Reliability and Optimization for k-out-of-n: G Mixed Standby Retrial System with Dependency and J-Vacation

Abstract

Based on the design and potential application of wind-solar storage intelligent power generation systems in engineering practice, this paper develops a novel reliability model of k-out-of-n: G mixed standby retrial system with failure dependency and J-vacation policy. The working components in the system have redundant dependencies. When any component of the system fails and the repairman is working or on vacation, the failed component goes into the retrial space. If the retrial space has no failed components, the idle repairman goes on vacation, which may last for up to J consecutive vacations, until at a minimum one failed component appears in the retrial space on a vacation return. Firstly, the performance indexes of the system under steady state are analyzed based on the Markov process theory. Secondly, an algorithm for modelling the failure process of the proposed model is developed through a Monte Carlo method, and numerical solutions for the reliability function and mean time to first failure (MTTFF) are presented. Then, some numerical examples are provided to demonstrate the influence of different parameters on the system reliability indexes. Finally, a system cost optimization model based on availability control is developed, and the optimal component configuration schemes for systems with no vacations and different maximum numbers of vacations J are compared and analyzed by genetic algorithm (GA).