Factors for Calculating Three$-$Sigma Limits for the Chart and R$-$Chart

Size of Sample $($n$)$ Factor for UCL and LCL for x$-$bar$-$Charts A$2$

Factors for LCL for

R$-$Charts D$3$

Factors for UCL for

R$-$Charts D$4$

$21\mathrm{.}8803\mathrm{.}267$

$31\mathrm{.}02302\mathrm{.}575$

$40\mathrm{.}72902\mathrm{.}282$

$50\mathrm{.}57702\mathrm{.}115$

$60\mathrm{.}48302\mathrm{.}004$

$70\mathrm{.}4190\mathrm{.}0761\mathrm{.}924$

$80\mathrm{.}3730\mathrm{.}1361\mathrm{.}864$

$90\mathrm{.}3370\mathrm{.}1841\mathrm{.}816$

$100\mathrm{.}3080\mathrm{.}2231\mathrm{.}777$

Source: $1950$ ASTM Manual on Quality Control of Materials, copyright American Society for Testing Materials. Reprinted with permission.

Thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world. Results from the last five samples are shown in the table. Calculate control limits for a chart that will monitor performance to target.

Sample # Observation $1$ Observation $2$ Observation $3$ Observation $4$

$10\mathrm{.}4860\mathrm{.}4990\mathrm{.}4930\mathrm{.}511$

$20\mathrm{.}4990\mathrm{.}5060\mathrm{.}5160\mathrm{.}494$

$30\mathrm{.}4960\mathrm{.}5000\mathrm{.}5150\mathrm{.}488$

$40\mathrm{.}4950\mathrm{.}5060\mathrm{.}4830\mathrm{.}487$

$50\mathrm{.}4720\mathrm{.}5020\mathrm{.}5260\mathrm{.}469$

$60\mathrm{.}4730\mathrm{.}4950\mathrm{.}5070\mathrm{.}493$

$70\mathrm{.}4950\mathrm{.}5120\mathrm{.}490\mathrm{.}471$

$80\mathrm{.}5250\mathrm{.}5010\mathrm{.}4980\mathrm{.}474$

$90\mathrm{.}4970\mathrm{.}5010\mathrm{.}5170\mathrm{.}506$

$100\mathrm{.}4950\mathrm{.}5050\mathrm{.}5160\mathrm{.}511$

A$)$What is the Central Line of the control chart $($x$)?$

$[$ Select $]$

B$)$ What is the Average Range R$?$

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C$)$ What is the upper control limit of your R$-$chart?

$[$ Select $]$