The optimal bivariate spare part ordering and replacement policy for a single component system suffering from both performance deterioration and random shocks is taken into consideration in this paper. To be specific, a deteriorating complex system is simultaneously subject to external shocks, while the influence of shock damage can be removed by minimal repair. A spare unit for replacement is regularly ordered associated with system operation time and the number of minimal repairs, or emergently ordered at system failure, whichever takes place first. Three different kinds of objectives where system availability, average cost rate, and expected cost effectiveness are compared and optimized respectively to seek for the optimal spare part ordering policy. The useful managerial insights and guidelines are twofold: (1) more influential factors, for example, the continuous operation time and the discrete number of repairs in this current research are encouraged to be incorporated into the spare unit ordering decision; (2) an optimal ordering policy in spare management constantly varies in the context of different optimization aims.