Parameter design or robust parameter design (RPD) is a statistical methodology used mostly in engineering fields as a cost-effective approach for improving the quality of products and processes. The primary goal of parameter design is to choose the levels of the control variables, which optimizes a defined quality characteristic. Modeling both the mean and variance is commonly referred to as dual modeling. In parametric dual modeling, estimations of the mean and variance parameters are interrelated. When one or both of the models (the mean or variance model) are mis-specified, parametric dual modeling can lead to faulty inferences. An alternative to parametric dual modeling is nonparametric dual modeling. However, nonparametric techniques often result in estimates characterized by high variability, which leads us to ignore important knowledge. We develop a dual modeling approach called dual model robust regression (DMRR), which is robust against user misspecification of the mean and/or variance models. Numerical and asymptotic results illustrate the advantages of DMRR over several other dual model procedures. The proposed method will be illustrated with simulations.