Optimal aborting policy for shock exposed missions with random rescue time

For systems operating in random environments, shock number threshold-based mission abort policies (MAP) have been modeled and optimized for balancing the mission success probability (MSP) and system survival probability (SSP). Among the abundant studies, only little work considered the multi-threshold MAP, where different numbers of shocks are acceptable (i.e., different threshold values for triggering mission abort) in different time intervals. The existing model, however, assumed that the threshold monotonically increases with the elapsed mission time and the rescue time is a determined function of mission abort time. In this work, the MAP is extended to the more general and effective non-monotonic threshold function for systems with practical random rescue time. A probabilistic method is proposed to evaluate MSP and SSP of the considered system for any given mission duration and multi-threshold MAP. The optimal MAP problem is further formulated and solved, maximizing the MSP while meeting a certain constraint on the SSP. A case study on an unmanned aerial vehicle surveillance system is provided to demonstrate the proposed model and effects of some model parameters (system performance rate and available resource, shock rates during primary mission and rescue procedure, shock resistance parameters) on the MSP and optimal MAP solutions.