Journal of the Korean Statistical Society 41 (2012) 49–60 Contents lists available at SciVerse ScienceDirect Journal of the Korean Statistical Society journal homepage: www.elsevier.com/locate/jkss Orthogonally blocked mixture component–amount designs via projections of F-squares M.L. Aggarwal a,* , Poonam Singh b , Vandana Sarin c , Bushra Husain d a Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, United States b Department of Statistics, University of Delhi, Delhi-1100 07, India c Department of Statistics, Kirorimal College, University of Delhi, Delhi-1100 07, India d Department of Statistics and O.R., Women’s College, Aligarh Muslim University, Aligarh-202002, U.P., India article info Article history: Received 21 October 2010 Accepted 16 May 2011 Available online 15 June 2011 AMS 2000 subject classifications: primary 62K20 secondary 62K10 Keywords: Mixture–amount experiments Orthogonal blocking Scheffé’s quadratic model Latin squares F-squares D-optimality A-optimality E-optimality abstract Orthogonal block designs for Scheffé’s quadratic model have been considered previously by Draper et al. (1993), John (1984), Lewis et al. (1994) and Prescott, Draper, Dean, and Lewis (1993). Prescott and Draper (2004) obtained mixture component–amount designs via projections of standard mixture designs, viz., the simplex-lattice, the simplex-centroid and the orthogonally blocked mixture designs based on latin squares. Aggarwal, Singh, Sarin, and Husain (2009) considered the case of components assuming equal volume fractions and obtained mixture designs in orthogonal blocks using F-squares. In this paper, we construct orthogonal blocks of two and three mixture component–amount blends by projecting the class of four component mixture designs presented by Aggarwal et al. (2009). © 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved. 1. Introduction The response to mixture experiments is usually assumed to depend only on the respective proportions of the q (≥2) components present in the mixture and not on the total amount of the mixture. The proportions of a mixture of q (≥2) components may be expressed as a q-vector x = (x 1 , x 2 ,..., x q ) / in the (q - 1) dimensional simplex S q-1 . S q-1 =  x : (x 1 , x 2 ,..., x q )     q  i=1 x i = 1, x i ≥ 0  . (1.1) Scheffé (1958, 1963) introduced models and designs for experiments with mixtures. Scheffé’s second order model including the block effect γ is E (y) = q  i=1 β i x i +  1≤i<j≤q β ij x i x j + γ Z u + e u . (1.2) * Corresponding author. Tel.: +1 901 678 3756; fax: +1 901 678 2480. E-mail addresses: maggarwl@memphis.edu (M.L. Aggarwal), pbs_93@yahoo.co.in (P. Singh), vandana_s_walia@yahoo.co.in (V. Sarin), bushra_husain@rediffmail.com (B. Husain). 1226-3192/$ – see front matter © 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jkss.2011.05.007