The augmentation of existing data for improving the path of steepest ascent

Response surface methodology is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several independent variables and the objective is to optimize this response. When we are at a point on the response surface that is remote from the optimum, such as the current operating conditions, there is little curvature in the system and the first-order model will be appropriate. In these circumstances, a preliminary procedure as the steepest ascent usually is employed to move sequentially in the direction of maximum increase in the response. To improve the estimation of parameters of the steepest ascent path, we present, in an efficient way, the augmentation of existing data such that the independent variables are made more orthogonal to each other. Additionally, when we estimate the true path using this method, the bias and magnitude of the covariance matrix of the estimated path is decreased, significantly.