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

自20世纪80年代初以来，线性或循环的n中取k：F系统及其相关系统得到了广泛的研究。这些系统由组件的数量n和可能导致系统故障的连续故障组件的最小数量k指定。这种类型的系统可以被看作是一个一维的可靠性模型，并可以扩展到多维版本。该系统可用于“卫星传感器系统”、“反应室温度测量传感器”和“360度宽TFT液晶显示系统”的可靠性模型。此外，在许多实际情况下，系统及其组件的状态被假定为两个以上的不同水平，从完美工作到完全失败。因此，研究者们将二元k-召唤系统的定义扩展到了多状态的情形，本研究定义了更适用于真实的世界的多维情形和多状态情形的扩展k-召唤系统。对于这些模型，我们提出了1）多维k-召唤系统可靠性的有效算法，2）大型多维k-召唤系统可靠性的上下界和极限定理，3）多状态k-召唤系统状态分布的有效算法。该系统的最重要的问题之一是获得最大化系统可靠性的最佳组件布置。此外，针对循环k-召唤系统的最优安排问题，提出了4）基于遗传算法的求解方法。

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.