Numerical method for fuzzy reliability analysis

Based on the mathematical transformation from fuzzy probability to random probability, an efficient numerical approach is proposed to estimate the fuzzy failure probability. The basic idea is that the calculation of the fuzzy failure probability can be transformed into estimating several truncated failure probabilities, which can be computed by using the classical random reliability methods. By using a normalized transformation, the fuzzy failure probability is transformed into a standard form, which can be approximately solved by the Gauss-Legendre quadrature formula. By this simple process, the fuzzy failure probability can be expressed by a weighted average of several truncated failure probabilities. To decrease the computational burden further, the quasi-Monte Carlo simulation is employed to solve the truncated failure probabilities. Several examples are employed to demonstrate the computational efficiency and accuracy of the approach. Finally, the proposed method is used to solve the fuzzy failure probability of an inside flap of an aircraft.