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Frac requiring rework (Frw )
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Project Degrades
F RW = 1/(s nt + 1)
Project Improves Unstable Equilibrium
0 2 4 6 8 10
Add New Tasks Strength (snt )
Figure 9. Basic Project Tipping Point Conditions
Figure 9 can be used to intuitively explain the behavior of projects near the tipping point.
The total backlog of projects to the lower left of the solid line decreases, and the project
improves. The total backlog of projects to the right of the solid line increases, and the project
degrades. The solid line represents possible tipping point conditions. A project can only remain
at a tipping point if the loop B1 completes work at exactly the rate as loop R1 adds work to the
project backlog (Eq. 2). In the absence of forces to keep the project stagnate, small digressions
from the tipping point conditions in either direction will cause the project to improve or degrade.
If either loop dominates, total backlogs will increase (R1 dominates) to project failure or
decrease (B1 dominates) to project completion. Therefore, the tipping point is an unstable
equilibrium.
Project conditions that move across the tipping point conditions shown in Figure 9
experience a change in project behavior mode from increasing to decreasing or vice versa. The
shape of Figure 9 reveals intuitive insights about project conditions that generate tipping point
dynamics. The negative slope of the tipping point conditions line indicates that projects that
have low add-new-task strength (snt) can tolerate a higher fraction of rework (FRW) before
degrading and projects with low rework fractions can tolerate higher add-new-tasks strengths.
However, the tipping point relationship between add-new-tasks strength and rework fraction is
not linear. A small increase in add-new-tasks strength greatly reduces the tolerable rework
fraction. But as add-new-task strength increases, the tolerable rework fraction decreases more
slowly, asymptotically toward a value of zero.
Project Trajectory Reversal and Schedule Pressure
We next investigate projects that begin on one side of the tipping point but, due to
endogenous or exogenous influences, are pushed past the tipping point and reverse their
behavior mode from improving to degrading or visa versa. As used here, project trajectory
reversal is when the status of a project initially improves but later degrades and eventually fails
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