Reliability for consecutive-[formula omitted]-out-of-[formula omitted]: F systems with shared components between adjacent subsystems

Abstract

Consecutive-k systems have well known for outstanding developments and extensive applications. In this paper, we propose consecutive-k-out-of-n: F systems with shared components between adjacent subsystems which extend the consecutive-k-out-of-n: F linear and circular models and the consecutive-kr-out-of-nr: F linear zigzag structure and circular polygon structure. They are referred to as an extension of linear zigzag structure and an extension of circular polygon structure respectively. The idea of computation for reliability is to cut the system into m subsystems and to get the reliability of every subsystem, then to obtain the system reliability in terms of reliabilities of all subsystems, the probability of occurrence of each event and the system structure. Based on this view, we obtain the reliability for the above two structures by combining the sum of disjoint products with finite Markov chain imbedding approach (FMCIA). A numerical example demonstrates the efficiency of the proposed method for our new models.