Problem $2$ Control Chart Constants

A process for filling liquid laundry detergent bottles monitors the volume in each bottle. The operations manager has

taken $5$ samples with $4$ observations $($bottles$)$ in each sample to determine if the variation in volume is reasonable.

The measurement unit is fluid ounces. Calculate the center line for a process control chart that indicates whether the

variation within samples is reasonable $($in a state of control$).$ Control chart constants table is attached here.

a: Calculate sample means $(),$ sample ranges $(R),$ mean of sample means $(),$ and mean of ranges $().$

b: Calculate UCLs and LCLs for average chart and range chart.

c: Construct the control charts $($average as well as range$)$

Control Chart Constants

Sample Size n

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$12$

$14$

$16$

$18$

$20$

$22$

$24$

$1\mathrm{.}880$

$1\mathrm{.}023$

$0\mathrm{.}729$

$0\mathrm{.}577$

$0\mathrm{.}483$

$0\mathrm{.}419$

$0\mathrm{.}373$

$0\mathrm{.}337$

$0\mathrm{.}308$

$0\mathrm{.}266$

$0\mathrm{.}235$

$0\mathrm{.}212$

$0\mathrm{.}194$

$0\mathrm{.}180$

$0\mathrm{.}167$

$0\mathrm{.}157$

$0$

$0$

$0$

$0$

$0\mathrm{.}076$

$0\mathrm{.}136$

$0\mathrm{.}184$

$0\mathrm{.}223$

$0\mathrm{.}284$

$0\mathrm{.}329$

$0\mathrm{.}364$

$0\mathrm{.}392$

$0\mathrm{.}414$

$0\mathrm{.}434$

$0\mathrm{.}452$

$3\mathrm{.}267$

$2\mathrm{.}575$

$2\mathrm{.}282$

$2\mathrm{.}115$

$2\mathrm{.}004$

$1\mathrm{.}924$

$1\mathrm{.}864$

$1\mathrm{.}816$

$1\mathrm{.}777$

$1\mathrm{.}716$

$1\mathrm{.}671$

$1\mathrm{.}636$

$1\mathrm{.}608$

$1\mathrm{.}586$

$1\mathrm{.}566$

$1\mathrm{.}548$

Use an Excel Spreadsheet