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Fab SPC Xbar-R Chart Worksheet

Xbar-R charts are the workhorse of fab SPC for film thickness, CD, sheet resistance and overlay. This worksheet turns subgroups of five site readings into subgroup means, ranges and control limits you can chart or paste into your SPC system.

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Subgroup / lot	Site 1 (nm)	Site 2 (nm)	Site 3 (nm)	Site 4 (nm)	Site 5 (nm)	Mean (Xbar)	Range (R)
						100.04	0.9
						100.48	0.9
						100.02	0.7
						100.34	0.8
						100	0.9
						100.28	0.9

Average of subgroup means (Xbar-bar)

100.1933

Average range (R-bar)

0.85

Xbar UCL

100.6838

Xbar-bar + A2 x R-bar, A2 = 0.577 for n = 5.

Xbar LCL

99.7029

Xbar-bar - A2 x R-bar.

R chart UCL

1.7969

D4 x R-bar, D4 = 2.114 for n = 5.

R chart LCL

D3 is 0 for subgroup sizes below 7.

Estimated within sigma (R-bar / d2)

0.3654

d2 = 2.326 for n = 5.

Constants are for subgroup size n = 5 (A2 0.577, D3 0, D4 2.114, d2 2.326). Use at least 20 to 25 subgroups before trusting limits, and recompute after a process change. Sort or plot the means and ranges against the limits to look for points outside limits and runs.

SPC from live measurement data

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How to use the worksheet

Each row is one subgroup, for example five sites on one wafer or one reading from each of five wafers in a lot. Replace the sample rows with your data, keeping five readings per row. The sheet computes the mean and range of every row, then the average of those means (Xbar-bar) and the average range (R-bar). The summary gives Xbar limits, R chart limits and the within subgroup sigma. Export to Excel to plot the points against the limits, or compare each row manually to find out of control points.

The method

Xbar-R charts track the process center with subgroup means and the spread with subgroup ranges. Control limits are three sigma estimates built from R-bar using tabulated constants. For n = 5 the Xbar limits are Xbar-bar plus or minus 0.577 x R-bar, the R chart upper limit is 2.114 x R-bar, and sigma is estimated as R-bar divided by 2.326. Control limits describe what the process does, not what the customer wants, so keep them separate from spec limits.

Check the R chart first: if spread is unstable, Xbar limits are not valid
Rational subgroups should capture short term variation only
Recalculate limits after a verified process change

Common mistakes

Frequent errors include using spec limits as control limits, mixing tools or chambers in one subgroup, computing limits from too few points and recomputing limits every time a point goes out. Another is using site to site variation as the subgroup when the real risk is lot to lot drift, which makes the limits too wide. Agree on what a subgroup represents before collecting data, then link out of control actions to your OCAP.

Frequently Asked Questions

Why subgroups of five?

Five is common in fabs because five-site measurement maps are standard and the Xbar-R constants are well known. The worksheet uses n = 5 constants, so enter exactly five readings per row.

How many subgroups do I need?

Use at least 20 to 25 subgroups from a stable period to set limits. Fewer points give unreliable limits. After that, hold the limits and only recompute after a verified process change.

Are control limits the same as spec limits?

No. Control limits come from process variation and show when the process changed. Spec limits come from design and customer needs. A process can be in control and still out of spec.

Should I use Xbar-S instead?

For subgroup sizes above about 8 to 10, Xbar-S is more efficient. For n = 5 the range method is fine and simpler to check by hand.

Netray can pull measurement data from your MES or database into a private SPC view with alerts, without moving data off your network.

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