Characteristic slip and characteristic earthquake models have been proposed for several decades. Such models have been supported recently by high-resolution offset measurements. These models suggest that slip along a fault recurs via similarly sized, large earthquakes. The inter-event strain accumulation rate (ratio of earthquake slip and preceding interseismic time period) is used here to test the characteristic earthquake model by linking the slip and timing of past earthquakes on the Haiyuan Fault. We address how the inter-event strain accumulation rate varies over multiple seismic cycles by combining paleoearthquake studies with high-resolution airborne light detection and ranging (LiDAR) data to document the timing and size of paleoearthquake displacements along the western and middle segments of the Haiyuan Fault. Our observations encompass 5 earthquake cycles. We find significant variations over time and space along the Haiyuan Fault. We observe that on the middle segment of the Haiyuan Fault the rates slow down or increase as an anti-correlated function of the rates of preceding earthquakes. Here, we propose that the inter-event strain accumulation rates on the middle segment of the Haiyuan Fault are oscillating both spatially and temporally. However, along the western segment, the inter-event strain accumulation rate is both spatially and temporally steady, which is in agreement with quasi-periodic and slip-predictable models. Finally, we propose that different fault segments within a single fault zone may behave according to different earthquake models.