Consider a three$-$station line with single$-$machine stations. The average processing times on stations $1,2,3$ are $15,12,$ and $14$ minutes, respectively. However, station $2$ is subject to random failures, which cause its fraction of uptime $($availability$)$ to be only $75$ percent. $($a$)$ Which station is the bottleneck of this line? $($b$)$ What are the bottleneck rate r b$,$ raw process time T$0,$ and critical WIP W$0$ for the line? $($c$)$ If availability of station $2$ is reduced to $50$ percent, what

d$)$ If station $2$s fraction of

uptime is $,$ where $0<0\mathrm{.}8.$ What is $$ of this $3-$station line? If $0\mathrm{.}8<1,$ what

is $?"$

Please answer d$)$

Hopp, Wallace J$.$; Spearman, Mark L$..$ Factory Physics $($p$.260).$ Waveland Pr Inc. Kindle Edition.