This study uses a finite element method based simulation methodology for in-situ railhead repair welding to investigate how welding process parameters impact the repaired rail quality. The methodology includes material modeling with cyclic plasticity, phase transformations, transformation-induced plasticity, and multi-phase homogenization. The weld process modeling includes a 3D heat transfer analysis and a 2D Generalized Plane Strain (GPS) mechanical analysis. The Heat source model used in the thermal simulation is calibrated using measurements from a repair welding experiment. To assess the performance of the repaired rail, mechanical rolling contact simulations are performed to estimate the risk of fatigue crack initiation. The process parameter study is based on the Swedish stick-welding railhead repair procedure and focuses on factors affecting the repair quality, such as preheating and operation temperature conditions as well as variations in repair geometry. Significant findings highlight both the inherent robustness of the process and regions susceptible to parameter variations. Specifically, the powerful final zig-zag weld passes provide effective resilience against variations in additional heating, and the start and end stretches of the repair welding are the most susceptible to parameter variations. Chamfered and deeper cutout repair geometries are found to be effective in mitigating adverse effects. In agreement with field observations, the simulations identify the fusion zone of the base and weld filler material as the critical region of the repaired rail in operation. This is attributed to the integrated effects of unfavorable microstructures, longitudinal tensile residual stresses from repair welding, and tensile stresses during operational traffic loads.