Consider the example in Section $8\mathrm{.}8.$ The arrival rate of jobs is $13\mathrm{.}5$ jobs per hour $($with

c$2$

a $=1)$ to a workstation consisting of five machines. Each machine nominally takes $0\mathrm{.}3$

hour per job with a natural CV of $1$

$2($that is$,$ c$2$

$0=0\mathrm{.}25).$ The mean time to failure for any

machine is $36$ hours, and repair times are exponential with a mean time to repair of

$4$ hours.

$($a$)$ Show that the SCV of effective process times is $2\mathrm{.}65.$

$($b$)$ What is the utilization of a single machine when it is allocated one$-$fifth of the demand

$($that is$,2\mathrm{.}7$ jobs per hour$)$ assuming ca is still equal to $1?$

$($c$)$ What is the utilization of the station with an arrival rate of $13\mathrm{.}5$ jobs per hour?

$($d$)$ Compute the mean cycle time at a single machine when allocated one$-$fifth of the

demand.

$($e$)$ Compute the mean cycle time at the station serving $13\mathrm{.}5$ jobs per hour.