Question $1($a$)$Describe and sketch four patterns that you might see on a control chartand explain the appropriate actions that should be taken to correct the process.$[8]($b$)$Outline the basic steps required to setup a statistical quality control system in a company.$[8]($c$)$The data below are X$-$bar and R values for $24$ samples of size n$=5$taken from a process that makes medical devices. The measurements are in millimetres.Sample numberX$-$barRSample Number X$-$barR$134\mathrm{.}531335\mathrm{.}48234\mathrm{.}241434\mathrm{.}06331\mathrm{.}641537\mathrm{.}15431\mathrm{.}541634\mathrm{.}97535\mathrm{.}051733\mathrm{.}54634\mathrm{.}161831\mathrm{.}73732\mathrm{.}641934\mathrm{.}08833\mathrm{.}832035\mathrm{.}14934\mathrm{.}872133\mathrm{.}721033\mathrm{.}682232\mathrm{.}811131\mathrm{.}932333\mathrm{.}531238\mathrm{.}692434\mathrm{.}22$Sum $($X$-$bar$)=816\mathrm{.}1$Sum $($ R $)=113$i$)$Set up two suitable chartsto monitor this process. Plot the charts. $($Show all your calculations$).[6]$ii$)$Based on the plot of the chartsand your rules for interpreting the charts,is the process in statistical control? Explain your answer?$[5]$ iii$)$Is the process capable of meetinga specification limit of $35\backslash$pm $4?$ Explain your answerand show your calculations