Reliability Analysis Of Repairable System With Warm Standbys And Vacation Policy

Multi-unit repairable system with warm standby units is a typical system in reliability theory. This system widely uses in many fields such as power systems, aviation systems and industrial systems. Repairman is one of the essential parts of a repairable system. In many real world, repairman can take vacation or perform some secondary tasks which can have the important influence on the system reliability measures and the economic benefit of the system. Therefore, it has the important theory significance and the application value to consider the repairman takes vacation in multi-unit repairable system with warm standby units.This paper studies three multi-unit repairable system models with warm standby units and repairmen's vacations. These models are new ones, which are the modificatory models or the spread of the related models in the references and have the important research value.Firstly, we study a multi-unit repairable system with warm standby units and N-policy multiple vacations of a single repairman. Firstly, using Markov process theory, we develop the differential-difference equations of the state probabilities of the system. Secondly, taking Laplace transform of the differential-difference equations, we obtain the Laplace expressions of the state probabilities. Finally, we obtain the explicit expressions of the state probabilities by computing the eigenvalues of the matrix and the inverse of the Laplace transform. Based on these expressions, we obtain the explicit expressions of the reliability and the mean time to first failure of the system. Numerical results to highlight the effects of various system parameters on the reliability measures of the system have been provided.Secondly, a multi-unit repairable system with warm standby units and N-policy vacations of two repairmen is studied. The explicit expressions of the state probabilities are obtained by Markov process theory and the inverse of the Laplace transform. Based on these expressions, we obtain the explicit expressions of the reliability and the mean time to first failure of the system. In addition, we give the method to calculate the reliability and the mean time to first failure of the system.Finally, a multi-unit repairable system with warm standby units and two repairmen is studied. One repairman never takes vacation and the other repairman takes N-policy multiple vacations. The analysis of this model is mainly from view point of the reliability theory. Using Markov process theory and the Laplace transformation method, we obtain the explicit expressions of the reliability and the mean time to first failure of the system. In addition, using recursive method, we derive the explicit expressions of the steady state availability, the steady state failure frequency of the system and some queue performance measures such as the average number of failed units in the system, etc.