An approximation to bi-normal probability distribution function in reliability analysis of structural system

Bi-normal probability distribution function is often used in reliability analysis of the structural system.Numerical integration of bi-normal distributions is uneasy to evaluate in practice.Based on multiplication theorem of probability,an effective approximation is presented to the bi-normal distribution with substituting the original conditional distribution by the standard normal distribution of the same expectation and variance.The comparative studies with the exact integration and the examples considered in the paper show that the proposed approximation of calculation formula is simple and has a good accuracy.