# Reliability Index

In addition to the Probability of Failure, another commonly used probabilistic measure of safety is the **Reliability Index**. The **Reliability Index** is listed in the **RocPlane** Info Viewer and Sidebar, and is defined as follows.

If one assumes that the distribution of safety factors, after a probabilistic analysis, is **normally** distributed (i.e. has a Normal Distribution), then Equation 1 is used to calculate the **Reliability Index**:

Eqn. 1

where:

*b* = Reliability Index,

*m* = Mean Factor of Safety,

*s* = Standard Deviation of FS

As can be seen from Equation 1, the **Reliability Index** represents the number of standard deviations that separate the mean Factor of Safety, from the critical Factor of Safety ( = 1 ).

- As a rule of thumb, the
**Reliability Index**should be at least 3 or greater, to have reasonable assurance of a safe slope design. - A
**Reliability Index = 0**, implies that the Mean Factor of Safety = 1. - A negative
**Reliability Index**indicates a Mean Factor of Safety less than 1.

If one assumes that the distribution of safety factors, after a probabilistic analysis, is **lognormally** distributed (i.e. has a Lognormal Distribution), then Equation 2 is used to calculate the **Reliability Index**:

Eqn. 2

where:

= lognormal Reliability Index

*m* = Mean Factor of Safety

V = coefficient of variation of Factor of Safety = *s* / *m*

*s* = Standard Deviation of FS

In reality, the Factor of Safety distribution is often best fit by a **Lognormal** rather than a **Normal Distribution**, and therefore Equation 2 is frequently used to calculate the (lognormal) **Reliability Index**. Remember that the **Lognormal Distribution** is only applicable for variables which are always positive, which is the case for Factor of Safety.

The **Reliability Index** information can be found in the **Info Viewer** and **Sidebar**, and is reported for both the Normal (Equation 1) and Lognormal (Equation 2) assumptions.