Consider an automated security test $($e$.$g$.,$ explosives$-$scanning$)$ station for checked baggage at CVG$,$ the Cincinnati$-$Northern Kentucky airport. The security test workstation is composed of a single machine that has a base$-$case test capacity of $5$ bags per minute. $($It takes, on average, $\mathrm{.}20$ minutes to process a bag.$)$ The squared coefficient of variation, SCV$,$ of the base processing time of the test operation is $0\mathrm{.}5625,$ making the standard deviation equal to $0\mathrm{.}15.$ The machine is subject to random failure with mean time to failure $($MTTF or uptime$),$

$=7$ hours and mean time to repair $($MTTR or downtime$),$

$=40$ minutes. The repair time is exponentially distributed with SCV$,$

$=1.$

Delays caused by the machine breakdowns are frowned upon by customers because they could cause customers to miss their flights. The department has been given $$10,000$ dollars that they can spend on improvements and they have $2$ choices. Which of these choices would you recommend?

Choice $1$: Increase the mean time to failure $($MTTF or uptime$),$

$=14$ hours with all other factors remaining the same.

Choice $2$: Decrease the mean time to repair $($MTTR or downtime$),$

$=20$ minutes. The new repair time is estimated to be exponentially distributed with SCV$,$

$=1.$ Leave all other factors the same as in the initial problem, i$.$e $$ MTTF would be equal to $7$ hours with this scenario.

In the answer prompt, explain which choice you would recommend and why.