Conference matrices for optimizing and applications

Abstract

The trial numbers have been dependent on the row numbers of Design matrices. At layout of three levels factors, we had used to apply Hadamard type L27(313) and ,mix type L18(2137). Lower subscripts means the trial numbers.We adapted the conference matrices C with composited by Legendre Symbol as the design matrices for optimizing. Also, we adapt the raw data instead of log transformation with contaminated by non-linear effects. And data analysis was changed from the decomposition of the sum of square style to regression analysis. It was difficult for researcher to treat the interaction effect between factors. Hadamard design matrices will use the linear graph to catch the interaction which was the subunit of design matrices. It will reduce the numbers of layout columns in design matrices. Mix type will confound the interaction to main effects. So, it will contaminate the main effects. Conference matrices has only the linear effects. So, we have adapted the new system to confirm the source of the factors on the interaction. It is the difference levels between factors by comparing the trial best condition(a) of the design matrices with the best combination(b) of the factor effect. The same level factors are relative the main factors and the different level factors are relative the interaction effects. So, after gathering new ways, we could reduce the trial numbers to 1/3-1/2 with the same result to the current optimization. We are going to propose to apply it for SDGs subjects.