On computing normal reliabilities

No expression currently used for computing reliabilities given by the normal distribution is adequate over the entire range of interest in structural design. Although the expressions may involve small absolute errors, they introduce excessively large relative errors in the failure probabilities over some ranges. It is impractical to have two expressions depending on the reliability index β. Two equations are proposed here. The simpler one involves relative errors smaller than 1.7% when β 1. The other introduces relative errors smaller than 2 × 10⁻⁴ when B 0 and smaller than 4.5 × 10⁻⁵ when β 1.