Optimal resource allocation for defending k-out-of-n systems against sequential intentional and unintentional impacts

Existing literature on system defense mainly considers single or multiple intentional impacts. However, intentional impacts (strategic attacks) and unintentional impacts (natural disasters) can happen sequentially in practice. To overcome this limitation, we conduct a study that considers the optimal resource allocation for defending a k-out-of-n system against sequential intentional and unintentional impacts, which is motivated by the defense of a solar power grid system against the sequential hacker's attack and solar storm. We study the optimal defense strategies under different occurrence orders of intentional and unintentional impacts and analyze the impact of critical parameters on the defender's optimal defense strategy by a case study. We also investigate the scenario in which the defender offers supplemental protection to the elements that survive the first impact. The case study indicates that deploying as many elements as possible in the first stage may not be the optimal strategy for the defender no matter the unintentional impact comes first or the intentional impact comes first. Providing supplemental protection can reduce the expected loss of the system when the unintentional impact comes first.