In this work, we consider a parallel compressor model (PCM), which decomposes a compressor encountering non-uniform inflow into a distorted and an undistorted subcompressor, respectively, to determine its overall operating point. The main advantage of PCM modeling is a significantly reduced computational workload. At the same time, modeling errors are introduced, which need to be quantified together with model input uncertainties. Therefore, we introduce a probabilistic setting where unknown parameters are modeled as random variables. We carry out a global sensitivity analysis, which allows to reduce the complexity of the probabilistic model, by setting unimportant input parameters to their nominal values. This analysis attributes portions of the model output variance (the fan efficiency for instance) to particular input parameters or input parameter combinations, through so-called Sobol coefficients. We further include a parameter describing the PCM inflow averaging process into the analysis, which allows to determine the influence of specific modeling choices onto the predicted efficiency. Efficient sampling methods are needed to estimate the sensitivity coefficients with a reasonable computational effort. A key advantage of the global approach is that nonlinear effects are fully taken into account, the necessity of which will be demonstrated by our numerical examples. The model is also compared to CFD reference simulations to quantify structural model errors. This comparison is based on area validation metrics comparing the stochastic distribution functions of the probabilistic PCM model and the reference data.