$11.$ Assume that a production process at one of LIFT airlines suppliers, Catering plastics $($Pty$)$

Ltd$,$ is being monitored for purposes of quality assurance. The supplier provides cateringrelated plastic dispensables for LIFT airlines$$ passengers.

The relevant production process is intended to average $61$ minutes each. Three separate

samples of six observations each have been taken. For each of the three separate samples,

the actual measurements $($in minutes$)$ of the six observations are reflected in Table $6.$ In

addition, the table reflects the respective means and ranges for each sample.

Table $6$: Samples and Measurements taken at Catering plastics $($Pty$)$ Ltd

$($fictional$/$assumed$)$

You are required to assist the operations manager at the supplier by completing the

relevant calculations for the $-$chart and R$-$chart, respectively.

IMPORTANT NOTES:

$$ Carry all your calculations through to two decimal places after the comma.

$$ While you are encouraged to show your calculations, you may at your own choosing only

provide the final answers $($in order to save time$).$

$$ To obtain the relevant factors for the sample size, please refer to Annexure A$,$ on p $15.$

For the relevant factors, you are required to use all the decimals as reflected in the

Annexure.

Answer the following questions:

$11\mathrm{.}1$ Calculate the overall mean and the average range. $\{1\}$

$11\mathrm{.}2$ Calculate the upper and lower control limits for the $-$Chart and R$-$chart,

respectively. $\{4\}$

$11\mathrm{.}3$ Is corrective action required? Justify your answer. $\{1\}$

$(6)$

Sample $1$ Sample $2$ Sample $3$

$586360$

$626262$

$596261$

$616362$

$606059$

$576158$

Mean $59,5061,8360,33$

Range $534$