Optimal replacement policy for a repairable system with multiple vacations and imperfect fault coverage

• We investigate repairable system with imperfect coverage having multiple vacations.
• By assuming geometric process, the reliability indices of the system are derived.
• We propose replacement policy maximizing expected profit rate after long run time.

The present investigation deals with the reliability analysis of a repairable system consisting of single repairman who can take multiple vacations. The system failure may occur due to two types of faults termed as major and minor. When the system has failed due to minor faults, it is perfectly recovered by the repairman. If the system failure is due to major faults, there are some recovery levels/procedures that recover the faults imperfectly with some probability. However, the system cannot be repaired in ‘as good as new’ condition. It is assumed that the repairman can perform some other tasks when either the system is idle or waiting for recovery from the faults. The life time of the system and vacation time of the repairman are assumed to be exponential distributed while the repair time follows the general distribution. By assuming the geometric process for the system working/vacation time, the supplementary variable technique and Laplace transforms approach are employed to derive the reliability indices of the system. We propose the replacement policy to maximize the expected profit after a long run time. The validity of the analytical results is justified by taking numerical illustrations.