Bias in a stress-strength problem

The bias of the maximum likelihood estimator for R≠Pr{ X<Y} where X and Y are independent normal random variables with unknown parameters is discussed. The bias is an odd function with respect to δ=gauf^-1 (R), where gauf(·) is the Cdf of the standard normal distribution, so the study is restricted to R ⩾0.5, or equivalently, δ⩾0. There exists δ₀>0 such that the bias is positive in the interval 0<δ<δ₀. R has a positive bias at least in the interval 0.84<R<0.94