A process is in statistical control with $\stackrel{}{x}=199$ and $\frac{?}{\text{b}\text{a}\text{r}}(R)=3\mathrm{.}5.$ The control

chart uses a sample size of $n=4.$ Specifications are at $200+-8.$ The quality

characteristic is normally distributed.

$($a$)$ Estimate the potential capability of the process.

$($b$)$ Estimate the actual process capability.

$($c$)$ How much improvement could be made in process performance if the

mean could be centered at the nominal valuea$)$If you were interested in protection for acceptance of a single lot from a vendor with whom you do

not expect to conduct much business, what criteria would you select, and why?

b$)$ The length of connector pins has an upper specification limit of $45mm$ and a lower specification limit

of $40mm.$ It is desirable that lots with a mean such that $8\%$ of the product is nonconforming, either

above the upper specification limit or below the lower specification limit$,$ be accepted $6\%$ of the time.

We wish to accept lots with a mean of $42\mathrm{.}5mm$ with a probability of $0\mathrm{.}94.$ The distribution of the length

of the connector pin is normal, with a standard deviation of $0\mathrm{.}8mm.$ Find the parameters of a variable

sampling plan and describe its operation.