On “ Initial ”, there are 20 samples of 6 items each. Determine the upper and lo

Question

On “Initial”, there are 20 samples of 6 items each. Determine the upper and lower control limits for mean and range, clearly showing each on the worksheet.

Next use vlookup in the “Initial” sheet to retrieve appropriate values from the “Factor Table” directly into your control limit formulas.

On “Initial”, create a control chart for means and a separate control chart for ranges that shows the upper and lower control limits along with the relevant data.

Initial:

Factor Table:

Item 1 2 3 4 5 6 Sample 1 11.87 11.76 11.86 11.92 12.04 11.84 2 11.90 11.88 11.74 11.81 11.95 12.15 3 12.15 11.99 11.96 11.99 11.74 11.87 4 11.95 11.99 12.11 12.02 11.83 11.87 5 11.94 11.90 12.15 11.75 11.96 11.84 6 12.07 12.13 12.25 11.90 11.94 11.96 7 12.28 12.11 12.15 11.81 12.13 11.92 8 12.15 11.81 11.74 11.76 12.21 11.89 9 12.18 11.89 12.01 12.28 11.83 12.27 10 12.12 11.95 11.88 12.27 12.00 11.86 11 12.18 12.17 12.04 11.81 11.92 11.73 12 12.22 12.18 12.09 11.98 11.88 12.21 13 11.94 11.85 12.08 11.85 11.81 12.29 14 11.85 11.76 11.96 11.81 12.23 12.13 15 12.18 12.01 11.86 12.13 12.18 11.79 16 11.86 11.70 11.79 11.81 12.27 11.88 17 11.73 11.80 12.13 12.10 11.90 11.70 18 11.97 12.05 12.19 11.71 11.89 11.77 19 11.73 12.06 11.89 11.94 12.19 12.09 20 12.07 11.84 11.71 11.98 11.91 11.76

Explanation / Answer

Now, note that we have 20 samples. Each sample has 6 observations.

First, we will start by calculating the group mean and the group range

Note that the formulate used in excel are:

Xbar = average(select the 6 cells in each row) function

Range = max() - min() function

Now, let us take the overall average of Xbar

X-bar-bar = 11.97

R-bar = 0.42

The above two are again determined using the average() function, this time vertically across the 20 samples

Control limits for R-bar:

UCL = D4R-bar = 2 x 0.42 = 0.84

LCL = D3R-bar = 0 (Note that these two values come from the second table under n = 6, as there are 6 observations in each sample)

Thus, the Upper Control Limits and the Lower Control Limits for the Range are as above (0.84, 0)

Similarly, the UCL and LCL considering X-bar are (A2 again corresponding to n=6):

UCL = X-bar-bar + A2R-bar = 11.97+(0.48 x 0.42) = 12.17

LCL = X-bar-bar - A2R-bar = 11.97-(0.48 x 0.42) = 11.97

To plot the graph, simply plot two lines each with the value = UCL, LCL, and plot X-bar-bar and R-bar as the variable line in each of the graphs.

Trust this with understanding, you will be able to finish the graphs!

Item 1 2 3 4 5 6 X bar R 1 11.87 11.76 11.86 11.92 12.04 11.84 11.88166667 0.28 2 11.9 11.88 11.74 11.81 11.95 12.15 11.905 0.41 3 12.15 11.99 11.96 11.99 11.74 11.87 11.95 0.41 4 11.95 11.99 12.11 12.02 11.83 11.87 11.96166667 0.28 5 11.94 11.9 12.15 11.75 11.96 11.84 11.92333333 0.4 6 12.07 12.13 12.25 11.9 11.94 11.96 12.04166667 0.35 7 12.28 12.11 12.15 11.81 12.13 11.92 12.06666667 0.47 8 12.15 11.81 11.74 11.76 12.21 11.89 11.92666667 0.47 9 12.18 11.89 12.01 12.28 11.83 12.27 12.07666667 0.45 10 12.12 11.95 11.88 12.27 12 11.86 12.01333333 0.41 11 12.18 12.17 12.04 11.81 11.92 11.73 11.975 0.45 12 12.22 12.18 12.09 11.98 11.88 12.21 12.09333333 0.34 13 11.94 11.85 12.08 11.85 11.81 12.29 11.97 0.48 14 11.85 11.76 11.96 11.81 12.23 12.13 11.95666667 0.47 15 12.18 12.01 11.86 12.13 12.18 11.79 12.025 0.39 16 11.86 11.7 11.79 11.81 12.27 11.88 11.885 0.57 17 11.73 11.8 12.13 12.1 11.9 11.7 11.89333333 0.43 18 11.97 12.05 12.19 11.71 11.89 11.77 11.93 0.48 19 11.73 12.06 11.89 11.94 12.19 12.09 11.98333333 0.46 20 12.07 11.84 11.71 11.98 11.91 11.76 11.87833333 0.36

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