Shock Model of K/N: G Repairable Retrial System Based on Discrete PH Repair Time

A discrete time modeling method is employed in this paper to analyze and evaluate the reliability of a discrete time K/N: G repairable retrial system with Bernoulli shocks and two-stage repair. Lifetime and shocks are two factors that lead to component failure, and both of them can lead to the simultaneous failure of multiple components. When the repairman is busy, the newly failed component enters retrial orbit and retries in accordance with the first-in-first-out (FIFO) rule to obtain the repair. The repairman provides two-stage repair for failed components, all of which require basic repair and some of which require optional repair. The discrete PH distribution controls the repair times for two stages. Based on discrete time stochastic model properties, priority rules are defined when multiple events occur simultaneously. The state transition probability matrix and state set analysis are used to evaluate the system performance indexes. Numerical experiments are used to illustrate the main performance indexes of the developed discrete time model, and the impact of each parameter variation on the system indexes is examined.