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

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

Taha-Hossein Hejazi (Sadjad University of Technology, Iran) and Leilanaz Akbari (Ferdowsi University of Mashhad, Iran)
DOI: 10.4018/978-1-5225-1639-2.ch002
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Abstract

In manufacturing and diverse industries, quality has a main role to increase the market share. Hence, producers focus their attention to design products or services with high quality to meet the customer's expectations. Quality characteristics of products usually expressed by variables called response variables. Today's complex systems have several performance attributes in responses and designers try to select the best combination of controllable factors that satisfies all quality characteristics simultaneously. Since there are often several conflicts in quality characteristics, such as measurement units, scale and optimality directions, there are different approaches in model building and optimization of multi response surface problems. Therefore, the study of simultaneous analysis and improvement methods of the outputs are of great importance.
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Background

Some previous literature reviews on three phase of RSM methodology are reviewed separately as below.

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).

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