A desirability functions-based approach for simultaneous optimization of quantitative and ordinal response variables in industrial processes

Abstract

The most important step for producing high quality products is the optimum  utilization of the manufacturing processes and its resources, which can be  accomplished by using optimal process settings. Extensive research works are reported in literature for optimization of process settings with respect to single as well as multiple quantitative response variables. However, in real world, often some aspects of product quality (e.g. dimensions, yield etc.) are measured quantitatively and some other aspects of product quality (e.g. color, finish etc.) are assessed qualitatively like 'poor', 'average', 'good' etc., which can be treated as ordered  categorical or ordinal variables. Only a few researchers have attempted to tackle the problem of simultaneous optimization of quantitative and ordinal response variables. But none of these approaches results in an efficient optimal solution with respect to the desirability values of all the individual response variables. It  motivated us to develop a more useful approach for   simultaneously optimizing  industrial processes with respect to quantitative as well as ordinal response variables. In the proposed method, the concept of desirability functions for  continuous quantitative variables is extended for ordinal response variables, and then process settings is optimized considering geometric mean of the individual desirability functions of continuous as well as ordinal response variables. A set of experimental data, which have been analyzed by the past researchers, are analyzed using the proposed method and the related results are compared. The comparison of results reveals that the proposed method leads to better optimal solution than the other methods.

Keywords: Quantitative responses, Ordinal responses, Multiple regression, Ordinal logistic regression, Desirability function, Optimization