Linearity Analysis - MSA 3rd edition, March 2002 page 93 formulas

F

fibnro

#1
Hello ,

Some questions regarding the MSA 3rd edition March 2002 Chapter III Section B page 93 :
6) the m shouldn't be removed from the formula of the slope a ?
What's the meaning of xo , xi and x bar in the lower and upper confidence bands ?
8)What's the meaning of xj , xi and x bar in the formulas of t for a and b ?

Many thanks .
 
Elsmar Forum Sponsor
F

fibnro

#3
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
 
F

fibnro

#4
Re: MSA 3rd ed March 2002 page 93 formulas

Hi there ,

I'm back again with an Excel material : on the 1st sheet you'll find briefly the guidelines for determining linearity , as mentioned in the MSA Manual 3rd Edition March 2002 pp92-94 and the Example-Linearity pp94-96 (if I understood well there are people who don't have access to this MSA Manual). On the 2nd sheet there is my remake (as an exercise) of the Example-Linearity mentioned above .
Regarding the calculation of the slope a of the linear regression , the m must be removed from the formula (the linear regression in Excel - Add trendline / Linear / Show formula / Display R-Sq value - proves that) . Even theoretically is a linear regression with g=n=number of parts = 5 cases .
Regarding the R-sq value from the linear regression made in Excel (0.9779) I made a calculation (R is the Bravais-Pearson simple correlation coefficient) and the result is OK . I don't know how is calculated the 71.4 percent value of the R-Sq in the MSA Manual on which their conclusion ("linear model may be not an appropiate model of this data") is based ; as far as I know , the closest the R to -1 or +1 (as in this case) the best .
Further on my remake is based on the assumption that after the linear regression being made we have g-1=4 degrees of freedom (Apparently 5 cases is not so much statistics , but the 5 cases have a background of 60 measurements). As shown on 2nd sheet there are three different calculations of s (obtaining the same result 0.0626)whichin my oppinion confirm this hypothesis . Finally the t-statistic calculations for a and b give(not much) different results compared to the MSA Manual .
On the 2nd sheet up in the right there are the calculations made using the formulas mentioned in the MSA Manual . The results are not OK in my oppinion .
I don't want to be misunderstood ; the reason of this is not pointing out some possible mistake in the MSA Manual , but to clarify it ; in some cases it could be the difference between a good or a bad decision to be taken .
Of course there is the possibility to buy a dedicated software and to avoid all this kind of problems . But even in such a case , the software must be validated .
So I'll appreciate if someone is able to look over my remake and to comment .
 

Attachments

Last edited by a moderator:

harry

Super Moderator
#5
Thread starter Similar threads Forum Replies Date
I Interpretation of MSA (Measurement Systems Analysis) Linearity and Bias Study Results Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
Rameshwar25 Linearity Problem (MSA - Measurement System Analysis) Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 5
Miner Intro to Measurement System Analysis (MSA) of Continuous Data – Part 3: Linearity Imported Legacy Blogs 15
D Linearity Analysis - AIAG's MSA Manual 3rd Edition - Question Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 10
D Linearity Analysis - Measurement System Analysis - AIAG MSA Manual 3rd Edition Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 14
L Measurement System Analysis (MSA) - Bias, Linearity and Stability Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 23
A Acceptance p-value for linearity and bias analysis in minitab results Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 0
L Gage Linearity and Bias Study Analysis - Minitab help needed Using Minitab Software 4
S Stability, Bias and Linearity samples - Measurement Systems Analysis Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 5
M Test method validation - Is MSA (MSA1, MSA2, MSA3 and linearity) a good solution? Medical Device and FDA Regulations and Standards News 1
A The FILE recommended by AIAG MSA 4ed for LINEARITY Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 0
W Using MPE (Mean Percentage Error) for Linearity and Type-1 study Measurement Uncertainty (MU) 1
B Linearity study on a non-linear gage General Measurement Device and Calibration Topics 7
P Purpose of calculating Ta, Tb & R Square in Linearity Study Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
M How calculate P value for Linearity and Bias using Excel Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
P The correct way to do a Linearity and Stability Study on a Critical Dimension Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
E Company-wide MSA - Measurement Equipment Bias, Linearity & Stability Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
G Bias & Linearity Study and the Uncertainty of Standards Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
M Are Bias, Stability, and Linearity studies required by TS 16949 7.6.1? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 4
E Gage Linearity and Bias Questions Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 5
E How to Properly Apply Linearity - How does it "Fit"? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
I Difficulty with calculated t-value for Linearity Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 7
T Bias & Linearity Study - How to calculate the P value for the Average Bias Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
A Bias Linearity Stability MSA Excel File with Formula Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 4
M Profilometer Patch - Gain does not match, Linearity and Stylus = Good General Measurement Device and Calibration Topics 4
V Excel Linearity Chart - drawing 95% CI line & set X-axis at the bottom Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 13
C Linearity and Bias Study Compliance Requirements Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 9
Rameshwar25 Linearity Study - Tolerance for which Ref Value Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
Rameshwar25 Trendline-Linearity - Questions related to Linearity study graph Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
T Gage Bias and Linearity - How to interpret the Minitab results Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 6
Rameshwar25 MSA Manual 4th Edition, Page 100 - What is wrong in the Linearity graph? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
C "Destructive" Linearity Study Methodology Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 6
S MSA 4th Edition formats in Excel wanted - GR&R, Bias, Stability and Linearity Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
F R-sq index in Linearity study Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
J Uncertainty Budget for the Optical Microscope - Deriving Linearity Uncertainty Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
S Linearity Calculation Worksheet (including formula) General Measurement Device and Calibration Topics 1
M Linearity, BIAS & Stability - How many studies do I need to do for a device? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
L Recommend a 3rd Party Certifier for Master Value in Linearity & Bias Study General Measurement Device and Calibration Topics 0
B Can any one help me in Linearity calculations & acceptance criteria Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
B In a Linearity Study covering the operating range is it necessary to do Bias Study? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 6
M When to use Linearity and Bias - appropriate for paper tensile strength? Quality Tools, Improvement and Analysis 6
A Linearity and Eccentricity Point Definitions - Ref: ISO/IEC 17025:2005 ISO 17025 related Discussions 1
S If I do Linearity and Bias Studies, are Stability Studies Required? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 5
I R-sq Value is Almost Zero - Linearity Study Question Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
B Any Easy Way to determine Linearity Study Acceptability? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
Ron Rompen MSA to perform Linearity and Stability studies on Variable Gauges with Minitab Ver 15 Using Minitab Software 6
V Linearity - R-sq evaluation - Where can we find R-sq evaluation criteria? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
A Linearity and Bias Study - Bias Study fails - Seeking advice Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 7
P Linearity & Bias Acceptable Percentage Guideline - Digimatic micrometer General Measurement Device and Calibration Topics 2
D MSA - Can Regular Calibration Replace Bias, Linearity and Stability Studies? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3

Similar threads

Top Bottom