Construction of Hyper GLaSS Design

Abstract

Euler (1779) has the credit to introduced Latin square and Hyper Graeco-Latin square and hence been studied by number of mathematicians. While a special type of Latin Square derived from Sudoku puzzle named Sudoku Square Design was developed by Garns (1979). To keep the experimental error within limits or reducing the error by using minimum resources and to get maximum information is the prime goal of the researchers, and developing new designs to modify already developed methods to get better results. The present study has three main objectives. The first part of this study is the construction of a new experimental design i.e., Hyper Graeco-Latin Sudoku Square Design (Hyper GLaSS Design), the merger of two designs i.e., Hyper Graeco-Latin Square Design and Sudoku Square Design. Blocking property of Sudoku Square Design is merged with Hyper Graeco-Latin Square Design. The purpose of the new design is to test three sets of treatments simultaneously in one experiment and allows investigation of six factors. Introducing the Block Sum of Square, the error sum of square is further reduced. Parameter estimation with fixed effect, random effect and mixed effect models with its ANOVA are mentioned in this part. The second part deals with finding the missing values. As missing values create problem in finding the estimates, and to get good and accurate results missing value for one observation, two observations with different conditions and also several missing values for Hyper GLaSS Design have been estimated. Third part is composed of a comparative study between Hyper GLaSS Design and Hyper Graeco-Latin Square Design with some numerical examples by using hypothetical data, also simulation study is performed by using R studio and relative efficiency of both the designs show that the proposed new design i.e., Hyper GLaSS iv Design is more efficient then Hyper Graeco-Latin Square Design and gives minimum error sum of square. Future work is possible to reduce the experimental error to explain the total sum of square to the maximum limit.