4Other Topics in Product Development and Optimization: Response Surface and Mixture Designs

4.1 Introduction

In the previous chapter, the case study on the development of an innovative dishwashing product discussed the design and analysis of a general factorial design to identify which formula maximizes the cleaning performance response.

The present chapter extends the topic of design and analysis of factorial designs by introducing two classes of designs particularly suited to fitting and analyzing response surfaces and for optimizing response variables: central composite designs (CCDs) and Box‐Behnken designs.

When the factors represent ingredients or components of a formulation, the total amount of which is fixed and we are interested in evaluating whether one or more responses vary when decreasing or increasing the proportions of the ingredients, mixture experiments can be designed and analyzed to take into account the dependence among components.

The first case study considers the development of a new polymeric membrane, with the goal being to maximize the product's elasticity. Based on previous results, the scientists identify the region of exploration to search for the factor levels that maximize product elasticity. The example shows how to plan a CCD or a Box‐Behnken design in line with specific interests. For the analysis of the design, given that the experimenters are relatively close to the optimum set of factor levels, a second‐order model is fitted to allow the ...

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