Minitab calculates the probabilities of misclassifications as both joint probabilities and
conditional probabilities when you enter at least one specification limit. For analyses
that offer the ANOVA method and the Xbar-R method, the results include the probabilities
of misclassification when you use the ANOVA method.

## Joint probabilities

Probability that part is bad and you accept it:

Probability that part is good and you reject it:

## Conditional probabilities

Probability that given a part is bad, you accept it (false accept):

Probability that given a part is good, you reject it (false reject):

## Notation

F_{(X,Y)} is the cumulative distribution function (CDF) of the bivariate normal random vector (X,Y)^{T} with:

mean, μ = (θ,θ)^{T}

F_{(X)} and F_{(Y)} are the corresponding marginal CDFs.

That is,