A Multiresponse Optimization Model for Statistical Design of Processes with Discrete Variables

Step 1: Data Collection

There are several approaches proposed in designing experiments. Response surface designs such as central composite design (CCD) and Box–Behnken can be used to fit the quadratic response surface model, which has linear and curvilinear effects for each of the factors along with all pairwise interaction effects. Box–Behnken design is known as economical design which requires only 3 levels for each factor and consists of a particular subset of the factorial design (khuri & Mukhopadhyay, 2010). Factorial design is applied to evaluate two or more factors simultaneously. This method divided into three parts such as; one-factor-at-a-time, full and fractional design which used to find the linear response (Montgomery, 2005). In order to find optimal design, several criteria proposed for multi response experiments. There are many methods of achieving optimal design such as simultaneous experiment design or sequential design (Ramachandran & Tsokos, 2015). Sequential design proposed by (Sitter & Forbes, 1997; Sitter & Wu, 1999). The most common criterion for multi response design is D-optimality, which expanded for linear multiresponse designs. (Atashgah & Seifi, 2007; Bischoff, 1993; Chang, 1994, 1997; Imhof, 2000; Kovach, 2009). Other criteria presented to find optimal design are; A-optimal, E-optimal (Wong, 1994), block design (Box & Draper, 1972; Das, Mandal & Sinha, 2003), and Bayesian design (Chaloner & Larntz, 1992; Chaloner & Vardinelli, 1995).