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,
