Tomoaki Akiba

Recursive formulas for the reliability of multi-state consecutive-k-out-of-n:G systems

In this paper, we provide an algorithm for evaluating the system state distribution for any multi-state consecutive-k-out-of-n:G system including the decreasing multi-state G system, the increasing multi-state G system, and other G systems. We evaluated our proposed algorithms in terms of the orders of computation time, and memory requirement. Furthermore, we conducted a numerical experiment to determine the actual computation time. Our proposed algorithm is more effective for systems with a large n.

Proposal of Simulated Annealing Algorithms for Optimal Arrangement in a Circular Consecutive-k-out-of-n: F System

Abstract A circular consecutive-k-out-of-n: F system consists of n components arranged along a circular path. This system fails if and only if k or more consecutive components fail. As the number of components n increases, the amount of calculation to solve optimal component arrangement problems in this kind of system exactly would be too much. In this paper, we propose two types of simulated annealing algorithms to obtain quasi optimal solutions for such problems. We compare their performances with a genetic algorithm proposed in the previous research work and demonstrate the advantage of our proposed algorithms through numerical experiments.

Evaluating methods for the reliability of a three‐dimensional k‐within system

Purpose – For the considered system, an enumeration method is applicable to evaluate the exact system reliability only for very small‐sized systems, because, when the size of system is large, it takes huge execution time. Therefore, the paper provides approximate values for the system reliability as useful for calculating the reliability of large systems in a reasonable execution time.Design/methodology/approach – The paper provides upper and lower bounds of the system reliability, and limit theorem for the reliability of our considered system in i.i.d. case.Findings – The paper experimentally finds that the proposed upper and lower bounds are effective when component reliabilities close to one or the value of k becomes larger. Next, it concludes approximate values for approximate equation derived from the limit theorem are always smaller than lower bound through numerical experiments.Research limitations/implications – The upper and lower bounds for the reliability of a system can be calculated by using ...

Analysis for a trend on the optimal arrangements in a multi-state consecutive-k-out-of-n:F system

In traditional reliability theory, both the system and its components are allowed to take two possible states: either working or failed. In the binary context, a system with n components in sequence is called a consecutive-k-out-of-n:F system if the system fails whenever at least k consecutive components in the system fail. Many studies have appeared over the years dealing with the reliability evaluation of binary consecutive-k-out-of-n:F system. For consecutive-k-out-of-n:F system, one of the most important problem in this system is the optimal arrangement problem wherein the solution is obtained by the arrangement of components with maximum system reliability. On the other hand, in the multi-state consecutive-k-out-of-n:F system, both the components and the system are allowed to be in M+1 possible state. One of the important problem in the multi-state consecutive-k-out-of-n:F system is the optimal arrangement problem wherein the solution is obtained by the arrangement of components with maximum expectation of system states. (Note: k means the number of consecutive components, whose failed components lead to the system failure. Though the number is not a scalar and should be expressed as a vector (k1,k2,…,kM).) In general, the optimal arrangements depend on the values of component state probabilities. It is known, however, that for some case, optimal arrangements do not depend on the values of component state probabilities but on the ranks of component state probabilities. In this study, we consider optimal component arrangement for a multi-state consecutive-k-out-of-n:F system which maximize the expectation of the system state when these components are arranged to the positions in the system. First, we investigated characteristics of optimal arrangements in multi-state consecutive-k-out-of-n:F systems when M=3 and maximum kl (l=1,2,3) is 2, by using analytical approach. We proposed characteristics of optimal arrangement in the systems when n=3, 4 and 5. From these results, we obtained characteristics and trends of conditional optimal arrangements with M=3 and maximum kls are 2. Next, we investigated characteristics of optimal arrangements in multi-state consecutive-k-out-of-n:F systems by using heuristic approach. From these results, we obtained a trend of optimal arrangements with other parameters.

An Approach for the Fast Calculation Method of Pareto Solutions of a Two-objective Network

The shortest path problem is a kind of optimization problem and its aim is to find the shortest path connecting two specific nodes in a network, where each edge has its distance. When considering not only the distances between the nodes but also some other information, the problem is formulated as a multi-objective shortest path problem that involves multiple conflicting objective functions. The multi-objective shortest path problem is a kind of optimization problem of multi-objective network. In the general cases, multi-objectives are rarely optimized by a solution. So, to solve the multi-objective shortest path problem leads to obtaining Pareto solutions. An algorithm for this problem has been proposed by using the extended Dijkstras algorithm. However, this algorithm for obtaining Pareto solutions has many useless searches for paths. In this study, we consider two-objective shortest path problem and propose efficient algorithms for obtaining the Pareto solutions. Our proposed algorithm can reduce more search space than existing algorithms, by solving a single-objective shortest path problem. The results of the numerical experiments suggest that our proposed algorithms reduce the computing time and the memory size for obtaining the Pareto solutions.

A Fast Calculation Method for the Partial Group of All Pareto Solutions at a Three-Objective Network

Abstract The multi-objective network model can be applied to common problems with many conditions, for example, optimal routing of a network connection to the Internet services, optimally scheduling of a production and distribution systems, and multistage-structured modeling for supply chain management systems, etc. The shortest path problem is an optimization problem for finding the shortest path connecting two specific nodes of a directed or undirected graph. When considering not only the distances between the nodes but also other information, for example, toll, fuel cost, or gradient, the problem is formulated as a multi-objective shortest path problem that involves multiple conflicting objective functions. To solve the optimization problem of multi-objective network is difficult because the multiple objectives have to be simultaneously optimized. Thus, few algorithms for this problem have been proposed. In this study, we use a three-objective shortest path problem to find the shortest path between two terminal nodes on a network, and we propose three efficient algorithms for obtaining the Pareto solutions based on the extended Dijkstra’s algorithm. We use our algorithms to find the partial group of all Pareto solutions. The results of the numerical experiments suggest that the proposed algorithms reduce the computing time and the memory size for obtaining the Pareto solutions. In addition, we show the algorithms could find almost set of solution in the Pareto solutions.