Reliability modeling and analysis for linear consecutive-k-out-of-n: F retrial systems with two maintenance activities

This paper focuses on a linear consecutive-k-out-of-n: F repairable retrial system with an unreliable repair facility, in which preventive maintenance (PM) and repair for working breakdowns are considered for the repair facility. When a component fails, it can be repaired immediately if the repair facility is idle. Otherwise, the failed one would enter the retrial orbit and try again according to the first in first out. Based on repair priority of key components, the steady-state probabilities of the system are derived by using Markov process theory and Crammer's rule. We analytically calculate steady-state indexes such as steady-state availability, steady-state failure frequency, and mean cycle time of the system. Furthermore, the Runge–Kutta method and the Laplace transform method are employed to obtain the reliability function and the mean time to first failure (MTTFF). Moreover, cost-effectiveness ratio (CER) analysis of the system is provided. Numerical experiments are conducted to illustrate the developed system model and perform influence analysis of PM on steady-state availability and CER for the models with and without PM.