Q$.3$ A process consists of $4$ press tools each producing identical metal parts.

The parts are car interior fittings with a critical specification of $10\mathrm{.}5+-0\mathrm{.}4mm.$

The data set below represents the following situation over a $24$ hour production

run $(3$ X $8$ Hour shifts$)$:

Day Shift

Evening Shift

Night Shift

$($a$)$ Plot the data using a Multivari chart showing machine averages and

time averages.

$($b$)($i$)$ Analyse the situation during the day shift.

$($ii$)$ What modifications were made during the day shift and how

was the output of the process affected?

$($iii$)$ What modifications were made during the evening shift and how

was the process output affected?

$($iv$)$ Which shift gave the worst performance in relation to the

specifications assuming $$ is $0\mathrm{.}14$ and what would you have done?

Explain your answer.

$($c$)$ Incoming inspection is performed on the materials used by the press

machines. Acceptance sampling is applied. The following parameters

have been agreed:

$=0\mathrm{.}05,P_1=0\mathrm{.}018$

$=0\mathrm{.}01,P_2=0\mathrm{.}18$

Construct a single sampling plan and comment on its ability to hold the

above parameters