Reliability assessment of discrete-time k/n (G) retrial system based on different failure types and the δ-shock model

The k/n (G) system is a typical reliability system in engineering practice. However, research on this system under discrete-time and retrial conditions is still limited. This paper establishes a k/n (G) retrial system model under a discrete-time condition based on different failure types and the δ-shock model, whose objective is to investigate its various reliability measures and the relationship between measures and parameters. Two methodologies are utilized in this paper to evaluate the system’s various measures: the analytical method for the discrete-time Markov process and the Monte Carlo simulation method. The two methodologies are compared, and optimization is performed on certain measures concerning system parameters. A discrete PH distribution representation method for component lifetime under the δ-shock is presented, the relationship between various reliability measures of the system and various parameters is determined, and a novel approach for system reliability research based on the discrete PH distribution and the δ-shock is provided in this paper.