Reliability Analysis Of Gnedenko System With Vacation Of A Repairman

Series repairable system with warm standbys is an important system in reliability theory. Repairman is one of the essential parts of a repairable system, while the repairman who has vacation or is engaged in other work can have the important influence on the system reliability expressions and the economic benefit of the system. Therefore, it has theoretical significance and application value to consider Gnedenko system with repairman vacation.Firstly, new methods are employed to further research into Gnedenko system. System reliability and mean time to first failure of this system are obtained through analyzing system model. Availability and the failure frequency of this system are attained by utilizing broad Markov process theory and Laplace transform method.Secondly, Gnedenko system with repairman vacation is studied. Three models are set up in accordance with different vacation strategies: simple vacation Gnedenko system, multiple vacation Gnedenko system and K-vacation Gnedenko system. Some reliability expressions such as availability and the failure frequency of these systems are secured by utilizing broad Markov process theory and Laplace transform method. Moreover, the benefit of simple vacation Gnedenko system is discussed.Lastly, Gnedenko system that when the system fails the good part may be invalid and Gnedenko system that the time of the repairman vacation time is distributed generally are both studied. Some important reliability indexes are obtained, such as the mean time to first failure and the Laplace transformation of the availability.