A parameter design introduced by Taguchi provides a new quality control method which can reduce cost-effectively the product variation due to various uncontrollable noise factors such as product deterioration, manufacturing imperfections, and environmental factors under which a product is actually used. This experimental design technique identifies the optimal setting of the control factors which is least sensitive to the noise factors. Taguchi’s method utilizes orthogonal arrays which allow the investigation of main effects only, under the assumption that interaction effects are negligible.

In this paper new techniques are developed to investigate two-factor interactions for 2^t and 3^t factorial parameter designs. The major objective is to be able to identify influential two-factor interactions and take those into account in properly assessing the optimal setting of the control factors. For 2^t factorial parameter designs, we develop some new designs for the control factors by using a partially balanced array. These designs are characterized by a small number of runs and some balancedness property of the variance-covariance matrix of the estimates of main effects and two-factor interactions. Methods of analyzing the new designs are also developed. For 3^t factorial parameter designs, a detection procedure consisting of two stages is developed by using a sequential method in order to reduce the number of runs needed to detect influential two-factor interactions. In this paper, an extension of the parameter design to several quality characteristics is also developed by devising suitable statistics to be analyzed, depending on whether a proper loss function can be specified or not.