When a production facility is designed, there are various parameters affecting the number machines such as production capacity and reliability. It is often a tedious task to optimize different objectives, simultaneously. The other issue is the uncertainty in many design parameters which makes it difficult to reach a desirable solution. In this paper, we present a new mathematical model with two objectives. The primary objective function is considered to be the production capacity and the secondary objective function is total reliability. The proposed model is formulated on different units of production which are connected together in serial form and for each unit, we may have various machines. The resulted model is formulated using recent advances of robust optimization and solution procedure is analyzed with some numerical examples.