On Evaluating Variation of Desirability Function: A Monte Carlo Approach

The desirability function method is widely used for simultaneous optimization of several independent or uncorrelated responses. In practical application, a second order polynomial is usually employed to represent each response based on RSM, and a functional form of the overall desirability is obtained. This paper proposes a Monte Carlo approach to evaluate variation of the overall desirability function resulting from the variance of future responses, with input variables fixed at each optimum point. In this approach the variance of the estimated mean response as well as that of the random error are taken into consideration. Research shows that the probabilistic risk analysis using Monte Carlo simulation is a useful supplement to simultaneous optimization and robust analysis. A numerical example with two factors and three output responses is discussed for illustrative purpose.