Geodesic
On unbiased estimation of $P(Y$ in normal case
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part VI, Tome 136 (1984), pp. 5-12 
V. G. Voinov. On unbiased estimation of $P(Y
@article{ZNSL_1984_136_a0,
     author = {V. G. Voinov},
     title = {On unbiased estimation of $P(Y<X)$ in normal case},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--12},
     year = {1984},
     volume = {136},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_136_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Under assumption that normally distributed random variables $X$ and $Y$ are independent new expressions for minimum variance unbiased estimates of the probability $P(Y have been obtained. These estimates are given for two cases: - when distribution of $Y$ is comletely specified and when all parameters of the distributions of $X$ and $Y$ are unknown. The last estimate is nore suitable for practical applications than that of Downton [3].