Effect of Modeling and Transformation Approaches on Predictability and Error Metrics of Design of Experiment‐Based Optimization

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ABSTRACT Design of Experiment (DoE) is widely employed for formulation and process optimization. Current project studied the effect of different models and response data transformations, beyond recommended by DoE tool on prediction. DoE tool was used on a case study of central composite design‐based multifactor response surface methodology having three factors (X1, X2, and X3) and two responses (Y1 and Y2). Artificial neural network (ANN) software, InForm Version 5, was employed to empirically compare findings. DoE tool recommended quadratic and linear models for prediction, without data transformation for Y1 and Y2. Nevertheless, for Y1 and Y2, natural and base‐10 log transformations improved the model performance, as indicated by reduced SSE by 6.0% (Y1) and 3.7% (Y2) and RMSE by 16.1% (Y1) and 2.5% (Y2). With the above transformations, model re‐evaluation indicated that DoE recommended quadratic and linear models, respectively for Y1 and Y2 were best suited. With recommended and data driven models, the pairs of quadratic‐log and linear‐base‐10 log‐ transformations improved model predictability; increased R 2 by 3.6%, reduced root mean squared error (RMSE) by 16.1% and decreased predicted residual error squares (PRESS) by 19.7% (Y1) and improved R 2 by 0.4%, reduced RMSE by 2.5%, and decreased sum of squared error by 3.7% (Y2). Optimized factor levels generated with above model‐transformation pairs for Y1 and Y2 were close to ANN‐predicted levels. Indeed, DoE recommendation for data transformation (if required) and model selection must stand out from nonrecommended ones, but present results indicated otherwise warranting enhancement of features in DoE tools.

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