A fabrication plant operates a single process technology with the following data:

Layer Actual CT Std Dev of Actual CT Standard CT

$12\mathrm{.}30\mathrm{.}91\mathrm{.}4$

$22\mathrm{.}00\mathrm{.}81\mathrm{.}2$

$32\mathrm{.}41\mathrm{.}11\mathrm{.}3$

$42\mathrm{.}21\mathrm{.}11\mathrm{.}1$

$52\mathrm{.}10\mathrm{.}91\mathrm{.}3$

$61\mathrm{.}40\mathrm{.}50\mathrm{.}9$

Layers $1$ through $5$ end with a photo step, while layer $6$ ends at fab out.

In a computer simulation of the plant, the average number of lots being processed at any given

time was $72.$

$($a$)$What was the average active WIP level in the simulation?

$($b$)$What production rate was assumed in the simulation?

$($c$)$Assume the target cycle time is $12$ days and the production rate is the same as in

the simulation. Recommend target WIP levels by layer.

$($d$)$ Suppose there are two $12-$hour shifts per day and suppose actual WIP distribution

at the start of a shift is as follows: