Robust parameter design: Optimization of combined array approach with orthogonal arrays

Robust parameter design, originally proposed by Taguchi (1987. System of Experimental Design, vols. I and II. UNIPUB, New York), is an off-line production technique for reducing variation and improving a product's quality by using product arrays. However, the use of product arrays results in an exorbitant number of runs. To overcome the drawbacks of the product array several scientists proposed the use of combined arrays, where the control and noise factors are combined in a single array. In this paper, we use certain orthogonal arrays that are embedded into Hadamard matrices as combined arrays, in order to identify a model that contains all the main effects (control and noise) and their control-by-noise interactions with high efficiency. Aliasing of effects in each case is also discussed.