# Any Easy Way to determine Linearity Study Acceptability?

#### beaser3

##### Involved In Discussions
Does anyone know of an easy way to determine if a linearity study is acceptable? Each time I calculate it graphically on our software, it runs a straight line at zero. Does that seem correct? Could standard error or goodness of fit (both of which are calculated in the software) be used as an acceptable number? Ex: If standard error is below "whatever number" linearity is acceptable. Our procedure used to direct us to use the % tolerance for acceptability but that is no longer calculated in the software. Any help would be appreciated.

#### AndyN

##### Moved On
Re: Linearity study acceptability

It would help to know what the study is being performed on. Some types of measuring equipment might have other characteristics which could affect linearity, bias for example. Let us know and we'll try to help.

#### beaser3

##### Involved In Discussions
Re: Linearity study acceptability

Thanks for the quick response!

We do one time linearity studies on all of our equipment. Some examples are digital calipers, digital micrometers, microscopes, smartscope, etc. We only do this when the gage is purchased and it is never done again.

Staff member
Re: Linearity study acceptability

Interesting! I am intrigued that you only perform initially. Most instrument/equipment's linearity degrades with time.

Exactly how many points along a line are you choosing? Are they spread out along the area of interest, or clustered high, low, or middle?

As you well know , there are lots of ways to graph something. You could establish a raw value above/ below the line as an acceptance value.

I would think Goodness of Fit would benefit you if you are estimating/modeling. For example, you develop a linear formula to estimate some behavior, put in numbers, and see how close that formula predicts.

#### AndyN

##### Moved On
Re: Linearity study acceptability

Thanks for the quick response!

We do one time linearity studies on all of our equipment. Some examples are digital calipers, digital micrometers, microscopes, smartscope, etc. We only do this when the gage is purchased and it is never done again.
Not much point in doing the study really, IMHO, except as a baseline for a 'family' of equipment types. What you say about 'running through zero' probably will happen with new equipment.......

A

#### Atul Khandekar

Re: Linearity study acceptability

beaser3, Welcome!

If you have the AIAG MSA manual, it gives the criteria for acceptability based on two hypothesis tests: 1. that the bias is zero and 2. that it is uniform over the range of the gage. Also, if you search through the posts in this forum, you will probably find this issue discussed. The straight line at Zero is the 'ideal' Bias=0 line.

#### beaser3

##### Involved In Discussions
Thanks to all for the replys. This is getting a little bit clearer. On one study, my results show a standard error of .00012 and is flagged "UNACCEPTABLE" by the software. The graph still shows all points along the zero line though. Would this gage be accepatble?

#### Miner

##### Forum Moderator
Staff member
Can you attach the results and advise what software you are using?

Reference the attached file from Minitab data. This shows an unacceptable Linearity study. If the blue zero Reference line falls within the red confidence limits, the study is acceptable. You may also interpret the p-values for each reference value. If all p-values are greater than 0.05, the linearity is acceptable.

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