BCMS⁴W-ST: On the Bi-directional Circular Multi-State System with Spatiotemporal Sliding Window for Sequential Tasks

In industrial applications, circular systems possess the natural ability to rotate bi-directionally, which essentially provides redundancy to maintain higher system reliability. This paper proposes a new model of bi-directional circular multi-state system with a spatiotemporal sliding window for sequential tasks (BCMS⁴W-ST). The system contains n mutually independent multi-state elements (MEs) in a circle and can rotate bi-directionally. The system functionality depends on the ability of r consecutive MEs starting from any ME in either counterclockwise or clockwise directions for completing pre-specified sequential tasks within a limited completion time. A universal generating function technique is employed to describe and evaluate the system reliability. The reliability model is built by considering feasible performance assignment schemes of involved consecutive MEs, and a dynamic programming algorithm is introduced to efficiently determine the assignment scheme with the shortest completion time. Numerical experiments have demonstrated the proposed system model and the suggested algorithm. Finally, the element sequencing optimization for BCMS⁴W-ST is investigated as a viable way to improve system reliability. The proposed model and method support reliability analysis and improvement of circular multi-state sliding window systems with bi-directional rotation mechanism for completing sequential heterogeneous tasks.