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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