Minitab calculates the probabilities of misclassifications as both joint probabilities and conditional probabilities when you enter at least one specification limit.
Probability that part is bad and you accept it:
Probability that part is good and you reject it:
Probability that given a part is bad, you accept it (false accept):
Probability that given a part is good, you reject it (false reject):
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.