Optimal backup frequency in system with random repair time

This paper considers single-component repairable systems performing backup procedures to avoid repeating the entire work from scratch and thus facilitate fast system recovery in the case of failures. The mission succeeds if a specified amount of work can be accomplished within the maximum allowed mission time or deadline. The repair time is randomly distributed within a specified interval. Both failure and repair times are represented by known distributions. We first suggest a numerical algorithm to evaluate mission reliability, conditional expected cost and completion time of a successful mission. The backup frequency optimization problem is then formulated and solved for finding the inter-backup interval that maximizes mission reliability or minimizes expected mission cost while satisfying a desired level of mission reliability. Impacts of parameters including the maximum allowed mission time, data backup and retrieval times, repair and failure time distributions, and repair efficiency on mission reliability, cost and time as well as on the optimal solution are investigated through examples.