The Oceanside Apparel Company manufactures$$ men's knit shirts. The production process requires material to be cut into large patterned$$ squares, which are then sewn together. If the squares are not the correct$$ length, the final shirt will be either too large or too small. The target length is $45$ inches. In order to monitor the cutting$$ process, Oceanside managers took $22$ samples of four squares each and measured the lengths. For each$$ sample, they then calculated the sample mean and range.$$ Finally, they calculated the average sample mean $(45\mathrm{.}0$inches$)$ and average range value $(4\mathrm{.}0$inches$)$ for the $22$ samples. Managers felt that these values were$$ acceptable; that$$ is$,$ the process was in control.

LOADING... Click the icon to view the values of the A$2,$ D$3,$ and D$4$ constants.

Part $2$

a$.$

Upper Control Limit $($UCLX$)=$enter your response here. $($Enter your response rounded to two decimal$$ places.$)$

Part $3$

Lower Control Limit $($LCLX$)=$enter your response here. $($Enter your response rounded to two decimal$$ places.$)$

Part $4$

Upper Control Limit $($UCLR$)=$enter your response here. $($Enter your response rounded to two decimal$$ places.$)$

Part $5$

Lower Control Limit $($LCLR$)=$enter your response here. $($Enter your response rounded to two decimal$$ places.$)$

Part $6$

b$.$ Using the control charts you developed in part$$ a$,$ plot the following samples. Circle any that appear to be out of control.

LOADING... Click the icon to view the sample data.

Choose the correct X chart below.