Misclassification in Gauge R&R

[#1]

In the misclassification chart of variability gauge test,

is the following the same thing?

P(good part is falsely rejected) and P(part is good and is rejected)

P(bad part is falsely accepted) and P(part is bad and is accepted)

what does P(part is good) stand for statistically?

Also, what is the difference between "repeatability" and 'reproducibility"?

Thanks!

[#2]

Hi,

There is a difference between these probabilities.  P(good part is falsely rejected) and P(bad part is falsely accepted) are conditional probabilities.  You might want to use a conditional probability if you have prior knowledge about a part.  For example, if you have a part that you know to be good then the probability that your good part will be falsely rejected is given by the conditional probability, P(good part is falsely rejected).  Likewise, if you have a part you know to be bad then the probability that your bad part will be falsely accepted is given by the conditional probability, P(bad part is falsely accepted).  Now, P(part is good and is rejected) and P(part is bad and is accepted) are joint probabilities.  You might want to use a joint probability if you have no knowledge about a part.  If you have a part that you have no prior knowledge about, then the probability that the part is good and will be rejected anyway is given by P(part is good and is rejected) and the probability that the part is bad and will be accepted anyway is P(part is bad and is accepted).  Finally, P(part is good) is a marginal probability.  You might want to use this probability when you have no prior knowledge about a part, but you want to know the probability of the part being good. 

I hope this helps.

[#3]

The terms 'repeatability' and 'reproducibility' originally came from the formal definition of the gage R&R study. Repeatability considers the variation in measuring the same part with the same gage by the same operator multiple times. It answers the question, "How repeatable is the measurement?" Reproducibility considers the variation in measuring the same part with a different gage by a different operator. It answers the question, "How reproducible is the measurement?"

You might have acceptable repeatability but unacceptable reproducibility. Perhaps the second gage is not functioning properly or requires calibration. Perhaps the second operator is not following the measurement procedure or lacks training.

It is helpful to separate these different kinds of variation in the measurements.