Silicon photonic interconnect (SPI) is an attractive alternative for the power-hungry and low-bandwidth metallic interconnect in multiprocessor systems-on-chip (MPSoCs). When employing SPIs for wavelength-division multiplexing (WDM)-based applications, it is essential to precisely align the central wavelengths of different photonic devices (e.g., photonic switches) to achieve a reliable communication. However, SPIs are sensitive to fabrication non-uniformity (a.k.a. fabrication process variation), which results in wavelength mismatches between devices, and hence performance degradation in SPIs. This work presents a computationally efficient and accurate bottom-up approach to study the impact of fabrication process variations on passive silicon photonic devices and interconnects. We first model the impact of process variations at the component level (i.e. strip waveguides), then at the device level (i.e. add-drop filters and photonic switches), and finally at the system level (i.e. passive WDM-based silicon photonic interconnects). Numerical simulations are performed not only to evaluate the accuracy of our method, but also to demonstrate its high-computational efficiency. Furthermore, our study includes the design, fabrication, and analysis of several identical microresonators to demonstrate process variations in silicon photonics fabrication. The efficiency of our proposed method enables its application to large-scale passive SPIs in MPSoCs, where employing time-consuming numerical simulations is not feasible.