Please solve the following problems related to Control chart $($Chapter $3)$

ABC Inc. presents the length in centimeters of one part from the following table. Please calculate the Upper Control Limit $($UCL$)$ and Lower Control Limit $($LCL$)$ for both x$-$bar and $R-$chart.

Do you think the process is under control, why?

Table $1.$

$\backslash$table$[[$Sample #$,$Observation $1,$Observation $2,$Observation $3,$Observation $4],[1,0\mathrm{.}486,0\mathrm{.}499,0\mathrm{.}493,0\mathrm{.}511],[2,0\mathrm{.}499,0\mathrm{.}506,0\mathrm{.}516,0\mathrm{.}494],[3,0\mathrm{.}496,0\mathrm{.}5,0\mathrm{.}515,0\mathrm{.}488],[4,0\mathrm{.}495,0\mathrm{.}506,0\mathrm{.}483,0\mathrm{.}487],[5,0\mathrm{.}472,0\mathrm{.}502,0\mathrm{.}526,0\mathrm{.}469],[6,0\mathrm{.}473,0\mathrm{.}495,0\mathrm{.}507,0\mathrm{.}493],[7,0\mathrm{.}495,0\mathrm{.}512,0\mathrm{.}49,0\mathrm{.}471],[8,0\mathrm{.}525,0\mathrm{.}501,0\mathrm{.}498,0\mathrm{.}474],[9,0\mathrm{.}497,0\mathrm{.}501,0\mathrm{.}517,0\mathrm{.}506],[10,0\mathrm{.}495,0\mathrm{.}505,0\mathrm{.}516,0\mathrm{.}511]]$