Parameter estimation and model selection for detergent formulation #

Rahma Abdulahi, Dave Smith, Carlos Amador, Sara Jabbari

14:50 Tuesday in 4Q07.

Part of the Industrial mathematics session.

Abstract #

Sponsored by Procter and Gamble, we are focused on the removal of stains from clothing via the action of detergent within a washing machine and fitting a semi-mechanistic model incorporating the most relevant variables. Stains are sensitive to different aspects of the laundering process. The main factors that contribute are the mechanical action produced by different forces working on the fabric, the chemical action including the temperature, pH and various detergent ingredients and the porosity of the fabric to which the stain has been applied. A nonlinear semi-mechanistic model has been developed that takes these factors into account. Most importantly, nested in the model is a polynomial for which variables representing the chemical factors are included as linear, quadratic and interaction terms. The algorithm aims to add or subtract variables to ensure the best fit of the model to the stain removal data, thus informing us on which variables are most important in ensuring the best removal of the stain. In this talk, we will introduce a modified stepwise regression method to select relevant variables in the polynomial, present results and explore how the model’s predictive power varies over different stain types.