Question $1$

$($a$)$ Describe and sketch four patterns that you might see on a control chart

and 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 number X$-$bar R Sample Number X$-$bar R

$134\mathrm{.}531335\mathrm{.}48$

$234\mathrm{.}241434\mathrm{.}06$

$331\mathrm{.}641537\mathrm{.}15$

$431\mathrm{.}541634\mathrm{.}97$

$535\mathrm{.}051733\mathrm{.}54$

$634\mathrm{.}161831\mathrm{.}73$

$732\mathrm{.}641934\mathrm{.}08$

$833\mathrm{.}832035\mathrm{.}14$

$934\mathrm{.}872133\mathrm{.}72$

$1033\mathrm{.}682232\mathrm{.}81$

$1131\mathrm{.}932333\mathrm{.}53$

$1238\mathrm{.}692434\mathrm{.}22$

Sum $($X$-$bar$)=816\mathrm{.}1$

Sum $($ R $)=113$

i$)$ Set up two suitable charts to monitor this process. Plot the

charts. $($Show all your calculations$).[6]$

ii$)$ Based on the plot of the charts and your rules for interpreting the

charts, is the process in statistical control? Explain your answer?

$[5]$

iii$)$ Is the process capable of meeting a specification limit of $35\backslash$pm $4?$

Explain your answer and show your calculations. $[8]$