OPTIMAL DESIGN OF BINARY WEIGHTED k-OUT-OF-n SYSTEMS

In this paper, we consider the optimal design of the binary weighted k-out-of-n system. The binary weighted k-out-of-n: G system works if and only if the total utility of all working components is at least k. In the design process, we need to evaluate system reliability repetitively. The universal generating function (UGF) approach is used for this purpose when the system size is small or moderate. When the size of the system is large, the recursive approach is used, which is more efficient. Two optimal models are formulated. One is to minimize the expected total cost while guaranteeing the system reliability higher than a pre-specified value; the other is to maximize the system reliability with the constraints on total system cost. Genetic algorithms (GA) and Tabu Search (TS) methods are both used to solve the proposed optimization models. Since the key to a good TS algorithm is usually quite problem-specific policies and memory structures, there is no existing general TS tool available. Therefore more details of the TS approach used in this paper are discussed than the GA approach. The results obtained with these two methods are compared. The results illustrate that both methods are powerful tools for solving these kinds of problems. However TS is more efficient than GA in computation. The materials in this paper have been published in 19.