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

Question

You are constructing X-bar (means) and Range charts for a process in which you do not know the natural variability. You have collected samples of 9 readings over the past 15 days. The x-bar-bar (grand mean, average of averages) is 142 and the average range is 19.

Please show your work. Thank you.

You are constructing X-bar (means) and Range charts for a process in which you do not know the natural variability. You have collected samples of 9 readings over the past 15 days. The x-bar-bar (grand mean, average of averages) is 142 and the average range is 19 Using the table of control factors Factors for R-Chart D, 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 x-bar chart will be: Express with 1 decimal place

Explanation / Answer

UCL for X-bar chart can be calculated by using the formula= X-double bar+ A2 * R bar

here X double bar is 142, and R bar is 19 , A2 is constant and the value is 0.34

UCL= 142+ 0.34*19= 142+6.46= 148.46

UCL= 148.46

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