PLEASE SHOW ALL WORKINGS, FROM EXCEL TO GRAPHS,

STEP BY STEP

A quality control inspector working at a soft drink company has taken $10$ samples, with $3$ observations each, of the volume of bottles filled. The standard deviation of the bottling operation is unknown. The task is to develop control limits of $3$ standard deviations for the bottling operations based on this information. To do so$,$ draw an X$-$bar chart and an R$-$chart using a ruler and a pencil. Name the horizontal and vertical axes, and mark the centerline, UCL, and LCL on your diagram. Show the calculations for x$-$bars of all samples, ranges of all samples, and the formula for UCL, LCL$,$ and their calculations.

Explain the process performance in detail. $($Use the concepts addressed in the uploaded pdf file Control Chart Rules and Interpretation $\_$ BPI Consulting$1)$