Gas-insulated substation (GIS) equipment served in the traction power-supply system (TPSS) of the high-speed railway (HSR) suffers from extremely severe traction load conditions during its lifetime. In this paper, three major issues related to the actual field maintenance operations of GIS equipment in TPSS are addressed: 1) $s$ -dependent degradation and shock process; 2) both spatial and temporal failure thresholds of shocks; and 3) incomplete maintenance (i.e., nonignorable maintenance time). To model the deterioration and failure process of GIS equipment, the hard failure model and the soft failure model are proposed. The characteristic function is utilized to bridge the s -dependent degradation and shock process in the soft failure model, while the extreme shock model (with spatial threshold) and $\delta $ -shock model (with temporal threshold) are introduced in the hard failure model. Furthermore, the index of availability, which combines both reliability and maintainability, is derived under the incomplete maintenance consideration. Based on the balance of availability and maintenance cost, the maintenance strategy with periodic inspections for GIS equipment in the long-run time span is developed. Optimizations of three decision parameters (i.e., inspection period, extreme shock threshold, and $\delta $ -shock threshold) are implemented to achieve the best performance (with high availability and low maintenance cost) of the maintenance strategy.