A model to create orthogonal Graeco Latin square experimental designs
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CitationBashiri, M. ve Korani, E. (2009). A model to create orthogonal Graeco Latin square experimental designs. Maltepe Üniversitesi. s. 259.
Graeco Latin square designs and Latin square designs are using as experimental designs including more blocks. A Latin square arrangement is an arrangement of n symbols in n rows and n columns, such that every symbol occurs once in each row and each column. When two Latin squares of same order are superimposed on one another, in the resultant array if every ordered pair of symbols occurs exactly once, then the two Latin squares are said to be orthogonal or Graeco Latin square. Creating a Graeco Latin square arrangement is time consuming. However, it has good usage in scope of blocking design in DOE. It helps the SSE (Sum of Squares Error) of design to be pure because of disarticulation of block factors’ effects from the error effects. This paper proposes a model to arrange the position of pair words of Latin and Graeco. A heuristic approach to set the Graeco Latin Square design and a proposed Linear Assignment Model are two proposed methods to develop mentioned experimental designs. To solve the proposed linear model for any rank of square, we used Lingo software to program the problem. And finally some numerical examples were used to show the applicability of proposed methods.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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