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Critical path activity

As explained in Statistics Every Programmer Needs

A critical path activity is a project activity with no scheduling slack whose delay extends the project timeline.

A critical path activity has zero scheduling slack: its earliest and latest start or finish times match, so any delay extends the project timeline. Slack equals latest start minus earliest start, or latest finish minus earliest finish. section 13.3.3

Classify activities through critical path method analysis:

  • Use a forward pass to determine earliest start and finish times. section 13.3.3
  • Use a backward pass to determine latest start and finish times. section 13.3.3
  • Treat zero-slack activities as critical and activities with positive slack as noncritical. section 13.3.3
  • For completion-risk analysis, sum the variances of critical path activities when activity times are statistically independent. section 13.4

Automated reporting tool project

Activities A–E, G, and J–L have zero slack and therefore lie on the critical path. Activity F has five weeks of slack, H has five, and I has nine, allowing those activities to move without changing the overall timeline. section 13.3.3

Table 13.3 CPM results for the automated reporting tool project. Activities in any project have slack or no slack, which is derived by subtracting the earliest start from the latest start or, alternatively, by subtracting the earliest finish from the latest finish (it doesn’t matter). Activities with no slack are on the critical path, whereas activities with slack are not.
Activity
Earliest start (ES)
Earliest finish (EF)
Latest start (LS)
Latest finish (LF)
Slack (LS – ES)
Critical path?
A
0
3
0
3
0
Yes
B
3
5
3
5
0
Yes
C
5
8
5
8
0
Yes
D
8
13
8
13
0
Yes
E
13
16
13
16
0
Yes
F
8
12
13
17
5
No
G
16
20
16
20
0
Yes
H
12
15
17
20
5
No
I
12
15
21
24
9
No
J
20
24
20
24
0
Yes
K
24
27
24
27
0
Yes
L
27
29
27
29
0
Yes

Compare earliest and latest schedule times, slack, and critical-path classification for every project activity. section 13.3.3

How Statistics Every Programmer Needs covers it

How deep it goes
Calculates slack from forward and backward passes, then extends analysis to variance and completion probability under independence assumptions.
Examples
Uses an automated reporting tool project with activities A–L, schedule times, slack values, and estimated duration variances.
What it assumes
Assumes a project activity network and estimated activity times, while defining earliest times, latest times, and slack through schedule analysis.
What you can do after
Evaluate project schedules by classifying zero-slack activities and assessing how their uncertainty affects completion deadlines.
How it connects
Connects slack, critical path method, project variance, standard deviation, and probability of project completion.
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Statistics Every Programmer Needs. The section links point to the parts of the book it draws on.