Range chart using table $($Mean $($x$-$bar$)$ and Range $($

R$)$ Chart Factors$)$ from Chapter $13$ PPTs$.$

$3.$ Thirty samples of $18$ cans each are measured from a canning process while

it is in control. The mean of the thirty sample means is $15\mathrm{.}02$ ounces and the

average range is $0\mathrm{.}14$ ounces. What should the upper and lower control limits

be on a range chart to monitor this canning process in the future?

Answer: UCL $0\mathrm{.}225,$ LCL $0\mathrm{.}055$

p$-$chart using z$-$score

$4.$ The average proportion of defective is known to be $2\%.$ What should the

upper and lower control limits of a P$-$chart be if

n $=30$ and z $=3\mathrm{.}0?$

Answer: UCL $0\mathrm{.}097,$ LCL $0$

c$-$chart

$5.$ The average number of defects is $40$ per day. What should the upper and

lower control limits of a C$-$chart be if z $=2\mathrm{.}5?$

Answer: UCL $55\mathrm{.}8,$ LCL $24\mathrm{.}2$