Abstract
The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).
Highlights
Introduction{ } = A5g ( x′, y′, z′) ∈ Ag′ , g′ ≠ g y′ ≠ y corresponds to the treatments 5th associated to α
Designs of computer experiments drew a wide attention in the previous two decades and were still being usedHow to cite this paper: Rezgui, I., Gheribi-Aoulmi, Z. and Monod, H. (2015) U-Type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes
Among the various construction methods of these designs, the traditional combinatorial designs can be used as basic designs and the PBIB designs
Summary
{ } = A5g ( x′, y′, z′) ∈ Ag′ , g′ ≠ g y′ ≠ y corresponds to the treatments 5th associated to α This geometric representation describes a new association scheme, we call it for convenience, generalized rectangular right angular association scheme (5) with five associated classes, to which we give the following equivalent definition: Definition 6.
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