Five Samples Are Taken, with Five Observations Each ADetermine the Control Limits for the R-Chart

question 52

Essay

Five samples are taken, with five observations each. The sample findings are listed below. The sample values represent service times in minutes. ObservationNumber
$\begin{array}{|r|r|r|r|r|r|}\hline \frac{\text { Sample }}{\text { Number }} & 1 &2&3&4&5\\\hline 1 & 10.1 & 10.6 & 9.8 & 9.9 & 10.9 \\\hline 2 & 9.7 & 9.5 & 10.3 & 9.9 & 10.5 \\\hline 3 & 10.1 & 10.7 & 9.2 & 10.0 & 10.1 \\\hline 4 & 9.9 & 9.8 & 10.5 & 10.4 & 10.1 \\\hline 5 & 10.4 & 10.1 & 10.9 & 9.9 & 10.3 \\\hline\end{array}$
a.Determine the control limits for the R-chart.
b.Can it be concluded that the R-chart is in statistical control and proceed to develop the x-bar chart?

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Definitions:

Factory Overhead Cost Variance

The difference between the actual and budgeted indirect manufacturing costs.

Fixed Overhead

Costs that do not fluctuate with the level of production or sales, such as rent, salaries, and insurance.

Variable Overhead

These are costs that vary with production volume, such as materials and labor, as opposed to fixed overhead costs.

Direct Materials Cost Variance

The difference between the budgeted cost of materials and the actual cost used in production.