Q$1$

A process is in control with $\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})=100\frac{,}{b}ar(s)=1\mathrm{.}05,n=5.$ The process specifications are at $95+-10.$ The quality characteristic has a normal distribution. $($a$)$ Estimate the potential capability, $($b$)$ Estimate the actual capability, $($c$)$ How much could the fallout in the process be reduced if the process were corrected to operate at the nominal specification?

a$)$ potential capability

$C_P=\frac{\text{U}\text{S}\text{L}-LSL}{60}=\frac{10S-8S}{6(1\mathrm{.}12)}=2\mathrm{.}98,C_{PK},=$min$(\frac{\text{U}\text{S}\text{L}-}{30},\frac{-LSL}{36})$

$=\frac{S}{C_4}=\frac{1\mathrm{.}05}{0\mathrm{.}9400}=1\mathrm{.}12,=$min$(\frac{105-100}{3(1\mathrm{.}12)},\frac{100-85}{3(1\mathrm{.}12)})$

$,=$min$(1\mathrm{.}49,4\mathrm{.}47)$

$,=1\mathrm{.}49$

b$)$ actual capability