solution

Factors for Computing Control Chart Limits (3 sigma)

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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	11.90011.900	0.0220.022	7	11.90111.901	0.0210.021
2	11.90011.900	0.0320.032	8	11.90711.907	0.0200.020
3	11.89311.893	0.0170.017	9	11.89711.897	0.0140.014
4	11.90611.906	0.0410.041	10	11.90111.901	0.0150.015
5	11.89711.897	0.0230.023	11	11.90111.901	0.0220.022
6	11.90111.901	0.0210.021	12	11.90411.904	0.0320.032

For the given data, the

x double overbarx

=

nothing

inches (round your response to four decimal places).

Based on the sampling done,

the

control limits for 3-sigma

x overbarx

chart are:

Upper Control Limit

(UCL Subscript x overbarUCLx )

=

nothing

inches (round your response to four decimal places).

Lower Control Limit

(LCL Subscript x overbarLCLx )

=

nothing

inches (round your response to four decimal places).

Based on the

x overbarx -chart,

is one or more samples beyond the control limits?

?

Yes

No

.

For the given data, the

Upper R overbarR

=

nothing

inches (round your response to four decimal places).

The control limits for the

3-sigma

R-chart are:

Upper Control Limit

(UCL Subscript Upper RUCLR )

=

nothing

inches (round your response to four decimal places).

Lower Control Limit

(LCL Subscript Upper RLCLR )

=

nothing

inches (round your response to four decimal places).

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

?

Yes

No