Mathematical Analysis of Machine repair problem with common cause failure, hot spares and multiple repairmen

We study the machine repairable system comprising M operating machines, H spares and more than one repairman where “the partial server vacation” is applied on some of the repairmen. In this system, the first repairman never takes vacation and always available for servicing of failed machines while other repairmen goes to random length vacation whenever the number of failed machines are less than N, N +1 respectively. Machines may breakdown individually or due to common cause according to Poisson process. Vacation time and service time of repairmen is follows the exponential distribution. Recursive approach is used to obtain the steady state probabilities. A cost model is developed to determine the optimum value of failed machine maintaining the system availability. Sensitivity analysis is investigated for optimal conditions and also analyzes the reliability characteristics of the system.We study the machine repairable system comprising M operating machines, H spares and more than one repairman where “the partial server vacation” is applied on some of the repairmen. In this system, the first repairman never takes vacation and always available for servicing of failed machines while other repairmen goes to random length vacation whenever the number of failed machines are less than N, N +1 respectively. Machines may breakdown individually or due to common cause according to Poisson process. Vacation time and service time of repairmen is follows the exponential distribution. Recursive approach is used to obtain the steady state probabilities. A cost model is developed to determine the optimum value of failed machine maintaining the system availability. Sensitivity analysis is investigated for optimal conditions and also analyzes the reliability characteristics of the system