Calculation of weights from equal satisfaction surfaces

In this paper, some technical aspects concerning the quantitative evaluation of the quality of a process are detailed. Knowing the global satisfaction of a multi-output response and after drawing the equal satisfaction surfaces, the relationships leading to the values of the weights in the response function are established. An example applied to the chemistry field is given, concerning the synthesis of Ca10(PO4)6(OH)2. The objectives are to adjust the ratio (Ca/P) in the product and the specific surface area with respect to three parameters: the ratio (Ca/P) in the reactives, the temperature and the acidity.