Robust parameter design (RPD) is an effective tool, which involves experimental design and strategic modeling to determine the optimal operating conditions of a system. The usual assumptions of RPD are that normally distributed experimental data and no contamination due to outliers. And generally the parameter uncertainties in response models are neglected. However, using normal theory modeling methods for a skewed data and ignoring parameter uncertainties can create a chain of degradation in optimization and production phases such that misleading fit, poor estimated optimal operating conditions, and poor quality products. This article presents a new approach based on confidence interval (CI) response modeling for the process mean. The proposed interval robust design makes the system median unbiased for the mean and uses midpoint of the interval as a measure of location performance response. As an alternative robust estimator for the process variance response modeling, using biweight midvariance is proposed which is both resistant and robust of efficiency where normality is not met. The results further show that the proposed interval robust design gives a robust solution to the skewed structure of the data and to contaminated data. The procedure and its advantages are illustrated using two experimental design studies.