# Linearity Analysis - AIAG's MSA Manual 3rd Edition - Question

D

#### datony

in MSA edition 3,there are some equations for linearity analysis. like "s2=(∑yi2 – b ∑yi – a∑xiyi)/(gm-2)" in page 93, i am confused about how to use these eqations.for example, in the manual,it points out that "xi" is the refence value, does it mean "xi" is "2,4,6,8,10" as given in the example in page 94? as to "yi", does "yi" is the "bias average", like "0.491667,0.125, 0.025,-0.29167, -0.61667"? if "xi" and "yi" present the numbles as i thought,then we can't calculate out the value "ta","tb" as given in page 96. the equations is really confusing, i wonder if anyone can help me to make them clearer.
thank you very much!

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#### Darius

##### Quite Involved in Discussions
Re: Question on linearity analysis (msa 3 edition)

I don't know about MSA edition 3, but test for lineality in MSA is just test for a relationship between several "reference master" and the measure system.
ie.
Sample - Master - Measurement_Average
1 - 5.0 - 5.03
2 - 5.2 - 5.23
3 - 5.4 - 5.43
4 - 5.6 - 5.63
5 - 5.8 - 5.82
6 - 6.0 - 5.98

Calculate y(i)=A*x(i) + B

in this example y= -0.043*x +0.2553

A=> the slope, is taken as a percentage of lineality (the absolute value), it must be less than 10% to be OK.

Lineality = abs(A)*(process variation or tolerance) B

#### bowman

datony,
are you still interested in formula solving of linearity in msa 3rd edition ?

I have an excel worksheet with the complete solution and, of course, the demonstration about the incorrect formulas at page 96, given by an msa author Massimo

#### Howard Atkins

Staff member
Thank you and welcome to the cove

B

#### bowman

oh yes, tomorrow I will reply with the spreadsheet (including the e-mail from msa author, it is intresting)

maybe in the next months I will put on the net a free release of my gage managemant software (it works on Oracle DB).
At the moment is in italian but it is not difficult to translate it.

it is a pleasure to join the cove
Massimo

B

#### bowman

Here is the spreadsheet given me from an MSA guy.

here is the content of his letter:
------------------------------------------------------------
Dear Massimo
The questions you are asking with respect to the calculation of the parameters
and analysis of a straight line can be answered by reading a standard statistics
book or a book dealing with linear regression. The linearity analysis uses a
standard calculation of the slope, intercept, and confidence bounds of a linear
regression. The MSA manual is not intended to provide instruction in basic
statistics -- it assumes that the reader will have this basic knowledge.

I do not mean to put off your questions, but we set up the web feedback/question
capability to answer MSA queries not instruct others in statistics and/or debug
their scripting/programming. We are all volunteers; i.e. we do not get paid for
this service. I recommend that you contact a local competent statistician or
take a basic statistics course.

With that said, I have attached is an excel file with the details of the
calculations for the example in the MSA 3rd Manual. It should provide you with
further direction.

Greg
------------------------------------------------------------

------------------------------------------------------------
It ia a pitty you cannot find my first e-mail where I explained what I needed in more detail.

My doubts were from "s" calculation and |ta| results, because all my previous results (a,b etc.) are ok.
amd my problem was the lack of documentation about the intermediate results, and at the end of page 93, in |ta| formula, maybe correcting xj with x0 will be useful for me and could give less confusion: for example I shouldn't write you.
At page 94, |tb| has the same problem: xj becames xi but it is still x0. Please note at page 92 xi is equal to "reference value" and not x0 . please correct formula at page 94 or be more clear.
I'm sure I don't need a statistic course, believe me.
Despite of all, thank you for the clarification (now all of my doubts are clear) and thanks from the automotive community for your volunteer activity.
------------------------------------------------------------

Massimo

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#### Atul Khandekar

##### Quite Involved in Discussions
Many Thanks for sharing this file, Massimo... and Welcome to the Cove Forums!

#### cbearden

##### Involved In Discussions
Thanks for sharing that file....It was a great help...

Cyrus Bearden
Huntsville, AL.

B

#### bowman

it's ok,
you can image the days and hours I spent on msa with wrong formulas...

in the next months I will publish my gage software (for free, yes) that use also msa 3rd edition tests, maybe I will need help from all the Cove for a correct english translation, especially about technical terms.

Massimo

S

#### sammer

A very handy excel file indeed!!

Thank you very much Massimo....

sammer

I'll try and return the favour sometime soon.

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