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Nested How-To¶

This walkthrough runs a nested gage study: three operators, three parts each, two measurements per part. No part is measured by more than one operator, which is what makes the study nested.

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¶

A destructive weld pull test, run at three sites. Each site has its own operator and its own material, and the material cannot be moved between sites, so no part can be handed to a second operator.

Each operator took three parts from their own stock and pulled two coupons from each, recording the breaking load in kilonewtons to two decimal places. So a part here is one piece of stock, and the two measurements are two coupons cut from it. The specification is 19.00 to 21.00 kN.

Operator	Part	Load
A	1	19.55
A	1	19.50
A	2	19.87
A	2	19.84
A	3	20.23
A	3	20.13
B	1	19.81
B	1	19.83
B	2	20.11
B	2	20.01
B	3	20.17
B	3	20.32
C	1	19.94
C	1	19.92
C	2	20.12
C	2	20.15
C	3	20.43
C	3	20.46

Eighteen rows: three operators, times three parts each, times two measurements.

Part 1 appears three times and is three different pieces of stock

The Part column runs 1, 2, 3 under operator A, then 1, 2, 3 again under B, then again under C. Those are nine different physical parts, not three measured by everybody. In a nested study a part label identifies a part only within its own operator.

You do not need to renumber them 1 to 9. The analysis reads a nested part label as a position within its operator, so both ways of labelling describe the same study and give the same report. It will report nine observed parts.

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 19.
Select the data and start the analysis

Select A1:C19, including the header row. From the Excel ribbon: QXL Stat Tools > MSA / Gage R&R > Nested.
Assign the columns on the Data tab
- Tick Load under Measurement Columns.
- Tick Part under Part.
- Tick Operator under Operator (Optional).
Enter the specification limits

In the Specification Limits grid, on the Load row, type 19 under LSL and 21 under USL.
Leave the Options tab alone

Note that XbarR is disabled, with the reason shown beneath it. That method forms part and operator cells, and a nested layout has none. Automatic will choose expected mean squares, because the data are balanced.
Choose Finish

A new worksheet named MSA Nested appears.

What the report says¶

One analysis of variance table, and no interaction term¶

Source	DF	Adj SS	Adj MS	F	P
Operator	2	0.30443	0.15222	1.04	0.410
Part (Operator)	6	0.87957	0.14659	54.41	<0.001
Repeatability	9	0.02425	0.00269

There is one table, not two. A crossed study of this size would carry a Part × Operator interaction and, by default, would remove it and print a second table. A nested study has no interaction term at all, so there is nothing to remove and nothing to pool.

The part term is written Part (Operator), meaning the part effect within operator. Its 6 degrees of freedom are two per operator, three parts each less one.

The Gage R&R table¶

Source	Variance	Std Dev	Study Var (6 x SD)	% Contribution	% Tolerance
Total Variation (TV)	0.075581	0.27492	1.64953	100.00%	82.48%
Total Gage R&R (GRR)	0.003631	0.06026	0.36157	4.80%	18.08%
Repeatability (EV)	0.002694	0.05191	0.31145	3.56%	15.57%
Reproducibility (AV)	0.000937	0.03061	0.18367	1.24%	9.18%
Operator	0.000937	0.03061	0.18367	1.24%	9.18%
Part to part (PV)	0.071950	0.26823	1.60941	95.20%	80.47%
Part (Operator)	0.071950	0.26823	1.60941	95.20%	80.47%

The last row is the part term's member row, and note that it is labelled Part (Operator) here, the same nested name the analysis of variance table uses.

and beneath it:


%GRR	21.92%
%EV	18.88%
%AV	11.13%
%PV	97.57%
P/Tol Ratio	0.1808
Number of Distinct Categories (ndc)	6 (CI: 0.3833 to )

The distinct-categories interval has no upper end on this study

The cell really does read 6 (CI: 0.3833 to ) with nothing after the "to". It is not a transcription slip on this page.

The count is a ratio of the part spread to the gage spread, and this study's confidence interval on Total Gage R&R runs down to 0. A gage spread of zero makes that ratio unbounded, so the upper end of the interval is infinite and prints as nothing at all.

The count itself, 6, is unaffected. This is recorded as an engineering flag.

Repeatability is the larger half here¶

Unlike a study where the operators disagree, this one puts most of the measurement error in repeatability: 3.56 percent of the variance against reproducibility's 1.24 percent. In standard deviation terms that is %EV 18.88 against %AV 11.13.

So two coupons cut from the same piece of stock by the same operator vary more than the operators vary from each other.

A positive reproducibility with a non-significant operator test¶

Read the two together and they look contradictory:

Reproducibility is reported as 0.000937, a positive number, and %AV is 11.13.
The Operator F test is 1.04 with a p-value of 0.410, nowhere near significant.

Both are correct, and the combination is common. The component is a moment estimate, the difference between two mean squares divided by a coefficient, and it came out slightly positive. The F test asks a different question: whether that difference is bigger than sampling variation would produce on its own. Here it is not, so the test cannot distinguish the operators.

A reported component is an estimate, not a claim that the effect is real. The p-value is where that question is answered.

Had the difference gone the other way, the estimate would have come out negative and the report would have shown zero with a footnote saying a negative estimate was set to zero.

The part box plot has no boxes, and says so¶

Scroll to the charts and the Part Box Plot is empty, carrying this note underneath:

Not enough data to draw the boxes: a box needs at least 4 measurements per part, and every part here has fewer.

That is expected on this data rather than a fault. A box needs four measurements in its group, and in a nested study a part is measured by one operator only, so each of these nine parts has just its own two coupons. Two is below four, so no part gets a box.

The Operator Box Plot is unaffected and draws normally, because an operator's group gathers all three of their parts, which is six measurements.

To get part boxes on a nested study you would need at least four measurements per part, meaning four trials rather than two.

What the Stats Advisor says¶

Total GR&R (% Total Std Dev) is 21.92, in the 10 to 30 band, so the Advisor prints its marginal verdict in blue.
Number of Distinct Categories (ndc) is 6, and 5 or more is acceptable, so that verdict is black.

There is no interaction chart anywhere on the sheet, for the reason given above.

Things to try next¶

Run the same data as Crossed instead. It will report, because the layout is accepted, but the answer is to a different question: part 1 would be treated as one part measured by all three operators rather than three separate pieces of stock. Comparing the two reports is the clearest way to see that the choice between crossed and nested is about the data, not a preference.
Renumber the parts 1 to 9 and run it again as Nested. The report is identical, which is the labelling point made above.