Problem $1$:

X$($average$)=23$ MegOhms

UCLx $($Upper Control Limit$)=24$ MegOhms

Sample size $=$ n $=20$

New specification: LSL $=17$ MegOhms $($Lower Specification Limit$),$ no USL mentioned.

UCLx $=$ X$+3$S $=>$ S $=($UCLx $-$ X$)/3=(2423)/3=0\mathrm{.}333$

S $=0\mathrm{.}333$

S $=\backslash$sigma $/$ sqrt $\{$n$\}=>\backslash$sigma $=$ S x sqrt $\{$n$\}=0\mathrm{.}333$ x sqrt $\{20\}=0\mathrm{.}333$ x $4\mathrm{.}472=1\mathrm{.}489$

$\backslash$sigma $=1\mathrm{.}489$

CpK $=($X$-$ LSL$)/3\backslash$sigma $=(2317)/3$ x $1\mathrm{.}489=6/4\mathrm{.}467=1\mathrm{.}343$

CpK $=1\mathrm{.}343$

$\backslash$mu $=$ X$$

Z $=(\backslash$mu $$ LSL$)/\backslash$sigma $=(2317)/1\mathrm{.}489=6/1\mathrm{.}489=4\mathrm{.}029$

Z $=4\mathrm{.}029$

Summary:

$\backslash$sigma $=1\mathrm{.}489$

CpK $=1\mathrm{.}343$

Z $=4\mathrm{.}029$

Based on this calculation how do I calculate the reject rate in ppm$?$