Robust design (RD) has received much attention from researchers and practitioners for years, and a number of methodologies have been studied in the research community. The majority of existing RD models focus on the minimum variability with a zero bias. However, it is often the case that the customer may specify upper bounds on one of the two process parameters (i.e., the process mean and variance). In this situation, the existing RD models may not work efficiently in incorporating the customer’s needs. To this end, we propose two simple RD models using the ε?constraint feasible region method - one with an upper bound of process bias specified and the other with an upper bound on process variability specified. We then conduct a case study to analyze the effects of upper bounds on each of the process parameters in terms of optimal operating conditions and mean squared error. The majority of existing RD models focus on the minimum variability with a zero bias. However, it is often the case that the customer may specify upper bounds on one of the two process parameters (ie, the process mean and variance). In this situation, the existing RD models may not work efficiently in incorporating the customer’s needs. two simple RD models using the ε? constraint feasible region method - one with an upper bound of process bias specified and the other with an upper bound on process variability specified. We then conduct a case study to analyze the effects of upper bounds on each of the process parameters in terms of optimal operating conditions and mean squared error.