Badr Alghamdi
العربية
Lessons

Correlation: every estimate honest and the sum still late

Eight serial tasks estimated at 8, 10 and 16 days sum to 80. Independent, four runs in five finish inside the 96 day allowance. Fully correlated they do not, and no estimate changed.

For four in five simulated finishes, the sum finishes on time: P80 is 94.6 days against a fixed allowance of 96 days.
For four in five simulated finishes, the sum finishes on time: P80 is 94.6 days against a fixed allowance of 96 days.

Task variation

40%
0

When the sum finishes

When the sum finishesFor four in five simulated finishes, the sum finishes on time: P80 is 94.6 days against a fixed allowance of 96 days.Runs out of 5,000Allowance 96P50 90.4P80 94.67282.392.5102.8113Total duration, days
The allowance is 20% above the sum of most likely durations. P80 states a simulated frequency, not a guaranteed finish.
Sum of most likely durations80 days
Half finish by (P50)90.4 days
Four in five finish by (P80)94.6 days
Runs within the allowance86.4%

Here is the maths

Stated assumptions

Tasks run in series. Each has a most likely duration of 10 days. The triangular distribution keeps the realistic skew: its lower edge falls by half the spread and its upper edge rises by 1.5 times the spread. There are 5,000 runs with seed 1. The allowance is fixed at 120% of the sum of most likely durations.

How correlation enters

In a share of runs equal to the correlation, every task uses the same triangular draw. In the remaining runs, task durations are independent. This mixture preserves each task's distribution and gives every pair the stated correlation. It represents one possible dependence pattern. It adds no delay and changes no task estimate.

Worked example

With 8 tasks and spread 40%, each task has estimates 8, 10 and 16 days. The sum of most likely durations is 80 days and the allowance is 96 days. Independent tasks have P80 about 94.6 days. With correlation 1, P80 is about 103.8 days. The four in five reading changes from within the allowance to beyond it.

Check it yourself

Set spread to zero. Every task takes 10 days and correlation cannot move the finish.

This is a specified mixture of independent and fully shared variation. Correlation alone does not identify a joint distribution. The model does not include resource constraints, calendars, rework or a network of dependencies. It describes this model and does not choose a completion date.

Related