Repeatability Standard Deviation Formula in MSA 4th Edition

jelly1921

Quite Involved in Discussions
#1
In MSA fourth version, Guidelines for determining bias:
analysis of results - numerical

sigma repeatability = sigma r = sum(Xi-Xbar)^2/(n-1)

Is it correct?

I think it should be = (sum(Xi-Xbar)^2/(n-1))^0.5

or (sigma r)^2 = sum(Xi-Xbar)^2/(n-1)

Because in the following page example-bias

sigma r = 0.212019765 [=(sum(Xi-Xbar)^2/(n-1))^0.5]
instead of 0.044952381 [=sum(Xi-Xbar)^2/(n-1)]

Jelly
 
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Jen Kirley

Quality and Auditing Expert
Staff member
Admin
#3
I believe I have found the page in question.

On page 88 (Analysis of results - Numerical) the sigma formula listed in 6) is intended for use with an independent sample.

7) goes on to direct us to determine if the repeatability is acceptable by calculating %EV. It says "If the %EV is large then the measurement system variation may be unacceptable. Since the bias analysis assumes that the repeatability is acceptable, continuing the analysis with a measurement system with a large %EV will lead to misleading and confusing results." The t-statistic formula you cite with its .05 (95% confidence) is then introduced in 8) (pg. 88) and detailed in 9) (pg. 88-89), and is used to produce the results discussed on page 91.

Does this make sense?
 

jelly1921

Quite Involved in Discussions
#4
Thank Jennifer Kirley

The way is clear enough, no problem no that.

My qestion is that the formula in 6) of page 88 seems not right.
 
Last edited:

Jen Kirley

Quality and Auditing Expert
Staff member
Admin
#5
I anticipated a further question about it, so I made, and attached a calculator to exhibit the Bias Study in MSA Manual (4th ed) pp 87-92.

You can look at the formula for σb and see that it, and the result agrees with the MSA Manual. The math works out, I believe the formulas are correct.

The tool I have attached is meant to give you the perspective that the manual lacks - it does not work through the problem for us, it just shows you Table III-B 2 with results on page 92. If you know anything about Excel you can look at the formulas and see how they work.

The data array for the histogram is behind the graph.

I hope this helps!
 

Attachments

jelly1921

Quite Involved in Discussions
#6
I anticipated a further question about it, so I made, and attached a calculator to exhibit the Bias Study in MSA Manual (4th ed) pp 87-92.

You can look at the formula for σb and see that it, and the result agrees with the MSA Manual. The math works out, I believe the formulas are correct.

The tool I have attached is meant to give you the perspective that the manual lacks - it does not work through the problem for us, it just shows you Table III-B 2 with results on page 92. If you know anything about Excel you can look at the formulas and see how they work.

The data array for the histogram is behind the graph.

I hope this helps!
I do appreciate what you've done!

In your attachment, you use function to calculate standard deviation, instead of step by step without using the equation shown in 6) of page 88. I put the steps in the attachment.
 

Attachments

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