Abstract
Let Cm be a Conference matrix with m rows. Then, a matrix Dm with 2m+1 rows by combining Cm, －Cm and the center point C0 can be constructed. In this paper, we propose a parameter design method using Dm (±1) that is the product array of Dm and a two-level noise factor N (N1, N2), which may reduce the variance of a response and the number of experimental runs compared to the conventional method using L18 and SN ratio. The proposed parameter design has the following properties. 1) In Dm (±1), the best linear unbiased estimators of the linear effects of control factors, the linear effect of the noise factor, and the effects of the products of control and noise factors can be obtained by the regression analysis using a pseudo-inverse matrix without confounding by the effects of the products and the quadratic effects of control factors. 2) The graph of the responses for N1 and N2 is drawn using the estimated regression coefficients, and the levels of control factors are selected so that the responses for N1 and N2 are close to reduce the variance of the response. 3) Although the number of experimental runs of three-level orthogonal arrays increases by every 9, that of Cm increases to 50 by every 2 except for 22, 34, which may enable the construction of the experimental design with smaller experimental runs in the proposed method compared to conventional methods.
