Characterizing and comparing order-of-addition orthogonal arrays

Music City Center 

Given a set of parameters, several non-isomorphic order-of-addition orthogonal arrays can be generated to design an order-of-addition experiment. Under resource constraints, selecting the best from these candidate designs for the experiment can be practical to extract as much information as possible from the observed data. In this talk, I will introduce a series of numerical indices called centralized generalized wordlength pattern to characterize and compare order-of-addition orthogonal arrays. First, the J-characteristics will be justified for pairwise order matrices. Next, the centralized generalized wordlength pattern will be defined based on the sums of squared differences between the normalized J-characteristics of the pairwise order matrices determined by the fractional and full designs. Some theoretical and computational results will also be introduced for future work.

Experimental design

Hadamard matrix

Hamming distance

Inversion

J-characteristic

Projection property 

International Chinese Statistical Association