Abstract
•Linear consecutive multi-state sliding window system is considered.•The system components are heterogeneous warm standby subsystems.•Algorithm for determining dynamic demand satisfaction probability is developed.•Event transition method and universal generating function are used.•Optimal element distribution and sequencing problem is formulated and solved.
Motivated by practical applications such as heating systems, radar, and sensor monitoring, this paper models and analyzes a linear consecutive multi-state sliding window system with warm standby components (CSWS-WS). The system contains n linearly ordered components, each being a warm standby configuration of multiple elements with heterogeneous time-to-failure distributions and nominal performances. Thus, depending on the currently operating (online) element, each component may exhibit multiple states, corresponding to different failure behaviors and performance rates. The system function depends on the accumulated performance (sum of performance rates) of r consecutive components, referred to as a r-sized window. The system is considered being failed if the accumulated performance in each of at least m consecutive overlapping r-sized windows is lower than a random demand. To evaluate the reliability (demand satisfaction probability) of a CSWS-WS, a probabilistic model is first presented to determine the dynamic performance distribution of each warm standby component; a universal generating function-based method is then suggested for obtaining the dynamic demand satisfaction probability (DSP). Based on the DSP evaluation, the optimal element distribution and sequencing problem is formulated and solved for the CSWS-WS system. As demonstrated through examples, solutions to the considered optimization problems can facilitate a proper choice of element distribution and activation sequencing, maxmizing the minimum instananeous DSP or expected DSP over a certain mission time.