Compressor impellers for mass-market turbochargers are die-casted and machined with an aim to achieve high dimensional accuracy and acquire specific performance. However, manufacturing uncertainties result in dimensional deviations causing incompatible operational performance and assembly errors. Process capability limitations of the manufacturer can cause an increase in part rejections, resulting in high production cost. This paper presents a study on a centrifugal impeller with focus on the conceptual design phase to obtain a turbomachine that is robust to manufacturing uncertainties. The impeller has been parameterized and evaluated using a commercial computational fluid dynamics (CFDs) solver. Considering the computational cost of CFD, a surrogate model has been prepared for the impeller by response surface methodology (RSM) using space-filling Latin hypercube designs. A sensitivity analysis has been performed initially to identify the critical geometric parameters which influence the performance mainly. Sensitivity analysis is followed by the uncertainty propagation and quantification using the surrogate model based Monte Carlo simulation. Finally, a robust design optimization has been carried out using a stochastic optimization algorithm leading to a robust impeller design for which the performance is relatively insensitive to variability in geometry without reducing the sources of inherent variation, i.e., the manufacturing noise.