Optimal reassignment policy for a balanced system with multi-state subsystems supported by protective devices in a shock environment

Reassignment policies have been explored extensively due to their effectiveness in improving the reliability of systems with functionally interchangeable components. Additionally, the reliability of balanced systems with protective devices (PDs) has aroused research interests. To cope with the balanced requirement of the balanced systems with PDs, it is essential to apply the reallocation policy to extend the system lifetime. Nevertheless, no literature investigates the reallocation policy for balanced systems with PDs. Consequently, this paper investigates the optimal reassignment policy for a balanced system containing multiple subsystems with PDs. The system balance is characterized as the appropriate difference between the maximum and minimum state of subsystems. A new shock model is constructed to model the degradation of the proposed system, where the magnitude and duration of shocks are integrated to classify the shocks. The PD is activated to enhance the shock resistance of the corresponding subsystem once it degrades to a threshold. The finite Markov chain imbedding approach is utilized to derive the reliability indexes of the system. The optimal reassignment strategy and time can be derived via solving the optimization model with the objective of maximizing the system reliability. Finally, a practical example is presented to verify the proposed model.