In nonrepairable multifunctional systems, the lost function of a component can be restored by the same function from another component; therefore, the activation mechanism of redundant functions illustrates that multifunctional systems have resilience features. This study evaluates the resilience of multifunctional systems and analyzes the properties of system resilience first. To determine the optimal start-up strategy, a resilience-oriented start-up strategy optimization model for onsite monitoring systems (OMSs) is established to maximize system resilience under a limited budget. In this study, real-time reliability is regarded as the system performance to evaluate the system resilience, and a two-stage local search based genetic algorithm (TLSGA) is proposed to solve the resilience optimization problem. The results of our numerical experiments show that the TLSGA can more effectively solve the problems for OMSs, with high function failure rates and low component failure rates compared with classical genetic algorithms under 48 systems. Moreover, the optimal combinations of unmanned aerial vehicles (UAVs) for an OMS under a limited budget shows that UAVs with a higher carrying capacity should be given priority for selection. Therefore, this study provides an effective solution for determining the optimal start-up strategy to maximize the resilience of OMSs, which is beneficial for OMS configuration.