Designs with Partial Factorial Balance
TLDR
In this paper, a class of multidimensional experimental designs with partial factorial balance is introduced and the analysis of these designs is given in detail and several series of three, four and five dimensional designs are presented.Abstract:
In this paper a class of multidimensional experimental designs said to have partial factorial balance is introduced. These designs are shown to belong to the more general class of multidimensional partially balanced designs. The analysis of designs with partial factorial balance is given in detail and several series of three, four and five dimensional designs are presented.read more
Citations
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Journal ArticleDOI
On inverting circulant matrices
TL;DR: In this article, the inverse of a circulant matrix having only three nonzero elements in each row (located in cyclically adjacent columns) is derived analytically from the solution of a recurrence equation.
Book ChapterDOI
Non-orthogonal graeco-latin designs
TL;DR: The subject is reviewed from a combinatorial viewpoint, and unsolved problems are indicated.
Journal ArticleDOI
Optimal balanced fractional $3\spm$ factorial designs of resolution ${\rm V}$ and balanced third-order designs
Journal ArticleDOI
Multidimensional Balanced Designs
Donald A. Anderson,W.T. Federer +1 more
TL;DR: A general construction for m-way completely variance balanced designs where each factor has v levels, m is any integer less than or equal to k, and N = vk, where k = 2λ+1 and v = 4λ3 is a prime power is given in this article.
References
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Journal ArticleDOI
Some Basic Properties of Multidimensional Partially Balanced Designs
TL;DR: A general class of partially balanced (PB) block-treatment designs were introduced by Srivastava et al. as discussed by the authors, which is a generalization of the concept of connected block treatment designs.
Journal ArticleDOI
Four-Factor Additive Designs More General Than the Greco-Latin Square
TL;DR: In this article, the authors discuss a class of four factor designs in which the four factors are at m, n, p and q levels respectively, and the total number of runs is less than N = mnpq.