# Gage Bias and Linearity

Six Sigma – iSixSigma Forums General Forums General Gage Bias and Linearity

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• #253695

Spillner
Participant

How to determine if bias and linearity are acceptable

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#253775

MinitabUser1829
Participant

Take a look at the Minitab Help System, at the topic called Gage Linearity and Bias Study. Here is a direct link to the topic:

https://support.minitab.com/en-us/minitab/20/help-and-how-to/quality-and-process-improvement/measurement-system-analysis/how-to/gage-study/gage-linearity-and-bias-study/before-you-start/overview/

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#255904

Semoi
Participant

Personally, I feel that there are two parts, which are important:
1. How large are the results (=bias and non-linearity) compared to the tolerance range
2. How large are the results compared to the standard deviation of the process.
In order to combine these two considerations I would calculate the C_g and C_gk value, which judges the bias. To judge the non-linearity, I would modify the formula to account for the non-linearity. Here an example: Say your specification limits are [450, 520], the product follow a normal distribution with mean 495 and standard deviation 5. Since the tolerance range is 70 the C_g value is C_g = k* 70/(6*5) = k* 2.333 and C_gk = k*(520-495)/(3*5) = k*0.83. Usually, k is taken to be in the range [0.1, 0.3]. In addition, you have to decide which C_pk-value your products needs, and use this as the lower limit for the C_gk value — note that the two only differ by the factor k.
Since the linearity of a gauge is a bias for a specific reference value, we can use the upper formula for C_gk and plug in the largest difference between reference value and measurement result. Of course, this is a C_gk only for the specific reference value — make sure that your notation reflects this, e.g. by using C_gk(target=…). Like this you use a single quantity (the C_pk-value of your product) to determine whether or not your gauge is sufficient — in addition with a predefined k-value.

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#255905

Semoi
Participant

Link break or the text get changed. So it would be helpful if you could provide a short summary describing the key points.

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