Combined array approach for optimal designs

Robust parameter design, originally proposed by Taguchi (1987) is an offline production technique for reducing variation and improving product's quality. To achieve this objective Taguchi proposed the use of product arrays. However, the product array approach, results in an exorbitant number of runs. To overcome the drawbacks of the product array Welch, Wu, Kang and Sacks (1990), Shoemaker, Tsui and Wu (1991) and Montgomery (1991a) proposed the use of combined arrays, where the control factors and noise factors are combined in a single array. In this paper we study the concept of combined array for an intermediate class of designs where n = I (mod4), n = 2 (mod4) and n = 3 (mod4). The designs presented in this paper, though not orthogonal, offer a great reduction in the run-size.