Expected Production of a Single Repairman Machine-Maintenance System with Overnight Repairs

Assuming that the repair time and the working time of each machine is exponentially distributed, and that the system operates for a time period of given length starting with all machines in working order, an expression is found for the expected number of machine hours worked. This is proportional to the expected production of the system. The expression is complicated to evaluate, so upper and lower bounds for it are derived, which are of a simpler form.