Forward pass
ES = largest EF among the activities feeding this activity's start event
EF = ES + duration
Project duration = largest EF in the network
First pass through any network. An event occurs only when every activity feeding it is complete, so take the largest.
- ES
- Earliest start
- EF
- Earliest finish
Backward pass and slack
LF = smallest LS among this activity's successors
LS = LF - duration
Slack = LS - ES = LF - EF
Second pass, starting from the project duration. Compute slack both ways as a check.
- LS
- Latest start without delaying the project
- LF
- Latest finish without delaying the project
- Slack
- Zero on the critical path
Path slack
Slack of a path = critical path length - that path's length
Small networks where every path can be listed. The longest path is the critical path and the project duration.
- critical path length
- Longest total duration from start to finish
PERT expected time and variance
t-e = ( t-o + 4 t-m + t-p ) / 6
sigma^2 = ( ( t-p - t-o ) / 6 )^2
When activity durations are uncertain and three estimates are given. The most likely time does not appear in the variance.
- t-o
- Optimistic time, under optimal conditions
- t-m
- Most likely time, the most probable duration
- t-p
- Pessimistic time, under worst conditions
Probability of on-time completion
Path variance = SUM of variances of activities on the critical path
Path sigma = sqrt( path variance )
z = ( target date - expected project length ) / path sigma
After a PERT network is timed. Add variances, never standard deviations, and look z up in a normal table.
- target date
- The completion date being tested
- expected project length
- Sum of expected times along the critical path