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Type 1 gage study

Cg, Cgk and the bias t-test from repeated measurements of one reference part, with a run chart.

Input

Example dataReplace with your own measurements

Measurements

Paste, open a CSV, TSV, TXT or XLSX file (up to 20 MB), or drop it on the field. Files are read in this browser only.

10,01
10,02
9,99

Individual values
1 column

One column, in the order the measurements were taken
Decimals: 12,5 or 12.5

One column · 50 rows
Read as: single column · decimal point · 50 individual values (subgroup size 1) · header row skipped

ColumnsDecimal

Data as understood — first 10 of 50 rows
#	Value
1	24.999
2	25.001
3	25.003
4	24.999
5	25.001
6	25.002
7	24.998
8	25.002
9	25.002
10	24.999

+40 more rows

One reference part (a master or setting gage with a known value) measured repeatedly by one gage, ideally 50 times and at least 25, in the order the measurements were taken.

Reference part and gage

Reference value

Resolution (optional)

Resolution: the smallest step the gage shows. A warning appears when it is more than 5% of the tolerance.

ToleranceLower and upper specTol = USL − LSL.Tolerance widthType Tol directly, e.g. 0.1 for ±0.05.

LSL

USL

Tolerance (USL − LSL)

Options (Minitab defaults)

Percent of tolerance (K)

Study variation (L × s)

Alpha for the bias test

Minimum Cg and Cgk

Cg compares K% of the tolerance with L standard deviations: K 20 and L 6 are Minitab's defaults (L 5.15 covers 99% instead of 99.73%). 1.33 is the commonly used minimum for Cg and Cgk; your customer may require another value.

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Results

1.59Cg · repeatability

1.46Cgk · repeatability and bias

Acceptable — Cg 1.59 and Cgk 1.46 are both at least 1.33

The bias of 0.00086 is statistically significant (p = 0.005 < α = 0.05): the gage reads high on average.

50 measurements · mean 25.00086 · s 0.00209 · bias 0.00086 · Tol 0.1

MeasurementOutside the bandReferenceRef ± 0.1·TolMeanHistogram

Basic statistics
Statistic	Value
Reference	25
Mean	25.00086
StDev	0.00208992
6 × StDev (SV)	0.0125395
Tolerance (Tol)	0.1
Resolution	0.001
N	50
Min	24.997
Max	25.005

Bias (one-sample t-test)
Statistic	Value
Bias	0.00086
T	2.91
DF	49
P-value (test bias = 0)	0.005
Alpha	0.05

Capability
Statistic	Value
Cg	1.59
Cgk	1.46
%Var(Repeatability)	12.54%
%Var(Repeatability and Bias)	13.72%
Minimum Cg and Cgk	1.33
K (percent of Tol)	20%
Ref ± 0.1·Tol	24.99 – 25.01

Download offline versionSingle HTML file · v1.4 · 552 KB · works without internet

Method

Purpose: a Type 1 gage study checks one gage before a Gage R&R: one operator measures one reference part with a known value (a master or setting gage) many times, ideally 50 and at least 25, under the usual conditions. It judges repeatability and bias, not reproducibility or linearity.
Data: one column of measurements in the order they were taken (a header row is skipped). Several columns are not accepted, because their order would be a guess. Empty cells are skipped.
Statistics: x̄ = mean, s = standard deviation with n − 1, study variation SV = L · s, Tol = USL − LSL (or the tolerance width typed in), bias = x̄ − reference.
Cg = (K/100 · Tol) / (L · s) and Cgk = (K/200 · Tol − |bias|) / (L/2 · s), with K = percent of the tolerance (default 20) and L = number of standard deviations (default 6): Minitab's formulas and defaults. With them Cg = 0.2 · Tol / 6s and Cgk = (0.1 · Tol − |bias|) / 3s. %Var(Repeatability) = K / Cg = 100 · L · s / Tol and %Var(Repeatability and Bias) = K / Cgk, defined only while Cgk is above 0. With K = 20, Cg = 1.33 corresponds to %Var = 15%.
Bias test: one-sample t-test of bias = 0, t = bias / (s / √n) with n − 1 degrees of freedom and a two-sided p-value. p below alpha (default 0.05) means the bias is statistically significant. A significant bias is not by itself a failure: Cgk shows whether it matters for the tolerance. The sign of t follows the bias (negative when the gage reads low).
Verdict: acceptable when both Cg and Cgk are at least the minimum, 1.33 by default. Minitab reports the indices without a verdict; 1.33 is the commonly used limit (e.g. in automotive gage guidelines), and some customers ask for more. Use the limit your customer or your own procedure gives.
Warnings: fewer than 25 measurements; a resolution above 5% of the tolerance (the common rule that a gage should resolve 1/20 of the tolerance); Cgk at or below 0 (|bias| ≥ K/200 · Tol); a reference value outside LSL–USL; measurements outside Ref ± K/200 · Tol.
Charts: the run chart shows the measurements in order with the reference, Ref ± K/200 · Tol (0.1 · Tol with K = 20) and the mean, as Minitab's Type 1 run chart; look for trends, jumps and steps of the resolution. The histogram shows the same lines; its bins follow the Cpk tool (Freedman-Diaconis, 5–25 bins, edges between resolution steps).
Results use the decimal sign of the pasted data. The results CSV follows it too: decimal comma gives “;” between columns. It lists every statistic and the measurements with their deviation from the reference.
Files: CSV, TSV and TXT are read as if pasted (UTF-8, UTF-16, otherwise Windows-1257). XLSX: choose the sheet and the columns or a cell range; formula cells use the value Excel last saved, dates are kept as text. Files up to 20 MB are read in this browser only and never uploaded.
XLSX files are read with SheetJS Community Edition 0.20.3, Apache License 2.0 (license), loaded only when an Excel file is opened or created.