Energy dissipation devices are widely employed to improve the performance of structural systems under earthquake input. In particular, the use of viscous dampers represents a valuable and cost-effective solution to achieve a structural performance enhancement (Christopoulos et al. 2006; Soong and Dargush 1997; Takewaki 2011). Viscous dampers provide a resisting force proportional to the relative velocity between the damper ends to the power of an exponent a. This exponent can assume values in a wide range, usually between 0.15 and 2 (Constantinou and Symans 1992). In structural engineering applications, values lower than 1 are preferred to limit the increase of forces for velocities beyond the design ones. Many methodologies were proposed in the last decades for the optimal design of viscous damper properties in buildings subjected to seismic ground motion records (Constantinou and Symans 1992; Martinez-Rodrigo and Romero 2003; Uriz and Whittaker 2001). The main limitation of these methodologies is that they do not account explicitly for the uncertainties in the earthquake input or in the model. Thus, they cannot be employed to control directly the seismic risk of the protected structure and of the dampers. More recent works have demonstrated the important effect of the exponent a on the propagation of these uncertainties in the seismic response assessment of buildings equipped with viscous dampers. Di Paola et al. (2007) and Tubaldi and Kougioumtzoglou (2015) proposed a stochastic dynamic approach based on the equivalent linearization of the damper behaviour to study the problem. Tubaldi et al. (2014) and Dall’Asta et al. (2016) analyzed the performances of respectively single degree of freedom (SDOF) and multi degree of freedom (MDOF) systems with nonlinear viscous dampers by developing response hazard curves for values between 0.15 and 1, whereas Guneyisi and Altay (2008) carried out fragility studies on systems equipped with linear viscous dampers. The work of Lavan and Avishur (2013) analyzed the influence of the uncertainties concerning model parameters on the seismic performance. Dall’Asta et al. (2017) studied the specific effects of the damper property variability by linking the tolerance allowed in quality control tests and production tests to the relevant variability of the risk of exceedance of the most interesting parameters controlling the seismic performance.