The time in minutes to replace vehicle wiper blades at a service center was monitored using a mean and a range chart. Six samples of n $=20$ observations were obtained and the sample means and ranges were computed:

Sample Mean Range Sample Mean Range

$13\mathrm{.}06\mathrm{.}4243\mathrm{.}13\mathrm{.}46$

$23\mathrm{.}15\mathrm{.}5053\mathrm{.}06\mathrm{.}46$

$33\mathrm{.}11\mathrm{.}4163\mathrm{.}09\mathrm{.}45$

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Factors for three$-$sigma control limits for x$$

and R charts

FACTORS FOR R CHARTS

Number of Observations in Subgroup,

n Factor for

x$$

Chart,

A$2$ Lower

Control Limit,

D$3$ Upper

Control Limit,

D$4$

$21\mathrm{.}8803\mathrm{.}27$

$31\mathrm{.}0202\mathrm{.}57$

$40\mathrm{.}7302\mathrm{.}28$

$50\mathrm{.}5802\mathrm{.}11$

$60\mathrm{.}4802\mathrm{.}00$

$70\mathrm{.}420\mathrm{.}081\mathrm{.}92$

$80\mathrm{.}370\mathrm{.}141\mathrm{.}86$

$90\mathrm{.}340\mathrm{.}181\mathrm{.}82$

$100\mathrm{.}310\mathrm{.}221\mathrm{.}78$

$110\mathrm{.}290\mathrm{.}261\mathrm{.}74$

$120\mathrm{.}270\mathrm{.}281\mathrm{.}72$

$130\mathrm{.}250\mathrm{.}311\mathrm{.}69$

$140\mathrm{.}240\mathrm{.}331\mathrm{.}67$

$150\mathrm{.}220\mathrm{.}351\mathrm{.}65$

$160\mathrm{.}210\mathrm{.}361\mathrm{.}64$

$170\mathrm{.}200\mathrm{.}381\mathrm{.}62$

$180\mathrm{.}190\mathrm{.}391\mathrm{.}61$

$190\mathrm{.}190\mathrm{.}401\mathrm{.}60$

$200\mathrm{.}180\mathrm{.}411\mathrm{.}59$

a$.$ Using the factors in the above table, determine upper and lower limits for mean and range charts. $($Do not round intermediate calculations. Round your mean value to $3$ decimal places and range value to $4$ decimal places.$)$

a$1.$ Is the process in control?

multiple choice $1$

The process is in control.

The process is not in control.

b$.$ The time in minutes needed to assemble security cameras at a production facility was recorded for eight samples of $15$ observations each, and means and ranges were computed. Using factors from the above table, compute control limits for the means and ranges. $($Round your answers to $3$ decimal places.$)$

Sample Mean Range Sample Mean Range

$17\mathrm{.}10\mathrm{.}5257\mathrm{.}21\mathrm{.}46$

$26\mathrm{.}92\mathrm{.}4868\mathrm{.}01\mathrm{.}55$

$37\mathrm{.}25\mathrm{.}5077\mathrm{.}80\mathrm{.}53$

$47\mathrm{.}54\mathrm{.}5187\mathrm{.}63\mathrm{.}49$

b$1.$ Is the process is in control.

multiple choice $2$

The process is in control.

The process is not in control.