A powerful method to approximate the probability of failure is FORM. As a by-product of FORM, the design-point $\mathbf{u}^\star$ is obtained, which is the most probable point for failure. The length of vector $\mathbf{u}^\star$ corresponds to the FORM reliability index $\beta_\mathrm{FORM} = \|\mathbf{u}^*\|$. The normalized vector of $\mathbf{u}^\star$ corresponds the the FORM $\alpha$-factors: $\alpha_i = \frac{u_i^\star}{\beta_\mathrm{FORM}}$, with $i\in\{1,\ldots,M\}$ and $M$ the total number of uncertain model parameters. The FORM $\alpha$-factors provide a useful sensitivity metric.
A useful property of the FORM $\alpha$-factors is that their sign can be used to identify whether the corresponding uncertain model parameter is of the demand or the capacity type. More specifically, the sign of $\alpha_i$ can be used to identify whether a change of the value of $X_i$ will have a positive or a negative impact on reliability.
- If the sign of $\alpha_i$ is positive, then an increase of $X_i$ (e.g., by increasing the mean of $X_i$) will result in a decrease of the reliability (i.e., an increase of the probability of failure). Such a behavior can typically be observed for model parameters that are of the demand type (e.g., load variables).
- If the sign of $\alpha_i$ is negative, then an increase of $X_i$ (e.g., by increasing the mean of $X_i$) will result in an increase of the reliability (i.e., a decrease of the probability of failure). Such a behavior can typically be observed for model parameters that are of the capacity type (e.g., resistance variables).
Note: The discussion above is only valid for statistically independent uncertain model parameters.
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