An Efficient Branch and Bound Algorithm for the Optimal Arrangement Problem in the Linear Consecutive-k-out-of-r-from-n:F System(<Special English Issue>-Information and Operations Management)

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  • Yamamoto Hisashi
    Faculty of System Design, Tokyo Metropolitan University
  • Akiba Tomoaki
    Information Management Engineering, Yamagata College of Industry and Technology
  • Yun Won Young
    Department of Industrial Engineering, Pusan National University

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Other Title
  • An Efficient Branch and Bound Algorithm for the 0ptimal Arrangement Problem in the Linear Consecutive-k-out-of-r-from-n:F System
  • Efficient Branch and Bound Algorithm for the 0ptimal Arrangement Problem in the Linear Consecutive k out of r from n F System

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A linear consecutive-k-out-of-n:F system consists of n components in a line. The system fails if and only if k or more consecutive components fail. A great deal of research work in this topic has been conducted since the beginning of the 1980s. The consecutive-k-out-of-r-from-n:F system is an extended system of a linear consecutive-k-out-of-n:F system. This system similarly consists of n linearly ordered components. The system fails if and only if there are at least k failed components among any r consecutive components. So, this system can represent quality control problems and inspection procedures, radar detection problems, and so on. The optimal arrangement problem in the linear consecutive-k-out-of-r-from-n:F system is to obtain the arrangement (optimal arrangement) that provides maximum system reliability within all the arrangements of components when all components don't necessarily have the same failure probability. In this paper, we propose an efficient algorithm based on a branch and bound method, for the optimal arrangement problem in the linear consecutive-k-out-of-r-from-n:F system. Our proposed algorithm conducts the following procedures (1) Searches only the arrangement that satisfies the necessary conditions for optimal arrangement, (2) Obtains reliability of the system and subsystems efficiently by "Malinowski and Preuss (1995)," and (3) Removes searches for arrangements that are no useful. We executed numerical experiments for solving an optimal arrangement problem in order to evaluate the proposed algorithm. From the results of actually solving the optimal arrangement using a computer, we showed the efficiency of our proposed algorithm, although the conclusions within the range of our executed experiments. We also show combinations of component failure probabilities that the proposed algorithm can solve more efficiently.

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