Joint optimization of multi-stage work intensity selecting and maintenance policy for a two-dimensional balanced system

Most existing research on balanced systems based on component state only considers the one-dimensional linear structure, but many engineering systems are two-dimensional. Driven by this reality, a two-dimensional balanced system reliability model is proposed. All components are arranged in a two-dimensional matrix, and divided into grids of equal size. The system is required to complete a task containing several phases. The system has several optional work intensities such that it can complete more tasks under a higher work intensity, but the failure rate also increases. When the maximum difference of component states in each grid is less than a predetermined threshold, the system is balanced. When the system is unbalanced, or the total number of failed components in a grid exceeds a limit, it fails. To complete more tasks and reduce the loss caused by system failure, a joint policy of work intensity selecting and maintenance is proposed. A Markov decision process is used to describe the system operation process. The optimal results are calculated by the value iteration algorithm. Finally, a two-dimensional manufacturing system is taken as an example to verify the effectiveness of the proposed joint strategy.