Performance Analysis Of The Machine Repairable Problem With Warm Standbys Under Vacations

Machine Repairable Problems with warm spares have important applications in reallife, such as in manufacturing system, industrial system and power system and so on.Models of Machine Repairable Problems with vacation policies and warm spares areconsidered in the paper. Moreover, the phenomenon of balking and reneging of failurespares and systems with many repairmen are considered. Then two new models are set up.They are extension of the previous related models. They are more practical and can depictmany practical problems better.Firstly, this paper studies steady-state performances of a machine repairable systemwith warm spares plus balking and reneging under multiple synchronous vacations.Steady-state probability equations are obtained by Markov process method, and accurateexpressions of steady-state probability are derived by using blocked matrix methods. Thena cost model is developed to determine the optimal number of servers to minimize thetotal expected cost of the system per unit time. Numerical analysis is also presented.Secondly, steady-state performances of a machine repairable system with warmspares plus balking and reneging under N-policy vacations are studied. Steady-state proba-bility equations are obtained by Markov process method and accurate expressions of thesteady-state probability are derived by using blocked matrix methods. Then a profit modelis developed in order to determine the optimal values of the number of spares and thenumber of repairmen simultaneously. Numerical analysis is also finished.Finally, transient performances of a machine repairable system with warm spares plusbalking and reneging under N-policy vacation are studied. Differential-difference equatio-ns of state probabilities are obtained by Markov process theory, and accurate expressionsof the failure state probability are derived by using matrix theory and inverse of Laplace-transform. Then some performance measures of the system such as instantaneous availabi-lity, instantaneous breakdown frequency and reliability and so on are presented. Finally,numerical results and influence of time on instantaneous availability, instantaneous break-down frequency and reliability are presented by numerical methods.