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Construct the 3-sigma x-chart and the 3-sigma R-chart

Auto pistons at Yongpin Zhou's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:

Day Mean(mm) Range(mm)
1 156.9 4.2
2 153.2 4.6
3 153.6 4.1
4 155.5 5.0
5 156.6 4.5

Construct the 3-sigma x-chart and the 3-sigma R-shart for this dimension, using the data observed in the table above.

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

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