Problem $10-29($Algo$)$

The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five were taken

at one$-$hour intervals. Use three$-$sigma control limits$.$ Use Exhibit $10\mathrm{.}13.$

a$.$ Calculate the mean and range for the above samples.

Note: Do not round intermediate calculations. Round your answers to $3$ decimal places.

b$.$ Determine $x^{?}=$ and $\frac{?}{\text{b}\text{a}\text{r}}(R).$

Note: Do not round intermediate calculations. Round your answers to $3$ decimal places.

c$.$ Determine the UCL and LCL for a $\stackrel{}{x}-$chart.

Note: Do not round intermediate calculations. Round your answers to $3$ decimal places.

d$.$ Determine the UCL and LCL for $R-$chart.

Note: Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Do not round intermediate calculations. Round your

answers to $3$ decimal places.

e$.$ What comments can you make about the process?

Process is in statistical control.

Process is out of statistical control.