Some robust parameter designs from orthogonal arrays

Robust parameter design, originally proposed by Taguchi [System of Experimental Design, Vols. I and II, UNIPUB, New York, 1987], is an offline production technique for reducing variation and improving a product's quality by using product arrays. However, the use of the product arrays results in an exorbitant number of runs. To overcome this drawback, 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 non-isomorphic orthogonal arrays as combined arrays, in order to identify a model that contains all the main effects (control and noise), their control-by-noise interactions and their control-by-control interactions with high efficiency. Some cases where the control-by-control-noise are of interest are also considered.