# MSA with only 1 replica, why varcomp for repeatibility is not zero?

Discussion in 'Gage R&R and MSA - Measurement Systems Analysis' started by laffranchinis, Jan 30, 2020.

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1. ### laffranchinisMember

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Hi all,

Quick question:

Theoretically, if for a MSA all the samples will be measured by the operators only once, we should not have information about the repeatability, right?
Why also Minitab give me varcomp and all the other information about repeatability?

Samuele

2. ### MinerModeratorStaff Member

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3. ### laffranchinisMember

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Hi Miner,

Here below the data and analysis:

Thanks in advance for the help
Samuele

4. ### MinerModeratorStaff Member

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This has to do with how ANOVA works. ANOVA will calculate the total variation, then the variation due to the operators and the variation due to the parts. It then subtracts the operator and part variation from the total variation as unexplained variation. In a normal study with replicates this would be the repeatibility. In this case it would be experimental error.

5. ### laffranchinisMember

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Hi Miner,

Maybe I am missing somethings, but when calculating the variations following formula are used (I found them on support.minitab.com) :
with

But the degree of freedom should be: a x b x (n-1) where n is the number of replicates, also 1 in this special case. So from the mathematical point of view, DF=0 and it should not be possible to calculate the variance of the repeatability.

any other comment/explanation will be welcome !
Samuele

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