# Statistical Process Control: Factors for control limits

Please see attached problem.

Refer to table - Factors for computing control limits (3 sigma) for this problem.

Twelve samples, each containing five parts, were taking from a process that produces steel rods.

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 10.002 0.013 7 10.001 0.008

2 10.002 0.014 8 10.003 0.011

3 9.993 0.005 9 9.995 0.002

4 10.004 0.024 10 9.999 0.011

5 9.999 0.013 11 10.003 0.012

6 9.999 0.012 12 10.006 0.007

For the given data, the x̄s =______inches (round your response to four decimal places)

Based on the sampling done, the control limits for 3-sigma x-bar chart are:

Upper Control Limit (UCLxbar ) =______ Inches (round your response to four decimal places)

Lower Control Limit (LCLxbar ) =______ Inches (round your response to four decimal places)

Based on the x-bar chart, the process is a) OUT OF CONTROL or b) IN CONTROL

For the given data, the R (average range of the samples) =______ Inches (Round to four decimal places)

The control limits for the 3-sigma R-chart are:

Upper Control Limit (UCLR) =_______inches (round your response to for decimal places)

Lower Control Limit (LCLR) =______ inches (round your response to four decimal places)

Based on the R-chart, the wire cutting process is a) OUT OF CONROL OR b) IN CONTROL

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#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached Excel file.