Analysis of No-Confounding Designs in 16 Runs for 9-14 Factors

Nonregular designs for 9-14 factors in 16 runs are a vital alternative for to theregular minimum aberration resolution III fractional factorials. Because there is no complete aliasing between the main factor and two factor interactions, these designs are useful as potential confusion in results is avoided. However, there is another associated complication to this kind of design due to the complete confounding for some of the two- factors. In this research, the focus is on using three different of methods and compare the results. The methods are: Stepwise, least absolute shrinkage and selection operator (LASSO) and the Dantzig selector method. In a previous research, Metcalfe discuss the nonregular designs for 6-8 factors design and studies several analysis methods. She also develops a new method, The Aliased Informed Model Selection (AIMS), for those designs. This research builds upon that. For this research, simulation is used to develop random models to analyze designs from the class of nonregular fractions with 9 – 14 factors in 16 runs using JMP scripting. Then, analyze the cases with the mentioned methods and find the success rate for each one. The model generations were random with only main factors, or main factors and two- factors interaction as active effects. Effect sizes of 2 and 3 standard deviations are studied. The nonregular design used in this research are 9 and 11-factors design. Results shows that there is a clear consistency for the main factors only as active effects using all the methods. However, adding the interactions to the active effects degrade the success rate substantially for the Dantzig method. Moreover, as the active effects exceed approximately half of the degrees of freedom for the design the performance for all i the methods decreases. Finally, some recommendations are discussed for further research investigation such as AIMS, other variation methods and Augmentation.