Reliability Analysis of Die Casting Machine System Having Two Types Repair Facility With Condition of Rest

We are taking two high pressure die casting machines case, initially the primary unit is working while the second unit is at cold standby, non priority is standby mode the unit cannot fail in standby mode. All the state possibilities for the system have been discussed. in up states and down states. On failure of the primary unit, standby and secondary unit is operative and failed unit is put under repair immediately. The secondary unit may be working to certain time called maximum allowable operative time. The maximum allowable operative time is over the second unit is put under rest if the primary unit is in progress. In this mode two types of repair facility is considered one ordinary repairman and other expert repairman. The expert repairman is only need based when the ordinary repairman fails to repair the failed primary unit. Secondary unit is always repaired by ordinary repairman. The Failure time of primary as well as secondary unit are exponentially distributed but with different parameters. The repair time distribution of primary unit is arbitrary for both expert repairman and ordinary repairman with different probability distributions. The repair time of standby unit follows exponential distribution. The distribution of rest time, maximum allowable operative time and patience time of ordinary repairman are also assumed to follow exponential distribution distributions with different parameters. Using mean time to system failure, steady state, availabilities, expected no of visit of the system, system behavior & profit function have been discussed in all possible cases.