Reliability analysis of consecutive -ks-outs-of-ns: F system with a circular polygon structure considering subsystems balance in shock environment

We develop a reliability model for a consecutive-ks-out-of-ns:F system characterized by a circular polygon structure operating in a shock environment, which is modeled as a homogeneous absorbing Markov process. This model enhances traditional system structures, making it more applicable to real-world engineering scenarios. Such systems are commonly found in applications like drone swarms, data transmission, and communication networks. Specifically, three types of random external shocks are considered, component failures may occur when an extreme shock arrives, or when the number of effective shocks reaches a fixed value. The balance of subsystems is assessed based on the operational states of all components within each subsystem. To estimate the corresponding state probability functions and other reliability metrics, we employ a two-step finite Markov chain imbedding approach along with phase-type distributions. A Monte-Carlo simulation algorithm to obtain the first failure time of the system. Finally, we present a numerical example involving drone swarms to demonstrate the practical application and effectiveness of the proposed model.