Monday, September 21, 2020

Schedule merge: the biggest hazard of all

Do you understand the risk you are running when two events come to a merging point in your schedule?
Here's the situation:
  • There's a series of tasks running along on one path, call it "A"
  • There's another series of tasks, not dependent on "A", running along on path "B"
  • But, all the events set to begin on path "C" can't begin until everything on paths "A" and "B" finish.

In effect, the completion of everything along "A" and "B" gates, or controls, the beginning of "C".

So, where is the hazard? 

The hazard is that "C" will be late starting if either "A" or "B" are late. Actually, that doesn't sound like such a big deal, so what's the problem here? 

It's all in the probabilities. Consider this example:

  • "A" probably late 1 chance in 4 [written as: 1/4], and
  • "B" probably late 3 chances in 10 [written as : 3/10].
Not great, but not too bad for either one of them. But what can we say about the chances for "C"?
We'll show in the discussion that follows that "C" will be late approximately 1 chance in 2. That's a good deal worse than 1/4 or even 3/10. It's a biggie if you are trying to figure out when "C" is going to kick-off.
Reasoning with probabilities
To deal with probabilities, we have to deal with a number of chances of "A" and "B" because probabilities are determined by observing variations in the same thing over and over.
So, for this example, let's use the common denominator of 4 x 10 for the number of chances (*).
  • In 40 chances, we expect "A" to to be late 10 times (1 chance in 4, 10 chances in 40), but on-time 30 times. Of course, "C" will be late those 10 times that "A" is late.
  • But when "A" is on-time, 30 chances (out of 40), the performance of "B" determines the performance of "C" ("B" late makes "C" late).

  • In 30 chances we expect "B" to be late 9 times (3 chances in 10, 9 chances in 30).
    But if late 9 times, then "B" is on-time 21 times

  • Consequently: "C" is expected to start on-time 21 of 40 trials, or just over 50% (about 1/2)

  • But, that means "C" is expected to be late almost half the time -- 10 late starts from the effects of Path A and 9 more from Path B. Altogether, that's 19 late starts out of 40  -- a serious performance degradation from either that of "A" [25% late, 10 out of 40] or "B" [30% late, 12 out of 40]

(*) the common denominator of 1/4 and 3/10 is 40

We can show all this with this mapping chart:


Path A

Path B

Path C

Probably late



1 – 21/40

Probably on-time




Independence simplifies:
Notice that along the bottom row, Path C is just the multiplication of Path A and Path B probabilities
Along the top row, the probabilities in all cases are just 1- bottom row, cell by cell. [the number 1 represents all possibilities]

These calculations are only valid if Path A is in every way independent of Path B. If not, then there is cross-talk between paths that will degrade the calculations. 

But in a project, what does independence mean?

  • No shared resources that could cause conflicts
  • No shared lessons-learned after the tasks on Path A or B begin
  • No changes in "A" because of what is happening in "B"
Now, in a in-person project, maintaining independence may be difficult, perhaps not even desired -- to wit: why not share?  But in a remote/virtual project, independence may be the order of the day, even if it is not desired. Another effect of the virtual thing, to be sure!


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