Self-piercing riveting (SPR) is one of the mechanical joining processes, and its application to Al/Fe dissimilar materials combination, which is hard to weld, is expanding in the automotive industry. The main process parameters in SPR are types of rivet and die, setting force, and rivet setting speed. Previously, the relationship between the main process parameters and output parameters such as cross-sectional characteristics and joint strength has been studied to optimize the SPR process. In practical applications, there are unexpected and abnormal process conditions such as poor fit-up, angular misalignment, edge offset distance, and inaccurate setting and pre-clamping forces, and their effects on the joining quality have not been discussed. In this study, parametric investigation was performed using an experimental design on SPR joints for 1 mm-thick high strength steel (590 DP) and 2 mm-thick Al alloy (Al5052-H32). The main effect of each level of the abnormal process parameters on the output parameters was statistically investigated, and the analysis of variance was performed for each abnormal process parameter. In the range of abnormal process conditions applied, the set force was the most significant factor affecting the output parameters, and the effect of pre-clamping force on the output parameters was the least significant.