The quality$-$control plan for a certain production process involves taking samples of size $4.$ The results from the last $32\mathrm{.}00$ samples can be summarized as follows:

$32\mathrm{.}00$i$=1$X$$i$=712\mathrm{.}5$

$32\mathrm{.}00$i$=1$Ri$=143\mathrm{.}7$

$32\mathrm{.}00$i$=1$si$=62\mathrm{.}5$

Compute the $3\backslash$sigma control limits for the S chart. $($Round the final answer to three decimal places.$)$

The LCL is $0$ Numeric Response $1.$Edit Unavailable. $0$ correct..

The UCL is $4\mathrm{.}426$ Numeric Response $2.$Edit Unavailable. $4\mathrm{.}426$ correct..

Explanation

The sample size is n $=4.$ The lower and upper limits for the S$-$chart are B$3$ s$$

and B$4$ s$$

$,$ respectively.

From the control chart table, B$3=0$ and B$4=2\mathrm{.}266.$

s$$

$=62\mathrm{.}5/32=1\mathrm{.}9531.$ Therefore, LCL $=0$ and UCL $=4\mathrm{.}426.$

Solution

The $3\backslash$sigma control limits for the S chart is LCL $=0$ and UCL $=4\mathrm{.}426.$