Reliability analysis of 6-component lattice load-sharing Markov repairable system with spatial dependence

Abstract

This paper proposes a new model that generalizes the traditional Markov repairable system to the case of spatial dependence among components. The components of the system are identical and arranged in two lines and consist of a lattice. The performance of each component depends on its spatial "neighbours" and the number of failed components in other lines. Markov process is adopted to model the performance of the system. The state space and transition rate matrix corresponding to a 6-component lattice load-sharing system with spatial dependence are presented. Availability of the system is obtained via Markov theory and Laplace transform method. A numerical example is given to illustrate the results in this paper. The states of the system are partitioned into four state sets: security, degraded, warning, and failed. The probabilities of visiting to four state sets are also discussed in the numerical example. The work might provide a basis for the reliability analysis of load-sharing systems with interacting components that themselves be arranged in some two-dimensional spatial pattern.