A study on evaluating and designing method for extended consecutive-k-systems

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A linear or circular consecutive-k-out-of-n : F system and its related systems have been extensively studied since the early 1980s. These systems are specified by the number n of components and by the minimum number k of consecutive failed components that could cause system failure. This type of system can be regarded as a one-dimensional reliability model and can be extended to multi-dimensional versions. This system might be used in reliability models for "Sensor system by using Satellite", "Feelers for measuring temperature on reaction chamber" and "TFT Liquid Crystal Display system with 360 degree wide area."Furthermore, the states of the systems and their components are assumed to take more than two different levels, ranging from perfectly working to completely fail, in many practical situations. Therefore, researchers have extended the definitions of the binary consecutive-k system to the multi-state cases.In this study, we defined extended consecutive-k systems for multi-dimensional case and multi-state case, which are more applicable to real world. For these models, we proposed 1) efficient algorithms for the reliability of multi-dimensional consecutive-k systems, 2) upper and lower bounds of the reliability and limit theorems of the large multi-dimensional consecutive-k systems, 3) efficient algorithms for the system state distribution of multi-state consecutive-k systems. One of the most important problems for this system is to obtain the optimal component arrangement that maximizes the system reliability. Furthermore, for optimal arrangement problems of a circular consecutive-k system, we proposed 4) evaluation methods for solving this problem, based on Genetic Algorithm.