Optimal replacement rules in inspected shock-exposed asymmetric dual-component system with cascading effect

Motivated by practical examples in diverse application domains (e.g., power systems, electric and autonomous vehicles, propulsion engines, data centers), this paper presents a novel model of an asymmetric dual-component system subject to random external shocks and secondary shocks due to the cascading effect, causing deterioration and even failures of system components. To combat those shocks and alleviate the risk and cost of failures, the system is subject to periodic inspections and preventive component replacements based on shock occurrence statuses, incurring non-negligible additional cost. To minimize the expected mission cost (EMC), we formulate and solve a new optimization problem that determines the optimal inspection and replacement policy (IRP) defined by the number of inspections and values of three shock-based replacement rule parameters. A probabilistic method based on system state transitions is put forward for deriving the EMC of the considered system, based on which an EMC evaluation algorithm using a forward procedure is developed. The proposed algorithm is verified using Monte Carlo simulations. A case study of a dual battery powered sensor system is conducted to demonstrate the proposed model and influences of several model parameters on the EMC and the optimal IRP solutions, leading to some useful managerial recommendations. Parameters investigated include cost parameters linked to the system downtime, inspections as well as component replacements and failures, shock occurrence and resistance parameters, and mission time.