$8\mathrm{.}1.$ A process is in statistical control with $\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})=20$ and $s=1\mathrm{.}2.$ Specifications are at $LSL=16$ and USL$=24.$

$($a$)$ Estimate the process capability with an appropriate process capability ratio.

$($b$)$ Items that are produced below the lower specification limit must be scrapped, while items that are above the upper specification limit can be reworked. What proportion of the process output is scrap, and what proportion is rework?

c$)$ Suppose that scrap is four times as expensive as rework. Does this suggest that moving the process center could reduce overall costs? What value of the

process target would you recommend?

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