You are constructing X-bar (means) and Range charts for a process for which you

Question

You are constructing X-bar (means) and Range charts for a process for which you do not know the natural variability. You have collected samples of 5 readings over the past 15 days. The x-bar-bar (grand mean, average of averages) is 150 and the average range is 20.

Please show your work. Thank you.

You are constructing X-bar (means) and Range charts for a process for which you do not know the natural variability. You have collected samples of 5 readings over the past 15 days. The x-bar-bar (grand mean, average of averages) is 150 and the average range is 20 Using the table of control factors Factors for R-Chart D3 Factor for X-Chart Sample Size n 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31 0.29 0.27 0.25 0.24 0.22 0.08 0.14 0.18 0.22 0.26 0.28 0.31 0.33 0.35 3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.72 1.69 1.67 1.65 10 12 13 15 The UCL for the Range chart will be: Express with 1 decimal place

Explanation / Answer

To be calculated:

UCL for the Range Chart

Given Values:

X-bar-bar (or Grand Mean) = 150

R-bar (or Average Range) = 20

Number of Samples = 5

Solution:

UCL for the range chart can be calculated as;

UCL = X-bar-bar + (A2 x Range-bar)

From the given table of control factors, we can observe that;

For (n = 5), A2 = 0.58

Putting all the values in the above formula, we get;

UCL = 150 + (0.58 x 20)

UCL = 161.6

The UCL for the range chart is 161.6

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