This work aims to present an analysis of the effect of parametric uncertainties on the vibration control performance of a rod with periodically distributed piezoelectric patches that may be either independently connected to electrical shunt circuits or interconnected through an electrical line of inductors. In both cases, the capacitance of piezoelectric patches are considered as stochastic parameters following a known probability density function distribution. Then, Monte Carlo simulations are performed to evaluate mean values and confidence intervals of the frequency response functions to assess the robustness of each solution and to compare different solutions in terms of nominal and robust performances. The effect of other electrical components, such as circuits resistances, on the robustness is also analyzed.