Re: MSA 3rd ed March 2002 page 93 formulas
Hi ,
Here I am again with the Linearity formulas problems in the MSA manual 3rd Edition March 2002 pages 93-94 and Example pages 94-96 .
I have just basic knowledges of Statistics and perhaps is one reason for the difficulties encountered with those formulas .
I think another reason could generate some confusion in the Manual are the Notations . For example , in all cases should be number of appraisers=k , number of parts=n (not g) and number of trials=r (not m) , to avoid possible confusions in some cases with the g and the m of the d2*Table .
Regarding the a slope formula (page 93) of the best fit line , the Notations should be xi (not x) and yi (not y) in order to be consistent with the notations previously used for defining the best fit line : i being previously defined as the index for the parts , xi the reference values and yi their bias averages .
What's for sure is that m should be removed from the formula , being a linear regression with number of cases = g = number of parts . The confirmation comes from the linear regression for the Example (pages 94-96) made in Excel .
Now another question is if m should be consequently removed from the other formulas : for s ; lower and upper confidence bands ; statistic t .
With regard to the formulas of lower and upper confidence bands , it appears "a given x0 " which I assume is one of the xi values . I assume x bar is the average of the xi reference values
In the formula of statistic t calculated for the a slope (page 93) it appears
a xj (?) , j being previously defined as the index for the number of trials (repetead number of measurements on each part) .
However , trying to work the Example of pages 94-96 , I was not able to obtain the same results .
I e-mailed to AIAG , but there two kind ladies (Lisa and Karen) were unable to help me .
I try to understand and apply the Linearity study as guidelined in the Manual at pages 92-94.
Previously I use to estimate Linearity by 2 methods :
a) Linearity = abs(a=slope)*Process Variation
%Linearity = Linearity*100/Process Variation = abs(a)*100 [%]
The closest to zero the best .
b)Conducting a bias study for 3-5 parts which characteristic values cover the tolerance range ; for each part zero must fall between the lower and upper confidence bands of the bias ; closest the bias values of the parts the best