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Type 1 Gage Study How-To

This walkthrough runs a complete Type 1 study: one part, measured twenty-five times, by one appraiser, on one gage, against a known reference value.

The finished report says the gage repeats acceptably but reads high, and the bias is large enough to be worth acting on, so there is something to read rather than a clean pass.

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

One setting master, a gage block certified at 10.000 mm, measured twenty-five times with the same bore gage by the same person over one morning. The gage reads to three decimal places, so its resolution is 0.001 mm. The characteristic being controlled is specified at 9.800 to 10.200 mm.

Diameter
10.013
10.016
10.009
10.001
10.007
10.000
10.013
10.029
10.006
10.005
10.019
10.017
10.014
10.001
10.012
10.021
9.996
10.007
9.989
9.996
9.990
10.010
9.997
10.016
10.015

Twenty-five readings in one column. That is the whole of a Type 1 study's data: no part column, no operator column, no replicate number, because there is only one part and one operator and every row is a replicate.

Look down the column before running anything. The readings spread over about 0.04 mm, which is a tenth of the 0.400 mm tolerance, and that is the repeatability the study is about to put a number on. Notice also that most of them sit above 10.000. The part is certified at exactly 10.000, so that lean is bias, and the study is about to test whether it is real.

Twenty-five is the recommended minimum

This study has exactly twenty-five readings, which is why no sample size note appears on the report. Run the same study with twenty and the sheet prints Note: You have only provided 20 measurements, the recommended minimum is 25. under the summary statistics. The study still runs.

Steps

  1. 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 the header in row 1 and data in rows 2 through 26.

  2. Select the data and start the analysis

    Select A1:A26, including the header row. From the Excel ribbon: QXL Stat Tools > MSA / Gage R&R > Type I MSA Gage Study (Repeatability Only).

    The report is written straight away, from the default options, and the dialog opens on top of it. The numbers on the sheet at this moment are incomplete, because the dialog has not yet been given the reference value or the specification limits. That is expected.

  3. Confirm the measurement column on the Data tab

    Tick Diameter under Data Columns if it is not already ticked. There is nothing else to do on this tab.

  4. Fill in the per column grid on the Options tab

    Move to the Options tab. The top group, Per Measurement Column, holds one row headed Diameter. Type into that row:

    • Reference Value: 10
    • LSL: 9.8
    • USL: 10.2
    • Resolution: 0.001

    Each entry takes effect when you leave the box, and the worksheet is rewritten each time. Leaving both specification limits empty would leave every capability figure as N/A, because a tolerance needs both.

  5. Leave the study options alone

    Percentage of Tolerance: stays at 0.2, Number of Standard Deviations: at 6 and Alpha for the bias test: at 0.05. These are the values the report below was produced with.

  6. Record what the study was of, then finish

    Under Gage Information, fill in as much as you want to keep with the sheet. For this walkthrough, put Bore gage 4 in Gage Name: and Setting master in Part Name:.

    Choose Finish.

Reading the report

The worksheet is named Type 1 Gage Study. The run chart is at columns D to O and the statistics table at columns Q and R. Working down that table:

Row What you should see
LSL 9.800
USL 10.20
Tolerance Width 0.4000
Percentage of Tolerance 20.00%
# Standard Deviations 6.000
Reference Value 10.00
Resolution 0.001000
Sample Size 25
Mean 10.01
StDev 0.009931
6*StDev 0.05959
Bias 0.007960
T 4.008
P-Value <0.001
Cg 1.343
Cgk 1.075
% Repeatability 14.90%
% Repeatability and Bias 18.60%
% Resolution 0.25%
Resolution Acceptable Yes

Every number is printed to four significant digits, which is why Mean reads 10.01 while the arithmetic behind Bias used 10.00796.

What the report is telling you

The gage repeats. Six standard deviations of measurement spread is 0.05959 mm against a 0.400 mm tolerance, so % Repeatability is 14.90%, just inside the 15% the cell note names. Cg is 1.343, just above the 1.33 the cell note names. Both pass, and both pass narrowly.

The gage reads high, and that is not chance. The mean is 0.00796 mm above a reference value certified at 10.000. The t test on that difference gives 4.008 on 24 degrees of freedom and a p value below 0.001, so the P-Value cell is printed red and bold: at an alpha of 0.05 the bias is significant. Hover the Cgk cell and the note says adequate systems have Cgk above 1.33.

The bias is what costs you. The two figures that ignore bias pass; the two that include it fail. Cgk drops to 1.075 and % Repeatability and Bias rises to 18.60%, past the 15% in its note. The difference between the two pairs is the whole message of this study: the gage is precise enough, but it is not reading the right number, and a bias is the kind of problem you can fix by adjusting the gage rather than by replacing it.

The resolution is not the problem. 0.001 mm against 0.400 mm of tolerance is 0.25%, far under the 10% of the rule of tens, so Resolution Acceptable reads Yes.

The run chart

Run Chart - Diameter plots the twenty-five readings in the order they were taken, against Observation. Three flat lines cross it:

  • Center, green, at 10.00. It sits at the reference value rather than the mean, because a reference value was given.
  • Upper, red, at 10.04, and Lower, red, at 9.960. The two are 0.0800 mm apart, which is the 20% of tolerance you left in Percentage of Tolerance:.

Every reading is inside the band, which is the picture of Cg being above 1. But look at how they sit inside it: almost all of them are above the green line, and none is near the lower red line. That lopsidedness is the bias the table just tested, and it is easier to see here than in any number.

Try changing one thing

The dialog is still available through Modify, and each of these rewrites the sheet immediately.

Clear the reference value. Bias, T, P-Value and Cgk all become N/A, and % Repeatability and Bias goes with them, because it is computed from Cgk. The green Center line moves from 10.00 to the mean of the readings, and the chart suddenly looks balanced. The study has lost its ability to see bias at all, which is why a reference value is worth the trouble of getting one.

Clear the LSL and leave the USL. Everything that needs a tolerance becomes N/A, the two red lines disappear from the chart, and a note appears under User Supplied Data saying that both limits are needed. One limit is not half a tolerance.

Set the percentage of tolerance to 0.1. The reference span halves, so Cg halves to 0.6713, while Cgk falls further than half, to 0.4041, because the bias did not shrink with the span. The red lines close in to 10.02 and 9.980, and the highest reading is now outside them. Nothing about the gage changed; you asked a harder question of it.

See Also