The normal conditioned on t-distribution when the correlation is one
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The conditional probability that Y ≥ L, given that (Y−μ)/sy ≥ −k, is evaluated where Y is N(μ, σ 2), L is a given constant (a specification limit), and is the usual unbiased estimator of σ2 based on a preliminary sample of size n. Tables of k are given for use in raising the proportion of Y’s above L from γ (before screening) to δ (after screening) for δ = 0.90, 0.95, 0.99, and 0.999. These tables correspond to the limiting case as the correlation approaches one for the screening procedure given by Owen and Su (1977). Tables for the case where the correlation is less than one were given by Owen and Haas (1977).
[1] D. Owen. Tables for Computing Bivariate Normal Probabilities , 1956 .
[2] Tables of the Normal Conditioned on t-Distribution , 1978 .
[3] Donald B. Owen,et al. Screening Based on Normal Variables , 1977 .