New Reliability Sensitivity Algorithm for Complicated Implicit Limit State Equation and Its Engineering Applications

For the complicated implicit limit state equation, a new algorithm was presented to analyze the reliability sensitivity. On the basis of the advanced first order and second moment method, the partial derivatives of the failure probability to the distribution parameters of the process variables were formulated. The process variables, which are the implicit functions of the basic input variables, were generally in terms of the comprehensive variables. In order to obtain the final sensitivities of the failure probability to the distribution parameters of the basic variables, the rule of the implicit function derivative was used. In the formulae of final sensitivities, the sensitivities (usually in terms of process sensitivities) of the distribution parameters of the process variables to those of the basic variables were concerned. Therefore, the approximate quadratic analytical relationship among the process variables and the basic variables were constructed by employing the non-linear regression. Then the process sensitivities are derived accurately in general case, which make it possible to obtain the final sensitivities. The presented algorithm is applied to the reliability sensitivity estimation of an aero engine turbine disc under low cycle fatigue conditions. The good agreement between the quantitative calculation and the quality analysis shows the feasibility of the presented algorithm.