The uncertainty importance analysis for the fault tree and its probability density evolution algorithm

In the conventional system reliability, the fault probability of the bottom events is assumed as the determinate value. However, the fault probability of the bottom event is usually uncertain which would result that the system fault probability is uncertain. In order to evaluate the effect of the uncertainties of the fault probability on the system fault probability, based on the structure function of the fault tree, the moment-independent importance measure (MIIM) model for the system reliability is developed. This IM model could not only measure the influence of the uncertainty of the fault probability on the entire system fault probability distribution, but also can provide the ranging of the fault probabilities. The probability density evolution model is developed to solve the IM efficiently. An electromechanical actuator system is employed to test the rationality and validity of the presented MIIM. The efficiency and accuracy of the developed algorithm also is tested.