Optimal mission abort policy for k-out-of-n: F balanced systems

This paper studies the optimal mission abort policy for the k-out-of-n: F balanced system performing a specific mission continually for a period of time. The system consists of m sectors and each sector is composed of n components. The components fail due to internal failure or external shocks. If one component fails, one component in the remaining sectors should be forced down or one forced-down component in the same sector should be resumed to keep balance. In this paper, balance is achieved when the number of working components in each sector is same and the system fails if there are at least k failed and forced-down components in any sector. Two probability indexes, mission success probability and system survivability, are derived by using the Markov process imbedding method. Two optimization models with consideration of maximizing mission success probability and minimizing the expected cost are presented. Moreover, a case study of the unmanned aerial vehicle performing a mission is given to demonstrate the results under study.