$2.$ Develop $3$ sigma level process control charts for monitoring weight of firewood in bags. An inspector performed sampling over $4$ weeks of time frame. Each time, $4$ observations were made as below. Calculate and show values for UCL, CL$,$ and LCL using the factors provided in below table $($do not calculate these values using standard deviation from raw data$).$ Draw variable control charts $($mean and range$).$ Discuss your conclusion. Draw using Excel or hand draw and scan.

week $1$ week $2$ week $3$ week $4$

$20282030$

$24302820$

$22212624$

$26242626$

Factors for $3$ Sigma level $($page $195$ of textbook$)$

Sample Control Limit Factor Control Limit Factor

Size for Sample Mean for Sample Range

n A$2$ D$3$ D$4$

$21\mathrm{.}88003\mathrm{.}267$

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

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

$50\mathrm{.}57702\mathrm{.}116$

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

$150\mathrm{.}2230\mathrm{.}3481\mathrm{.}652$

$200\mathrm{.}1800\mathrm{.}4141\mathrm{.}586$

$250\mathrm{.}1530\mathrm{.}4591\mathrm{.}541$