Setup time on a certain production machine is $3\mathrm{.}0$ hours. The batch size is $36$ parts, and the operation cycle time is $2\mathrm{.}5$min. Parts are processed sequentially. The reliability of this machine is characterized by a mean time between failures of $47$ hours and a mean time to repair of $48$min. The average hourly production rate of the machine is $8\mathrm{.}0$ pieces per hour. Taking into account the availability of the machine, determine its average hourly production rate $($pieces per hour$).$