Easy in theory, difficult in practice

The term "critical path" is unfortunate. 

While a critical path does denote the longest sequence of activities through a project network diagram from start to finish, the activities along the critical path (also unfortunately named "critical activities") might not be those which possess the greatest uncertainty.

Why should this concern us?

It can be tempting to focus on critical path activities from a schedule variance perspective, but if sufficient contingency buffers have not been added to non-critical paths, realization of negative risks impacting those will turn them into critical paths.

This phenomenon can be simulated by use of Monte Carlo simulation. By providing the level of confidence or an estimate of duration distributions for activities and then running a Monte Carlo simulation with a reasonable number of iterations we can get a prediction as to how frequently a non-critical path becomes the critical path. This can then be used to appropriately size contingency buffers for those paths to reduce this likelihood.

While on the topic of critical path, schedule variance calculations in earned value can be fooled. Because most network diagrams will have multiple parallel paths, some of which are critical and some not, if sufficient non-critical paths are ahead of schedule relative to critical paths, schedule variance might be positive but the project will still be late. One way to avoid being caught off guard by this is to also calculate schedule variance on your critical path activities alone.

The term "critical path" is unfortunate. 

While a critical path does denote the longest sequence of activities through a project network diagram from start to finish, the activities along the critical path (also unfortunately named "critical activities") might not be those which possess the greatest uncertainty.

Why should this concern us?

It can be tempting to focus on critical path activities from a schedule variance perspective, but if sufficient contingency buffers have not been added to non-critical paths, realization of negative risks impacting those will turn them into critical paths.

This phenomenon can be simulated by use of Monte Carlo simulation. By providing the level of confidence or an estimate of duration distributions for activities and then running a Monte Carlo simulation with a reasonable number of iterations we can get a prediction as to how frequently a non-critical path becomes the critical path. This can then be used to appropriately size contingency buffers for those paths to reduce this likelihood.

While on the topic of critical path, schedule variance calculations in earned value can be fooled. Because most network diagrams will have multiple parallel paths, some of which are critical and some not, if sufficient non-critical paths are ahead of schedule relative to critical paths, schedule variance might be positive but the project will still be late. One way to avoid being caught off guard by this is to also calculate schedule variance on your critical path activities alone.