An Accurate Probability-of-Failure Calculation Method

Based on rules of transformation of stochastic variables, a general and complicated multiple probability of failure integral is transformed to a more convenient integral. The two main advantages are: 1) The generally complicated integration area is transformed to a rectangular integration area where numerical integration techniques easily apply. 2) Under quite weak restrictions the integral dimension is reduced by one. Errors related to truncation of integration limits, the numerical integration technique and approximate integrand expressions are analyzed. An upper error bound due to truncation of integration limits is given. Approximate integrand expressions are recommended to save computer time. A 5-dimensional fatigue calculation example is given.