Control charts, specifically the $x$ bar $(\stackrel{}{x})$ and $R$ charts, are often used in statistical process control $($SPC$)$ to monitor the variability and central tendency of a process over time. Consider a scenario in the manufacturing process for a specific component where you are monitoring the diameter of a manufactured bolt. The diameter measurements of bolts at regular intervals were collected from the manufacturing process. Five samples of data were collected daily to monitor the quality of the production process for the bolt, as shown in Table $2.$

Table $2$: Bolt Measurement Data

$\backslash$table$[[$Day $1,$Day $2,$Day $3,$Day $4,$Day $5,$Day $6,$Day $7],[15\mathrm{.}04,15\mathrm{.}02,15\mathrm{.}03,15\mathrm{.}00,15\mathrm{.}01,15\mathrm{.}00,15\mathrm{.}01],[15\mathrm{.}08,15\mathrm{.}00,15\mathrm{.}02,15\mathrm{.}00,14\mathrm{.}99,14\mathrm{.}99,15\mathrm{.}01],[15\mathrm{.}02,14\mathrm{.}97,15\mathrm{.}00,15\mathrm{.}02,14\mathrm{.}98,14\mathrm{.}98,15\mathrm{.}02],[15\mathrm{.}03,14\mathrm{.}96,14\mathrm{.}99,15\mathrm{.}01,15\mathrm{.}00,15\mathrm{.}00,15\mathrm{.}00],[15\mathrm{.}00,15\mathrm{.}00,14\mathrm{.}96,15\mathrm{.}09,15\mathrm{.}01,15\mathrm{.}01,15\mathrm{.}06]]$

$($a$)$ Calculate all the control limits for the $x$ bar $(\stackrel{}{x})$ and $R$ charts.

$(10)$

$($b$)$ Plot the data from Table $2$ into the $x$ bar $(\stackrel{}{x})$ and $R$ charts.

$(8)$

$($c$)$ Interpret the results obtained from the control charts.

$(2)$

$($Total $/$ Jumlah: $20)$