A Modified Desirability Function Approach for Mean-Variance Optimization of Multiple Responses

Abstract

A generic problem encountered in process improvement involves simultaneous optimization of multiple responses (so-called ‘critical response/output characteristics'). These types of problems are also referred to as ‘multiple response optimization (MRO) problems'. The primary goal of any process improvement initiative is to determine the best process operating conditions that simultaneously optimizes various critical ‘response characteristics'. Conventional desirability function approach uses response functions, target values, specifications to convert a MRO problem to a composite single objective optimization problem. The single objective function is maximized to determine near optimal conditions based on specific metaheuristic search strategy. The solution quality is expressed in terms of closeness of mean to target values and reduced variance around targets. Researchers generally impose hypothetical boundary conditions on variance to achieve satisfactory solutions. In this paper, an unconstrained modified desirability function is proposed, which do not require boundary conditions on variance, to determine efficient solution for MRO problem. Various case studies from open literature are selected to verify the superiority of the proposed approach over conventional desirability approach.