Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30123
On the Optimality of Blocked Main Effects Plans

Authors: Rita SahaRay, Ganesh Dutta

Abstract:

In this article, experimental situations are considered where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks, not necessarily of same size. Assuming the block sizes to be even for all blocks, for the case n ≡ 2 (mod 4), optimal designs are obtained with respect to type 1 and type 2 optimality criteria in the class of designs providing estimation of all main effects orthogonal to the block effects. In practice, such orthogonal estimation of main effects is often a desirable condition. In the wider class of all available m two level even sized blocked main effects plans, where the factors do not occur at high and low levels equally often in each block, E-optimal designs are also characterized. Simple construction methods based on Hadamard matrices and Kronecker product for these optimal designs are presented.

Keywords: Design matrix, Hadamard matrix, Kronecker product, type 1 criteria, type 2 criteria.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1127509

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 699

References:


[1] M. Bose, and S. Bagchi, “Optimal main effect plans in blocks of small size,” Statist. Probab. Lett., vol. 77, 2007, pp. 142-147.
[2] C. S. Cheng, “Optimality of some weighing and 2n fractional factorial designs,” Ann. Statist., vol. 8, 1980, pp. 436-446.
[3] A. Das, and A. Dey, “Optimal main effect plans with nonorthogonal blocks,” Sankhy¯a, vol. 66(2), 2004, pp. 378-384.
[4] G. Dutta and R. SahaRay, “D- and E- optimal blocked main effects plans with unequal block sizes when n is odd,” Statist. Probab. Lett., vol. 107, 2015, pp. 37-43.
[5] M. Jacroux, C. S. Wang and J. C. Masaro, “On the optimality of chemical balance weighing designs,” J. Statist. Plann. Inference, vol. 8, 1983, pp. 231-240.
[6] M. Jacroux, “A note on the construction of optimal main effects plans in blocks of size two,” Statist. Probab. Lett., vol. 78, 2008, pp. 2366-2370.
[7] M. Jacroux, “On the D-optimality of orthogonal and nonorthogonal blocked main effects plans,” Statist. Probab. Lett., vol. 81, 2011, pp. 116-120.
[8] M. Jacroux, “On the D-optimality of nonorthogonal blocked main effects plans,” Sankhy¯a B, vol. 73, 2011, pp. 62-69.
[9] M. Jacroux, “A note on the optimality of 2-level main effects plans in blocks of odd size,” Statist. Probab. Lett., vol. 83, 2013, pp. 1163-1166.
[10] M. Jacroux and K. B. Dichone, “On the E-optimality of blocked main effects plans when n ≡ 3 (mod 4),” Statist. Probab. Lett., vol. 87, 2014, 143-148.
[11] M. Jacroux , and K. B. Dichone, “On the E-optimality of blocked main effects plans when n ≡ 2 (mod 4),” Sankhy¯a B, vol. 77, 2015, 165-174.
[12] R. Mukerjee, A. Dey, and K. Chatterjee, “Optimal main effects plans with non orthogonal blocking,” Biometrika, vol. 89(1), 2002, pp. 225-229.
[13] S. C. Pearce, “Experimenting with blocks of natural size,” Biometrika, vol. 18, 1964, pp. 699-706.
[14] D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments. John Wiley & Sons, 1971.