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.

The use of technological aids in the processing of bacterially infected sugar beet

“…To date, it has been established that a universal way to obtain such an estimate can be an optimization parameter, which is a multiplicative criterion for several particular parameters. One of such methods is Harrington's generalized desirability function (D), which is intended to be used as an optimization criterion [14,15]. For the numerical value of the specified criterion, the desirability scale is usually used: very good 1.00-0.80; good 0.80-0.63; satisfactorily 0.63-0.37; bad 0.37-0.20; very bad 0.20-0.00.…”

“…The actual values of the state indicators for the variants of the experiment were presented in the form of a dimensionless scale of desirability based on regression dependencies [14]. In general, the generalized coefficient of desirability was obtained by the type of a multiplicative criterion by multiplying particular criteria that have the same weight in accordance with the geometric mean formula [15].…”

Manufacturing and Analysis of Overmolded Hybrid Fiber Polyamide 6 Composite

“…The conditions with the highest desirability value are considered as the best values for the targeted response [30,31]. To maximize the desirability function of each response, the following Equation can be used [32]:…”

Application of design mixture and desirability function in the optimization of pharmaco-technical parameters of macrogols-based suppositories

“…The use of the notion of absolute desirability, introduced by Derringer and Suich (Sahin et al, 2016;Şimşek et al, 2013;Preece and Cornell, 1982;Pal and Gauri, 2018), makes it possible to optimize the choice of mixture parameters on the basis of the Physico-chemical characteristics of Macrogols. In this way; for each answer Yi(x), the desirability function di (Yi) varies between 0 and 1 di (Yi) = 0 representing a totally undesirable value of Yi and di (Yi) = 1 representing the desirable or ideal response value.…”