# AIAG's MSA Manual 3rd Edition Attribute Gage Study - Calculating the UCI and LCI

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#### jsamson

MSA 3rd Edition Attribute Gage study

I'm in the process of getting our Attribute Gage studies up to MSA 3rd Edition. I have managed to get my way through all of it, but am having a small issue with calculating the UCI and LCI. To calculate these I am using an equation from one of my Stats book for Confidence Interval for proportions. The issue is that I'm gettin different answers from what MSA has in their example. Can someone please help me, with finding the correct equations to use.

thanks.

A

#### Atul Khandekar

jsamson said:
I'm in the process of getting our Attribute Gage studies up to MSA 3rd Edition. I have managed to get my way through all of it, but am having a small issue with calculating the UCI and LCI. To calculate these I am using an equation from one of my Stats book for Confidence Interval for proportions. The issue is that I'm gettin different answers from what MSA has in their example. Can someone please help me, with finding the correct equations to use.

thanks.
First off, Welcome to the cove!

The MSA manual uses the exact confidence intervals for Bianomial distribution for LCI/UCI. You'll have to look up some good stats book on how to calculate the limits.

I remember, sometime back there was an excel sheet for attribute study someone had posted here as attachment - you can 'Search' for it .

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#### Alex Kobzar

Can anybody suggest how to calculate the binomial UCI/LCI to get the results suggested in MSA?
...p+/-1.96*(p*q)^(0.5) for the sample on page 131 results in (94%; 74%), when MSA sais (93%, 71%)

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B

#### Barbara B

There must be a mistake in one of the calculations: The CI is symmetric around p, leading to:
for the first CI p=1/2*(94+74)=84
for the second CI p=1/2*(93+71)=82

Barbara

B

#### bleoj69

The typical CI formula for Binomial distribution you see in Stats books is using the normal approximation approach. This will not work when p = 0 or p = 1.

The MSA manual is using the Clopper-Pearson interval for binomial distribution. See http://stat.wharton.upenn.edu/~tcai/paper/1sidedCI.pdf pp. 19-20.

How to compute: (Let's use the example in the manual p.131)

Total inspected : 50
# Matched (x): 42

UCI = BETAINV(1-alpha/2, x+1, n-x)
LCI = BETAINV(alpha/2, x, n-x+1)

Special case:
if x = n, UCI = 1 and use alpha instead of alpha/2 in the LCI formula.
if x = 0, LCI = 0 and use alpha instead of alpha/2 in the UCI formula.

Try it in Excel. You should now have the same result as that found in the manual.

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#### Alex Kobzar

Wow!

so much!!!!!!
...with ALFA = 0.05 the calculation gives:
n = 50
x = 42
93.85% = UCI (MSA = 93%)

n = 50
x = 42
71% = LCI (MSA = 71%)

n = 50
x = 39
90.64% = UCI (MSA = 89%)

n = 50
x = 39
64% = LCI (MSA = 64%)

...MSA is not exact(?).

#### Attachments

• MSA.xls
13.5 KB · Views: 1,081
Last edited:
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#### roland_lu

Alpha =0.05, not 0.1

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Alex,

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#### Alex Kobzar

Right, the formula works.

#### Attachments

• CI.xls
15 KB · Views: 565
N

#### nurcan

alpha in UCI LCI formula

Hello all,

Alpha in UCI LCI formula is taken as 0,05 for the example in MSA manual. Does the value of alpha depend on sample size? Can I use this 0,05 for both 20 samples and 100 samples?

Thanks a lot,

Nurcan