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:

Mineral-Based Lubricants

Lubricants derived from mineral oils used to reduce friction and wear in machinery and engines.

Lubricity

The property of a substance that reduces friction between surfaces in motion.

Boil Temperatures

The temperatures at which liquids change to gases, varying with the atmospheric pressure and the chemical composition of the liquid.

Ring Gear Tooth

A tooth on the outer edge of a ring gear, engaged by the pinion gear to transmit torque in a differential.