I am using the CRE question bank for preparing the exam, and this one has been bothering me:
A system has an exponential repair distribution with MTTR=4 hrs. To maintain warranty, a two hour preventive maintenance must be performed every 200 operating hours. A crew size of two is always used for maintenance and repair. The failure distribution follows an exponential distribution with an MTBF of 500 hours. What is the long term expected (maintenance + repair) hours per operating hour of this equipment?
The correct answer was given as
[(200/500) repairs/per 200 oper.hrs x 2crew x 4hrs MTTR +2 x 2 (4 hours of maintenance/200 oper.hrs)/200 hrs =0.036
I have two doubts:
1 . Why the number of repairs for 200 oper.hrs is calculated as 200/500? Shouldn't it be 1-exp(-200/500) instead?
2 . Why does the usage of 2 crews matter? We are calculating the time that the system is not available, not the resource needed for keeping system operation, why we should multiple 2 when 2 crews are needed for maintenance/repair?
Would anyone be able to provide convincing clarifications for this? Thank you!