A process is in control with $\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})=50$ and $\frac{?}{\text{b}\text{a}\text{r}}(s)=3.$ The process specifications are at $45+-5.$ The sample size

$n=4.$

$(1)$ Estimate the potential capability $C_p$

$(2)$ Estimate the actual capability $C_{pk}$

$(3)$ Estimate $C_{pm}$

$(4)$ Estimate the process fraction of nonconforming.

$(5)$ If we move the process mean to $45,$ repeat the questions $(1)-(4)$