Geometric risk

Each of the core risk metrics has an corresponding geometric version (i.e. using mulitplication rather than addition). In some cases, these geometric versions can help highlight skew that may be present in the equivalent arithmetic metric.

Geometric Activity Risk

The Geometric Activity Risk metric is defined as:

$$Risk=1-\frac{\sqrt[N]{(F_{1}+{1})\times{...}\times(F_{i}+{1})\times{...}\times(F_{N}+{1})}}{M}=1-\frac{\sqrt[N]{\displaystyle\prod_{i=1}^{N}F_{i}+{1}}}{M}$$

Where:

• $F_{i}$ is the total float (i.e. total slack) of activity $i$
• $N$ is the number of activities in the project
• $M$ is the maximum float of any activity in the project, i.e. $\max{(F_{1},F_{2},{...},F_{N})}$

Geometric Criticality Risk

The Geometric Criticality Risk metric is defined as:

$$Risk=\frac{\sqrt[N]{\displaystyle\prod_{i=1}^{N}W_{i}}}{W_{C}}$$

where:

• $W_{i}$ is the criticality weight of activity $i$
• $W_{C}$ is the criticality weight of (black) critical activities
• $N$ is the total number activities in the project

Geometric Fibonacci Risk

The Geometric Fibonacci Risk metric is defined as:

$$Risk=\frac{\sqrt[N]{\displaystyle\prod_{i=1}^{N}\varphi_{i}}}{\varphi_{C}}$$

where:

• $\varphi_{i}$ is the Fibonacci weight of activity $i$
• $\varphi_{C}$ is the Fibonacci weight of (black) critical activities (equivalent to $\varphi^{3}$)
• $N$ is the total number activities in the project

For more details see:

• Activity risk
• Criticality risk
• Fibonacci risk