Problem $4.$ A company has developed four different coating processes. The table below gives the specifications and the manufacturing process mean and standard deviation for each process.

a$.$ Please determine the $C_{pk},$ FTY $($First Time yield$)$ and the DPU $($Defects Per Unit$)$ for each process.

b$.$ If each of these processes coating were applied sequentially to a single surface, show the overall $C_{pk},$ FTY$,$ and DPU

PROCESS

MYLAR

SILICONE

VAPOR DEPOSIT

SPRAY OVERALL:

SPECIFICATIONS

NOM

$0$

$0$

$0$

$0$

PROCESS

MEAN SIGMA

$0\mathrm{.}0003$

$0\mathrm{.}0100,0\mathrm{.}0040$

$0\mathrm{.}0080,0\mathrm{.}0040$

$0\mathrm{.}0030,0\mathrm{.}0005$

PERFORMANCE

$C_{PK}$ FTY DPU