Reliability Modeling and Optimization of Circular Multi-State Sliding Time Window System with Sequential Demands

Abstract

This paper proposes a new model of circular multi-state sliding time window system with sequential demands (named CMSTWS-SD). This model is an extension of the multi-state sliding window systems with considering temporal window width defined by the required completion time. For the proposed model, the system contains n multi-state elements (MEs) arranged in circular structure, and any ME can be designated as the starting point for completing the pre-specified sequential tasks. The system function depends on its capability of completing the sequential tasks within the required mission time from any possible starting points. The reliability model of the CMSTWS-SD is formulated by investigating the performance assignment schemes of each elements group starting on different MEs and adopting the extended universal generating function (UGF) technique. We suggest an approach of states aggregation to reduce the computational burden caused by the raising number of system states. Furthermore, we develop a dynamic programming algorithm for determining the optimal performance assignment scheme with minimum completion time. Since the sequence of MEs strongly affects the system reliability of considered CMSTWS-SD, we further study the optimal element sequencing problem. Numerical experiments of the system reliability evaluation and the element sequencing optimization are conducted for illustration.