Multi-state k-out-of-n: F network system performance evaluation by considering a balance dependence mechanism

In recent years, the balanced system reliability models have attracted a lot of research interests because of its strong application potential, for example in the fields of unmanned systems, energy supply systems, and production systems, etc. Network models exist widely in reality, which gives birth to the research of equilibrium system model under network structure. This study extends the binary-state k-out-of-n model to a multi-state framework, where both the components and system could exhibit varying operational conditions. In specific, firstly, the definition of the k-out-of-n: F balanced system is given by introducing a multi-state system model in which the components could be fully operational, partially operational, or failed. Secondly, we describe the system balance condition which is redefined to maintain an equal number of operational components in different working levels across in an individual sector. Thirdly, the new reliability formulas will be derived that account for the system reliability, utilizing both the order statistics and Markov chain model techniques. Finally, numerical examples highlight the practical implications and improved realism of the proposed reliability models.