https://krishi.icar.gov.in/jspui/handle/123456789/71141
Yates F (1936) Incomplete randomised blocks. Ann Eugen 7(2):121–140
Zahran A, Anderson-Cook CM, Myers RH (2003) Fraction of design space to assess prediction capability of response surface designs. J Qual Technol 35(4):377–386