Problem $10-25($Algo$)$

Resistors for electronic circuits are manufactured on a high$-$speed automated machine. The machine is set up to produce a large run of resistors of $1,000$ ohms each. Use Exhibit $10\mathrm{.}13.$

To set up the machine and to create a control chart to be used throughout the run, $15$ samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three$-$sigma control limits$.$

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

Note: Round "Mean" to $\backslash (\backslash$mathbf$\{2\}\backslash )$ decimal places and "Range" to the nearest whole number. b$.$ Determine $\backslash (\backslash$overline$\{\backslash$bar$\{$X$\}\}\backslash )$ and $\backslash (\backslash$bar$\{$R$\}\backslash ).$

Note: Round your answers to $3$ decimal places.

c$.$ Determine the UCL and LCL for a $\backslash (\backslash$bar$\{$X$\}\backslash )$ chart.

Note: Round your answers to $\backslash (\backslash$mathbf$\{3\}\backslash )$ decimal places.

d$.$ Determine the UCL and LCL for $\backslash ($ R $\backslash )-$chart.

Note: Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Round your answers to $\backslash (\backslash$mathbf$\{3\}\backslash )$ decimal places.

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

Process is out of statistical control

Process is in statistical control