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Extended How-To¶

This walkthrough runs an Extended study, which is the tool to reach for when there is a factor besides part and operator. Here that factor is the fixture the part is clamped in, and the study has two of them.

The finished report shows something neither a Crossed nor a Nested study could have found: the fixture contributes twice as much measurement variation as the operators do. That is the reason to run Extended rather than to ignore the fixture and let its effect hide inside repeatability.

The data is on this page rather than in a file to download. Press Copy for Excel, then paste it into a blank worksheet.

The data¶

Four machined bosses, measured in millimetres. Three operators each measured every boss, twice in each of two fixtures, so every combination of part, operator and fixture is present. The specification is 49.00 to 51.00 mm.

Part	Operator	Fixture	Bore
1	A	F1	49.75
1	A	F1	49.66
1	A	F2	49.70
1	A	F2	49.63
1	B	F1	49.69
1	B	F1	49.59
1	B	F2	49.74
1	B	F2	49.73
1	C	F1	49.62
1	C	F1	49.71
1	C	F2	49.78
1	C	F2	49.80
2	A	F1	49.82
2	A	F1	49.83
2	A	F2	49.86
2	A	F2	49.91
2	B	F1	49.84
2	B	F1	49.88
2	B	F2	49.97
2	B	F2	49.87
2	C	F1	49.85
2	C	F1	49.92
2	C	F2	49.92
2	C	F2	49.95
3	A	F1	50.07
3	A	F1	50.01
3	A	F2	50.09
3	A	F2	50.05
3	B	F1	49.99
3	B	F1	50.09
3	B	F2	50.09
3	B	F2	50.12
3	C	F1	50.09
3	C	F1	50.18
3	C	F2	50.15
3	C	F2	50.14
4	A	F1	50.24
4	A	F1	50.22
4	A	F2	50.28
4	A	F2	50.31
4	B	F1	50.36
4	B	F1	50.28
4	B	F2	50.44
4	B	F2	50.35
4	C	F1	50.22
4	C	F1	50.32
4	C	F2	50.37
4	C	F2	50.36

Forty-eight rows: four parts, times three operators, times two fixtures, times two measurements.

Steps¶

Put the data in Excel

Press Copy for Excel above the table. In Excel, open a blank worksheet, click cell A1, and press Ctrl+V. You should have headers in row 1 and data in rows 2 through 49.
Select the data and start the analysis

Select A1:D49, including the header row. From the Excel ribbon: QXL Stat Tools > MSA / Gage R&R > Extended.
Assign the columns on the Data tab
- Tick Bore under Measurement Columns.
- Tick Part under Part.
- Tick Operator under Operator (Optional).
- Tick Fixture under Additional factor columns.
That last list is the one a Crossed or Nested study does not have, and ticking a column there is what brings the factor into the model.
Enter the specification limits

In the Specification Limits grid, on the Bore row, type 49 under LSL and 51 under USL.
Set the model on the Model tab

The Model tab now lists three factors: Part, Operator and Fixture.
- Leave all three Type: drop-downs on Random. Each set of levels is a sample standing in for more: these operators for operators generally, these two fixtures for the fixtures in use.
- Leave every Nested in: on (None). Every part was measured in both fixtures by every operator, so nothing is nested.
- Under Interactions, clear every checkbox. This walkthrough fits main effects only.
- Leave Part-to-part variation alone. The fixture is part of the measurement system, not a property of the parts, so it should stay in reproducibility.
Check the Model structure tree before moving on. With nothing nested it should list the three factors flat, with no indentation.
Leave the Options tab alone

The Extended options group is available here, but its defaults are what this walkthrough uses: study variation multiplier 6, confidence level 0.95.
Choose Finish

A new worksheet named MSA Extended appears.

What the report says¶

One analysis of variance table¶

Source	DF	Adj SS	Adj MS	F	P
Part	3	2.50545	0.83515	391.38	<0.001
Operator	2	0.02885	0.01443	6.76	0.003
Fixture	1	0.03967	0.03967	18.59	<0.001
Repeatability	41	0.08749	0.00213

There is one table, not two, because no interaction was declared. Interaction removal runs by default, but with nothing to consider it removes nothing.

All three factors are significant. Note the Fixture F of 18.59 against the Operator F of 6.76: the fixture is the stronger effect of the two, which is the finding this study exists to produce.

The Gage R&R table¶

Source	Variance	Std Dev	Study Var (6 x SD)	% Contribution	% Tolerance
Total Variation (TV)	0.073884	0.27182	1.63090	100.00%	81.55%
Total Gage R&R (GRR)	0.004466	0.06683	0.40099	6.05%	20.05%
Repeatability (EV)	0.002134	0.04619	0.27716	2.89%	13.86%
Reproducibility (AV)	0.002333	0.04830	0.28978	3.16%	14.49%
Operator	0.000768	0.02772	0.16632	1.04%	8.32%
Fixture	0.001564	0.03955	0.23730	2.12%	11.87%
Part to part (PV)	0.069418	0.26347	1.58084	93.95%	79.04%
Part	0.069418	0.26347	1.58084	93.95%	79.04%

The two rows indented under Reproducibility (AV) are the whole point of this study. They are the member terms the reproducibility total is the sum of, and they are what a Crossed study could not have separated.

and beneath it:


%GRR	24.59%
%EV	16.99%
%AV	17.77%
%PV	96.93%
P/Tol Ratio	0.2005
Number of Distinct Categories (ndc)	5

The distinct-categories cell carries no confidence interval here, because an Extended study reports no intervals at all.

Reproducibility is Operator plus Fixture, and you can see it add up¶

This is the clearest illustration in the help of what reproducibility actually means. The report's Reproducibility (AV) row is 0.002333, and underneath it sit two member rows, one per term:

Member term	Variance component
Operator	0.0007683
Fixture	0.0015642
Reproducibility total	0.0023325

0.0007683 plus 0.0015642 is 0.0023325, which is what the Reproducibility (AV) row shows rounded to six decimals as 0.002333.

Reproducibility is not the operator term. It is everything that is neither the residual nor part to part variation, summed, which here means the operator and the fixture together.

The fixture is roughly twice the operator. Two thirds of the reproducibility in this measurement system comes from which fixture the part was clamped in, not from who measured it.

A Crossed study could not have told you that. With no fixture column, the fixture effect would not have vanished: it would have been absorbed into repeatability, inflating it and leaving nothing on the report pointing at the fixture.

Repeatability and reproducibility are near enough equal¶

Repeatability is 2.89 percent of the variance and reproducibility 3.16 percent, so reproducibility is very slightly the larger of the two here. That is a different balance from a study where the equipment is the problem, and it points at the fixture rather than at the gage itself.

There are no confidence intervals¶

Look for the confidence interval table and there is none. On a Crossed or Nested report a 95% Confidence Intervals table sits directly under the Gage R&R table; on this one the Probabilities of Misclassification block follows straight on. An Extended study reports no intervals at all, whichever estimation method is used.

This is the price of the Model tab. If your study fits Crossed or Nested and the intervals matter, use that tool instead.

What the Stats Advisor says¶

Total GR&R (% Total Std Dev) is 24.59, in the 10 to 30 band, so the Advisor prints its marginal verdict in blue.
Number of Distinct Categories (ndc) is 5, exactly on the boundary the Advisor treats as acceptable, so that verdict is black.

Things to try next¶

Drop the Fixture column and run it as Crossed. The fixture effect does not disappear; it is absorbed into repeatability, which grows. Comparing the two reports is the most direct demonstration of what an additional factor buys you.
Tick the Part * Operator interaction on the Model tab and run it again. The report then carries two analysis of variance tables if the removal loop drops it at the 0.25 default, and one if it does not.
Move Fixture into Part-to-part variation. Every percentage changes, because the fixture's variance moves from the numerator of the gage comparison to the denominator. It is the wrong choice for a fixture, and doing it once makes the grouping rule concrete.