Optimal Time Interval Between Periodic Inspections for a Two-Component Cold Standby Multistate System

The establishment of the optimal time interval between inspections for multistate redundant systems considering availability and costs related to maintenance and production losses is a challenging issue. This paper extends previous research for redundant multistate systems where the time-to-repair cannot be neglected. Discrete-time Markov chains are used to define transition probabilities between the different system states and the costs related to each transition. To optimize the time interval between inspections, the total cost is minimized utilizing the Markov chains properties followed by a numerical search technique. Two models are analyzed and numerical examples are presented. System I is a binary system with cold standby redundancy and component repair, while system II is a multistate system with cold standby redundancy and component repair. The main contribution of the method presented in this paper is the establishment of the optimal time interval between inspections for cold standby systems comprised of components that have different levels of degradation and where the component state can be determined only through periodic inspections. Systems with these characteristics are widely applied in industry, but are still not fully modeled in the literature.