A lower bound of reliability calculating method for lattice system with non-homogeneous components. (August 2019) - Lin, Cong; Zeng, Zhaoyang; Zhou, Yan; Xu, Ming; Ren, Zhanyong
Highlights: A general two-dimension lattice system, " k -within- r × s -out-of- m × n " model, with non-homogeneous components is proposed. A lower bound of system reliability calculating method is developed by employing finite Markov chain imbedding approach. The system, in which the components are positioned in the cylinder shape, can be translated into the two-dimension lattice model to obtain the system reliability. Abstract: The lattice system in which the components are regularly distributed in a two dimensional area are studied due to the fact that it can be used to describe the system model in various applications, e.g., safety monitoring system, phased array radar, design of array antenna or liquid crystal display. In the previous research, the common shared assumption is that the lattice system is composed with homogeneous components. However, when we conduct a reliability evaluation of the system, this hypothesis is easy to be violated, because maintenance action may take upon to replace the aging components with new ones, which leads the residual life of the components are different from each other. In this paper we employ finite Markov chain imbedding approach and use the " k -within- r × s -out-of- m × n " model to obtain a lower bound calculating method for reliability of the lattice system with non-homogeneous components. By changing parameters or adding conditions, we propose some transformed models from the original one. Some numerical examples are applied to illustrate how to compute the reliability of these models and address some property of the lattice system.