Question $1$

a$)$ Provide instructions for production line operators on how to interpret a

control chart. You are to provide four rules based on four possible patterns

on how to interpret the data and suggest possible corrective actions to fix

any problems seen. Make a sketch of the four patterns.

$14$ marks

b$)10$ different samples of n $=3$ batches each have been taken during a $3-$

hour period from a production line that produces Pringles. The salt level

is measured and the individual observations from each sample are shown

as follows.

Observations $(\%$ salt content$)-($n $=3)$

Sample

k

$123$

x

R

$11\mathrm{.}21\mathrm{.}41\mathrm{.}61\mathrm{.}400\mathrm{.}4$

$21\mathrm{.}11\mathrm{.}51\mathrm{.}31\mathrm{.}300\mathrm{.}4$

$31\mathrm{.}20\mathrm{.}91\mathrm{.}51\mathrm{.}200\mathrm{.}6$

$41\mathrm{.}01\mathrm{.}51\mathrm{.}61\mathrm{.}360\mathrm{.}6$

$51\mathrm{.}71\mathrm{.}41\mathrm{.}61\mathrm{.}560\mathrm{.}3$

$62\mathrm{.}02\mathrm{.}32\mathrm{.}02\mathrm{.}230\mathrm{.}7$

$72\mathrm{.}02\mathrm{.}32\mathrm{.}02\mathrm{.}230\mathrm{.}8$

$81\mathrm{.}71\mathrm{.}61\mathrm{.}31\mathrm{.}530\mathrm{.}4$

$91\mathrm{.}52\mathrm{.}31\mathrm{.}21\mathrm{.}661\mathrm{.}1$

$101\mathrm{.}21\mathrm{.}51\mathrm{.}61\mathrm{.}430\mathrm{.}4$

Totals $=15\mathrm{.}775\mathrm{.}7$

c$)$ Design and plot an R$-$chart to monitor process variability.

$5$ marks

d$)$ Design and plot an

x $-$chart to be used in conjunction with the R$-$chart.

$5$ marks

e$)$ Comment on whether the process is in control and give an explanation

for your answer. What actions, if any, would you take?

$4$ marks

f$)$ Explain why it is best practice to use both R$-$charts and

x $-$charts together

to monitor a process. $7$ marks