# Methods and formulas for Type 1 Gage Study

Select the method or formula of your choice.

## Reference

The reference, Xm, serves as a point of comparison in a study. Usually, a reference value is determined by averaging multiple measurements of the reference part that are taken with lab-calibrated measuring equipment.

Ideally, Xm is close to the center of the tolerance zone for the characteristic that you measure.

## Mean

The mean of the measurements of a part is calculated by:

### Notation

TermDescription
Xithe measurement of the ith part
nthe number of measurements

## Standard deviation

The standard deviation of the measurements of a part is calculated by:

### Notation

TermDescription
the mean of n measurements
Xithe measurement of the ith part
nthe number of measurements

## Study variation (SV)

The study variation is calculated by:

### Notation

TermDescription
k1

Minitab uses the default value of 6 standard deviations from a standard normal distribution to represent 99.73% of your measurements.

To change this value, see the Options sudialog box. For example, use the multiplier 5.15 to represent 99% of your measurements.

Sthe standard deviation of the measurements

## Tolerance

The tolerance is specified for each component. You must enter either the tolerance or one of the specification limits.

Tolerance = USL – LSL or USL – 0 when the LSL is replaced by the natural zero.

### Notation

TermDescription
USLthe upper specification limit
LSLthe lower specification limit

## Resolution

The resolution is the specified gage resolution.

A guideline for the resolution is that it should not be greater than 5% of the tolerance. So, if you specify both the resolution and the tolerance, Minitab calculates whether the resolution is less than, greater than, or equal to 5% of the tolerance.

## Bias

The gage bias is calculated by the difference between the mean of the n measurements and the reference value.

### Notation

TermDescription
the mean of n measurements
Xmthe reference measurement

## T

The t-statistic for testing the null hypothesis that bias = 0 versus the alternative hypothesis that bias ≠ 0.

t follows the t-distribution with γ degrees of freedom, where γ = n – 1.

### Notation

TermDescription
nthe number of measurements
the mean of n measurements
Xmthe reference measurement
Sthe standard deviation of the measurements

## p-value

The p-value is associated with the t-statistic. It is the probability of obtaining a t-statistic as large or larger than the calculated one, assuming that the bias is zero. As the t-statistic increases, the p-value decreases. The smaller the p-value, the greater the evidence against the null hypothesis that the bias = 0.

## Cg

Capability indices are calculated only when the gage tolerance is specified. The capability of the gage is calculated by:

### Notation

TermDescription
Kthe percent of the tolerance for calculating Cg specified in the Options subdialog box, default = 20
SVthe study variation

## CgK

Capability indices are calculated only when the gage tolerance is specified. The capability of the gage, considering both the gage variation and the bias, is calculated by:

### Notation

TermDescription
Kthe percent of the tolerance for calculating Cg specified in the Options subdialog box, default = 20
the mean of n measurements
Xmthe reference measurement
SVthe study variation

## %Var (Repeatability)

% Var for repeatability compares the gage repeatability with the tolerance. % Var is calculated by dividing the study variation by the tolerance and multiplying by 100.

### Notation

TermDescription
Kthe percent of the tolerance for calculating Cg specified in the Options subdialog box, default = 20
SVthe study variation

## %Var (Repeatability and Bias)

% Var for repeatability and bias compares the gage repeatability and bias with the tolerance.

### Notation

TermDescription
Kthe percent of the tolerance for calculating Cg specified in the Options subdialog box, default = 20
the mean of n measurements
Xmthe reference measurement
SVthe study variation
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