Stochastic Systems with Reworking

In a wide class of real systems an element resuming the mission execution after a failure must redo some portion of work already performed before the failure. The considered systems are used in computing, continuous production and communication. To reduce the amount of work that should be redone, data backup procedures are introduced. On one hand these procedures reduce the amount of work lost after the failures, on other hand they increase the total amount of work in the mission by adding the backup actions. This paper presents a state-space event transition based numerical algorithm for simultaneous evaluation of mission success probability, expected mission completion time, and cost for standby systems with reworking. Due to the non-monotonic effect of the backup distribution on the mission performance indices, we formulate and solve the optimal backup distribution problem considering different combinations of optimization objectives and constraints. In the case of standby systems with non-identical elements, the elements activation sequence can influence the mission performance significantly. Therefore, we also consider an optimal element sequencing problem in reworking systems.