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Question $26$

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A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results : Machine #$1$ measurements $[18,16,12,18]$; Machine #$2$ measurements $[23,20,19,16]$; Machine #$3$ measurements $[19,19,20,23].$ Using the factors for three sigma control limits$,$ what are x$-$bar chart upper and lower control limits$?$

Question $26$Answer

a$.$

$35\mathrm{.}58$and $1\mathrm{.}583$

b$.$

$24\mathrm{.}36$and $12\mathrm{.}8$

c$.$

$20\mathrm{.}11$and $17\mathrm{.}05$

d$.$

$22\mathrm{.}72$and $14\mathrm{.}45$