The probabilistic short circuit analysis provides relevant information for power system planning and power quality assessment tasks. Traditional Monte Carlo methods (TMCMs) are usually applied to consider the randomness affecting short circuit operating conditions, but they require numerous iterations to properly characterize the network conditions. This paper proposes a mixed Taguchi-based method (MTBM) as a new alternative tool to account for the uncertainties affecting the inputs of probabilistic short circuit analysis. The MTBM significantly reduces the number of iterations required to properly address the randomness of inputs (environmental conditions, pre-fault conditions, fault characteristics), and allows diversifying the representation of inputs through a quantile-based selection of their levels. The proposed method is applied to unbalanced three-phase four-wire low-voltage (LV) distribution systems with photovoltaic systems (PVSs) operating in low voltage ride- through (LVRT) during the fault. Numerical applications related to a test system are presented, and the proposed MTBM is compared with the TMCM, the unmixed Taguchi-based method (UTBM), and the point estimate method (PEM). The proposed MTBM returns values very close to those of the TMCM (with average deviations ranging from 0.01% to 3.12%) and enables a fast and accurate analysis of faulted LV distribution systems with PVSs operating in LVRT.