About the Mean Value Method

The mean-value reliability index is calculated as a function of the mean and the standard deviation of $g\left(\mathbf{X}\right)$:

$$\begin{array}{}(4)& \beta =\frac{{\mu }_g}{{\sigma }_g}\end{array}$$

Given the reliability index from the preceding equation, the probability of failure can then again be calculated as $P_f=\mathrm{\Phi }(-\beta )$

The Mean Value method, based on a first-order Taylor’s expansion, is the most efficient (in terms of the number of function evaluations, or simulation program executions, needed to calculate the reliability) of the reliability analysis methods implemented in Isight. It requires only one-time failure function and sensitivity evaluations. However, the mean-value reliability index is accurate only for linear failure functions with normally distributed random variables. In most other situations, the mean-value reliability index is not accurate because the most probable point is not on the failure surface. Using a second-order Taylor’s expansion, a higher level of accuracy can be achieved. Obviously, there is a trade-off between expense (number of gradient calculations) and accuracy when choosing to include or neglect the higher-order terms in the expansion.