Question content area

Part $1$

Refer to Table S$6\mathrm{.}1-$ Factors for Computing Control Chart Limits $(3$ sigma$)$

LOADING...

for this problem.

Twelve$$ samples, each containing five$$ parts, were taken from a process that produces steel rods at Emmanual$$ Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results$$ were:

$$

Sample

Sample Mean$($in$.)$

Range$($in$.)$

Sample

Sample Mean$($in$.)$

Range$($in$.)$

$1$

$10\mathrm{.}002$

$0\mathrm{.}011$

$7$

$10\mathrm{.}001$

$0\mathrm{.}008$

$2$

$10\mathrm{.}002$

$0\mathrm{.}014$

$8$

$10\mathrm{.}005$

$0\mathrm{.}013$

$3$

$9\mathrm{.}991$

$0\mathrm{.}007$

$9$

$9\mathrm{.}995$

$0\mathrm{.}004$

$4$

$10\mathrm{.}006$

$0\mathrm{.}018$

$10$

$10\mathrm{.}001$

$0\mathrm{.}011$

$5$

$9\mathrm{.}997$

$0\mathrm{.}013$

$11$

$10\mathrm{.}001$

$0\mathrm{.}014$

$6$

$9\mathrm{.}999$

$0\mathrm{.}012$

$12$

$10\mathrm{.}006$

$0\mathrm{.}009$

Part $2$

For the given$$ data, the x double overbar

$=10\mathrm{.}002$

inches $($round your response to four decimal$$ places$).$

Part $3$

Based on the sampling$$ done, the

control limits for $3-$sigma x overbar

chart$$ are:

Upper Control Limit $($UCL Subscript x overbar

$)$

$=10\mathrm{.}9$

inches $($round your response to four decimal$$ places$).$

Part $4$

Lower Control Limit $($LCL Subscript x overbar

$)$

$=$ enter your response here

inches $($round your response to four decimal$$ places$).$

Part $5$

Based on the x overbar

$-$chart,

is one or more samples beyond the control$$ limits$?$

$$

No

Yes

$.$

Part $6$

For the given$$ data, the Upper R overbar

$=$ enter your response here

inches $($round your response to four decimal$$ places$).$

Part $7$

The control limits for the $3-$sigma

$$ R$-$chart are:

Part $8$

Upper Control Limit $($UCL Subscript Upper R

$)$

$=$ enter your response here

inches $($round your response to four decimal$$ places$).$

Part $9$

Lower Control Limit $($LCL Subscript Upper R

$)$

$=$ enter your response here

inches $($round your response to four decimal$$ places$).$

Part $10$

Based on the$$ R$-$chart, is one or more samples beyond the control$$ limits$?$

$$

No

Yes

$.$