ABSTRACT
This chapter considers a repairable system with a repairman, who can take multiple vacations within and beyond the cost free warranty period. If the system fails and the repairman is on vacation, it will wait for inspection of failed unit until the repairman is available. When the repairman comes back from his vacation, he starts inspection immediately if the system waits for inspection to check whether the unit is failed due to the negligence of the users or not. If it failed due to the negligence of the users then system warranty is completed and all the charges of repairs are borne by the users; otherwise the failed unit is repaired cost free to the users. On the other hand, if the repairman comes back from his vacation and system is working well then he will wait idly for fail arrival. A mathematical model of the system is developed based on the Markov process and under this formulation; the failure, inspection, and repair rates of the system follow a negative exponential distribution. Various expressions which depict the performance of the system such as reliability of the system, Mean Time to System Failure (MTSF), availability, profit function, busy, vacation, and idle times of the repairman have been derived. Finally, the effect of various parameters has been analyzed on the system reliability and expected profit through an illustrative example.
