This work presents an analysis of the effect of parametric uncertainties on the vibration control performance of a rod with periodically distributed piezoelectric patches that can be either independently connected to electrical shunt circuits or interconnected through an electrical line of inductors. In both cases, the capacitance of the piezoelectric patches is 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. Results have shown that vibration amplitude reduction worsen significantly due to the mistuning between structural natural frequency and circuit resonance frequency. Yet, interconnected circuits are more robust to these uncertainties than independent shunts because they ensure a mean response that is closer to the nominal one. It was then proposed to assess the effect of modifying the circuits’ resistance. Results have shown that increased resistance decreases variability when considering both environmental and manufacturing variabilities. This also favors the use of interconnected circuits that require increased resistance for robust vibration mitigation.