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STARS AND REGULAR FRACTIONAL FACTORIAL DESIGNS WITH RANDOMIZATION RESTRICTIONS
"... Abstract: Factorial and fractional factorial designs are widely used for assessing the impact of several factors on a process. Frequently, restrictions are placed on the randomization of the experimental trials. The randomization structure of such a factorial design can be characterized by its set o ..."
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Abstract: Factorial and fractional factorial designs are widely used for assessing the impact of several factors on a process. Frequently, restrictions are placed on the randomization of the experimental trials. The randomization structure of such a factorial design can be characterized by its set of randomization defining contrast subspaces. It turns out that in many practical situations, these subspaces will overlap, thereby making it impossible to assess the significance of some of the factorial effects. In this article, we propose new designs that minimize the number of effects that have to be sacrificed. We also propose new designs, called stars, that are easy to construct and allow the assessment of a large number of factorial effects under an appropriately chosen overlapping strategy. Key words and phrases: Block design, finite projective geometry, minimal (t − 1)cover, splitlot design, splitplot design, (t − 1)spread. 1.
On a Grouping Method for Constructing Mixed Orthogonal Arrays
, 2012
"... Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry. can be partitioned into 1,PG mn s 1,PG mn s 1 1mn ns s –1nflats such that each –1nflat is associated with a point in. An orthogonal array 1, nPG m s ..."
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Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry. can be partitioned into 1,PG mn s 1,PG mn s 1 1mn ns s –1nflats such that each –1nflat is associated with a point in. An orthogonal array 1, nPG m s 1 1mn nmn s snsL s can be constructed by using 1 1s mn ns points in 1, n PG m s . A set of 1 1sts points in n1,PG m s is called a –1tflat over GF(s) if it is isomorphic to. If there exists a 1,PG t s –1tflat over GF(s) in, then we can replace the corresponding 1, nm s PG 1 1ts s snlevel columns in 1 1mn nmn s snsL s by 1 1s s n stlevel columns and obtain a mixed orthogonal array. Many new mixed orthogonal arrays can be obtained by this procedure. In this paper, we study methods for finding disjoint –1tflats over GF(s) in in order to construct more mixed orthogonal arrays of strength two. In particular, if m and n are relatively prime then we can construct an 1,PG m s n 1 11 i sm s 1 i ss 1 n m n s