This paper proposes a new model that generalizes the multi-state sliding window system to the case involving sequential demands and time constraints. In this model, the system (named MSWS-SD&TC) contains n linearly or circularly arranged multi-state elements (MEs), and its function depends on the ability that each r-consecutive-ME group can meet the demands of sequential tasks subject to time constraints. The reliability model of the system is built with consideration of the optimal performance assignment scheme in each group of MEs. In order to effectively determine the optimal performance assignment scheme with minimum completion time in each r-consecutive-ME group, we develop a dynamic programming algorithm in this paper. We use a technique of universal generating function to represent the system states and evaluate the system reliability. Since the order of MEs has strong impact on the system reliability, we also investigate the optimal sequencing problem for the MEs in the system, and solve the problem with a genetic algorithm. Examples of evaluating system reliability and element sequencing optimization are presented for illustration.
- dynamic programming
- multi-state sliding window system
- optimal element sequencing
- sequential demands
- time constraint
- universal generating function