Concept: My last post described how to implement Window of Opportunity on your project. I omitted the math because you can use the metric effectively without knowing the math behind it.
Given that, why bother with the math at all?
This is a rare case in which Walt Lipke has not spelled out all the math behind a metric. Sceptics might wonder if there’s something dodgy about it.
To dispel any doubt, I’ve done the math. It might not be what Walt used to derive the metric (in fact, it probably isn’t, given his keen mathematical insight), but it works algebraically.
The formal derivation of the Window follows. Afterward, I’ve included an intuitive interpretation of the math. If you’re mathophobe, skip the algebra, and jump directly to the intuitive versionI'm biased, but I think it's as cool as the proof.
Practice: In general terms, find the fraction of the schedule complete at which TSPI = 1.10, given a specific efficiency rate. From that fraction, subtract the fraction of the schedule that has actually been earned. The difference is the Window of Opportunity.
The details of the derivation follow. Note that the starting point of the proof requires a transformation. See the Appendix for the details on how the transformation is achieved.
Figure 1
In equation 12, ES/PD represents the fraction of the schedule complete when TSPI = 1.10, given a specific efficiency rate. The fraction complete is referred to as, C. It is crucial to the calculation of Window of Opportunity, the equation for which follows:
Window of Opportunity = C – (ES/PD)
The Window of Opportunity is C (the fraction complete when TSPI = 1.10 at a specific efficiency) less the fraction of schedule actually earned. In practice, the current SPIt is used for the efficiency in calculating C, and the current Earned Schedule and Planned Duration are used for the second term.
Schematic
Figure 2
In Figure 2, the total duration is represented as a fraction equal to 1.00. The fraction complete when TSPI=1.10 at the current SPIt occurs at C3. It is calculated by equation 12. The fraction that is actually earned occurs at C2. It is calculated as ES/PD. Finally, the Window of Opportunity is represented as C3C2.
Intuitive Interpretation
Figure 3
Divide total project Duration into three parts. First, there is a fraction from Start to Threshold. Second, there is a fraction that has already been earned. It’s from Start to ES. Third, the difference between Threshold and ES is the Window of Opportunity.
I believe the key question is: what fraction represents completion at Threshold. I was able to derive the equation algebraically (equation 12), but its intuitive meaning took me a while to figure out. I try to explain it next.
Threshold occurs at some point on the time line. The position depends on, not one, but two durations: Planned Duration and Estimated Duration, and the two durations can differ. So, you must scale the threshold point to the relative size of the duration.
Why does having two durations necessitate scaling? Consider Figure 4.
Figure 4
From the start, the 80week mark is at the same position in both timelines. But, 80 weeks represents 80% of the top timeline and only 73% of the bottom timeline. For the fractional amounts, size matters. Scaling compensates for the difference.
That’s where Threshold is planned to occur. But, we must also consider where it (likely) will occur. And that depends on current schedule performance. To find the point, divide the threshold value by the current schedule efficiency (Schedule Performance Index for time).
With the relevant points set, we can calculate the fractions complete.
The first fraction is: Threshold * Relative Size. [1] Substituting the appropriate values that becomes: 1.1 * (Earned Duration / Planned Duration). [2]
The second fraction is: Threshold / Efficiency. Substituting the appropriate values: 1.1 / SPIt.
But, wait. There’s a wrinkle. Look at Figure 4 again.
The figure clearly shows that in the two scenarios, the StarttoThreshold amounts are identical. By contrast, it is the portion beyond Threshold which distinguishes the two scenarios. That's the portion which captures the fraction complete.
So, we must remove the whole runup to Threshold. Doing so gives us, respectively, ( (1.1 * ED / PD) – 1) and ((1.1 / SPIt) – 1).
Now, all we need to do is divide ((1.1 * ED / PD) – 1) by ((1.1 / SPIt) – 1), giving us the fraction complete at 1.1.
Again, that might give us pause. In what sense does the fraction represent completion at 1.1?
The first equation represents completion as planned. The second equation represents completion as estimated.
Division tells us how many units of the denominator are in the numerator, i.e., how many of the estimates are in the plan. And, that tells us the fraction which will be complete on the relative timeline. In other words, it's the fraction of the plan that will be achieved at 1.1. (Note the similarity to Percent Complete as expressed by ES / PD. It's the fraction of the plan that has been achieved.)
That genuinely sounds like percent complete.
The final step in calculating the Window of Opportunity is easy. Given the fraction just calculated, subtract the fraction already earned. The fraction earned is simply the Earned Schedule divided by the Planned Duration.
The result is the Window of Opportunity for recovery, the fraction of remaining time available before you will hit the pointofnoreturn.
Caveats
Boundary Conditions: the Window of Opportunity is bounded by conditions that are not called out in Walt’s publications. [3]
 If the efficiency is greater than the relative size of the duration (i.e., SPIt > (ED / PD)), the percent complete is automatically set to 1. Intuitively, this means that efficiency is so good that recovery is likely. In other words, the Window of Opportunity is wide open.
 If the fraction complete ((1.1 * (ED / PD) – 1) / (1.1 / SPIt) turns out to be greater than 1, it’s too late for recovery. Automatically reset the fraction complete to 0.
 If the fraction complete ((1.1 * (ED / PD) – 1) / (1.1 / SPIt) turns out to be less than 0, it’s too late for recovery. Automatically reset the fraction complete to 0.
Calculations of Window of Opportunity are appropriate only within these boundary conditions.
A Puzzle: The equivalence presented in EQ 12 is intriguing.
It says that the fraction complete which we have just deduced equals ES / PD, a commonly recognized measure of percent complete.
In what sense is “percent complete” based on time (ES vs PD) equivalent to “percent complete” based on schedule performance (TSPI=1.10 and SPIt)?
The answer can’t be simply that both are equal to percent complete and so are equal to each other. That just begs the question. But, then, what is the intuitive explanation?
I leave that as an exercise for the reader.
As promised, here is the Appendix with the derivation of the starting equation in the first proof.
Notes:
[1] Why do we multiply? Scaling is expressed by multiplication. Consider a simple example. We have a lens that magnifies objects to twice their normal size. We say the lens is 2x lens, i.e., it scales objects 2 times.
[2] Why does the fraction represent relative size? As the name implies, it’s the relationship between two entities. A ratio is one way to express it. We compare the estimate (ED) to the plan (PD) because the plan is the baseline against which we measure, i.e., ED / PD. Note that division is used in a different sense a bit later.
[3] The conditions can be found in Walt’s Prediction Analysis Calculator v2b by exposing the formula for “C”.
References:
Lipke, Walt. “The Probability of Project Recovery,” Project Governance & Controls Annual Review (Australia), September 2021, Vol. 4, Ed. 1, ISSN 26521016 (Online)
Lipke, Walt. “The Probability of Project Recovery,” PM World Journal, June 2016, Vol. V, Issue VI
Lipke, Walt. Prediction Analysis Calculator v2b. Earned Schedule.comes calculator.
