In modern quality engineering, dual response surface methodology is a powerful tool to monitor an industrial process by using both the mean and the standard deviation of the measurements as the responses. The least squares method in regression is often used to estimate the coefficients in the mean and standard deviation models, and various decision criteria are proposed by researchers to find the optimal conditions. Based on the inherent hierarchical structure of the dual response problems, we propose a hierarchical Bayesian approach to model dual response surfaces. Such an approach is compared with two frequentist least squares methods by using two real data sets and simulated data.