A method for the a priori estimation of the potential benefit that can be obtained from process control improvements is presented. The improved control benefit in this work arises from a shift in the mean operation toward a product specification or process constraint. The mean operation can be shifted toward the specification or constraint without increasing violation due to a reduction in the controlled variable variation attributable to the improved process control. The controlled variable variance reduction is determined based on minimum variance controller performance bounds. The shift in the mean operation is determined based on a specified fractional violation and cumulative probability distribution. The contribution of this work is a rigorous estimation method that can be used to economically justify and prioritize potential process control improvement projects. The method is illustrated using a waste heat recovery process where the estimated and actual benefits due to improved process control are compared.