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XB, R Control Chart Example

D. W. Parent

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We want to learn control charts

• We have oxide thickness data generated by the Poison Diffusion Furnace Company.

• The furnace is a single wafer processor• We have taken 5 data points per wafer

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We will use the first 20 runs to set our trial control limits

Calculate the average (XB) of each row.

Raw data

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Calculate the Range (R) of each row

Maximum value in the row minimum the minimum value in the row

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Calculate the Grand Mean (XBB) on the first 20 data points

Cell J2 calculates the grand meanWhile cell j3=j2, j4=j3…..

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Calculate the mean of the Ranges (RB)

Note: K3=K2…..

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Calculate the Upper and Lower control limits for XB (UCLXB, LCLXB) for a sample size of 5

UCLXB=XBB+RB*.58

LCLXB=XBB-RB*.58

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Calculate the Upper Control limit for R (UCLRB) and the Lower Control limit for R (LCLRB)

UCLRB=2.11*RB

LCLRB=0 by definition

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Plot the XB chart

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R

Notice we have one point outside the control limit. Maybe this was a typo whenthe data was entered. Remove the row that data point was from.

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Re-plot the XB chart

Looks good!

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Plot the RB Chart

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Ran

ge RRBUCLRLCLR

Looks like we have one bad point. Remove it and recalculate X and R charts

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Trial Limits look good!

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Now plot for whole data set

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Final Plots?

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ge R

ange

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The control limits seem to work for the XB chart, but not for the R chart. SinceWe did not use data from runs 21 to 100, maybe the points are not past the control limit, but the control limits are not right. Calcualte control lmits on the wholeSet.

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Final Plots?

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At this time it looks like the control limits have been calculated correctly, and we Recommend that these limits be used for this process going forward.