Abstract: The identification of dominant factors controlling slope stability and the investigation of their influence patterns under complex geological conditions have not yet formed a comprehensive system, and the interaction effects of multiple factors are difficult to decouple effectively. The sensitivity ranking based on limited simulation samples is uncertain, and some studies lack a reusable systematic workflow, resulting in insufficient comparability of analysis results among different engineering cases. To address this issue, a typical slope in an open-pit mine containing faults and weak interlayers was selected as the research object. The efficient factorial capability of orthogonal experimental design was combined with the advantages of grey relational analysis in handling small-sample and nonlinear problems, and a standardized sensitivity analysis framework from experimental design to numerical simulation and results analysis was constructed. The influence patterns and sensitivity of slope stability to the dip angle, cohesion, internal friction angle, thickness, and burial depth of the weak interlayer, as well as the fault dip angle, were analyzed. The results showed that the fault dip angle, burial depth of the weak layer, and internal friction angle of the weak layer were key factors controlling slope stability. The sensitivity ranking obtained by orthogonal experiments and grey relational analysis was highly consistent, namely, internal friction angle of the weak layer > burial depth of the weak layer > fault dip angle > cohesion of the weak layer > dip angle of the weak layer > thickness of the weak layer. The stability coefficient showed a generally linear variation with the parameters of the weak interlayer, and exhibited a distinctive nonlinear variation with the fault dip angle, which was described by a modified Gompertz model. As the dip angle of either a dip-slope fault or a reverse-dip fault gradually approached that of a vertical fault, the slope stability correspondingly increased.