Hey there...
Critical path analysis is a technique that identifies the activities necessary to complete a task, including identifying the time necessary to complete each activity and the relationships between the activities.
I couldn't get an example for it but here are the steps:
1. Divide the project into tasks
2. Estimate tasks
3. Create the network diagram
4. Draw initial Gantt (bar) chart
5. Perform resource levelling
6. Compress the schedule (if necessary).
Hope it helps...