Impact of correlated responses on the desirability function

Response Surface Methodology (RSM) is widely used in the industrial world to optimize processes. Most real-world applications of Response Surface Methodology involve multiple responses. The desirability function approach is widely used to simultaneously optimize multiple responses. This research addresses the impact on desirability function when responses are correlated. The impact is determined by estimating the variance of the desirability function and computing an approximate confidence interval based on this variance estimate.; A method is developed to compute the variance and a confidence interval for the desirability function. The desirability function is nonlinear in the input variables therefore, finding an exact expression for the variance is not straightforward. The method uses a Taylor Series approximation to compute the desirability function and its variance. Since the original formulation of the desirability function contains nondifferentiable points, a polynomial approximation is utilized.; The variance and confidence interval of the desirability function is numerically computed for multiple responses using different assumed correlation structures among responses. The coverage of the confidence interval for multiple responses and different correlation structures is determined using Monte Carlo simulations. Finally, the method is used to compute variance and confidence intervals using examples from the literature and from unpublished industrial settings.