Fast Algorithm for Optimal Arrangement in Connected-(m-1, n-1)-out-of-(m, n):F Lattice System

Taishin NAKAMURA  Hisashi YAMAMOTO  Tomoaki AKIBA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2446-2453
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2446
Type of Manuscript: PAPER
Category: Reliability, Maintainability and Safety Analysis
connected-(r, s)-out-of-(m, n):F lattice system,  optimal arrangement,  system reliability,  branch and bound method,  

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An optimal arrangement problem involves finding a component arrangement to maximize system reliability, namely, the optimal arrangement. It is useful to obtain the optimal arrangement when we design a practical system. An existing study developed an algorithm for finding the optimal arrangement of a connected-(r, s)-out-of-(m, n): F lattice system with r=m-1 and n<2s. However, the algorithm is time-consuming to find the optimal arrangement of a system having many components. In this study, we develop an algorithm for efficiently finding the optimal arrangement of the system with r=m-1 and s=n-1 based on the depth-first branch-and-bound method. In the algorithm, before enumerating arrangements, we assign some components without computing the system reliability. As a result, we can find the optimal arrangement effectively because the number of components which must be assigned decreases. Furthermore, we develop an efficient method for computing the system reliability. The numerical experiment demonstrates the effectiveness of our proposed algorithm.