# Gauge Performance Curve - MSA Manual Page 181 (4th Edtion)

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#### NumberCruncher

Hi

Why does the G.P.C. on page 181 not relate to the data on pages 178 and 179?

I have been through the calculations in OpenOffice, created a very basic "proof of principal" spreadsheet, got the same numbers as the example, drawn the graph - and got a different graph.

Is there a good reason why the left hand side of the graph (in the manual) has zero bias, but the right hand side has a bias of 0.05?

I have attached an Excel version of the spreadsheet, but as this has been converted from OpenOffice, whilst using Linux, I can't be certain it will work without a little 'repair' work. If so, my apologies in advance.

The calculations in yellow have zero bias, those in orange, 0.05 bias.

All comments welcome. It may be a few days before I get back to this.

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#### NumberCruncher

Hi Rameshwar

Many thanks for taking the time to read my post and the rapid response.

It will take me some time to go through the attribute G.P.C. section of the manual. I initially ignored this section as it refers to attribute data, which I am not looking at yet (one thing at a time). I strongly suspect that I have misunderstood or missed something.

However, the initial question remains. Why do the AIAG authors give me a set of calculations and data, then present a graph that doesn't relate to the numerical calculations on the previous pages?

For example, on page 178, the first calculation is for 0.5Nm, giving a probability of acceptance of 0.16. The graph on page 180 suggests that the probability of acceptance is roughly zero (too small a value to read off the graph).

Here are a few other idiosyncrasies.

Page 146, footnote "The 1.08 adjustment (unbiasing) factor is specific for a sample size of 20..."
What if I don't have a sample size of 20?

Why in the year 2011, are they still using the range to estimate standard deviations, then correct the range estimate with a table of factors (p203)? I have a pocket calculator that can calculate standard deviations.

Look up GRR in the index. The last two pages referenced are p226 and p227.
p229 is blank and p227 is the title page for the index!

p188 footnote. Another "unbiasing" factor pulled out of the statistical magician's hat.

I could go on, but I won't

It's very likely that the answer to many, if not all of the above questions can be found on this site. But why should anyone need to look so hard? The book should be sufficient.

Anyway, thanks again to Rameshwar. I shall go and do some more studying. I may well be back...

#### Rameshwar25

##### Quite Involved in Discussions
Dear
To have better understanding of GPC, i would suggest to from 145 to 150. The graph are on pg 149 and 150 and related data are on 147.
The study has been conducted for lower specification limit. After calculating bias and standard deviation, the graph has been extended from -0.02 to +0.02 ref values.
Ideally, the probability of accepting a part at USL and LSL is 0.5. But due to bias, the graph is biased towards accepting parts towards LSL.
The MSA manual (any edition) does not give you full explanation of any study. You need to refer prior editions or some other books for reference. Otherwise, the MSA manual will be too thick to handle.
for example, on page 100, R-sq value for linearity data is given 71.4%. The formula for calculation of this value is given in second edition of MSA manual. It has not been repeated here to lessen the number of pages.
Regarding pg 226 & 227, I would say that normally some pages are left blank in books so that reader can write down some important notes while reading. If reader makes notes in loose pages, he/she is likely to lose those pages.
Your graph with some modifications is attached herewith. I have just extended ref values upto 1.23.

Regards
Rameshwar

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#### NumberCruncher

Hi Rameshwar

Regarding my rant about the manual, my complaint is with AIAG, not with you. There is no point me in going on and on about it's deficiencies. The manual is not going to be changed and improved just because of me (although that would be good, and very flattering!).

Anyway, thanks for all of your effort and input, but as I said in my previous response, I now need to do some more study (including your comments about relevant pages), and this will take a few weeks because, like pretty much everyone else on the planet, I have to fit study into the gaps between life and a job.

Bye for now.

NumberCruncher

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