PMGT1865 Chap.8 Three Point Estimating and Expected Duration
Three Point Estimating and Expected Duration
The programme evaluation and review technique is a statistical tool for analysing and representing the tasks in a project, developed in parallel with the critical path method from the late 1950s. It is a critical path technique itself, so the network, the two passes and the merge and burst rules all carry straight over.
One thing changes and it changes everything downstream: the critical path method is deterministic, while this technique is probabilistic. Where the deterministic method relies on a single value expression of duration, here how long an activity takes is itself uncertain, and often widely so.
No reliable data exists to say what shape that variable takes for any given activity, so it is generally assumed to fall on the beta distribution, which can be skewed, while the distribution of a whole path is treated as normal and described entirely by its mean and standard deviation.
Those two numbers are what three estimates are used to produce, and the fundamental aim is to capture the variability of an estimate and carry it into the forecast.
What this chapter covers
- 01
Deterministic against probabilistic, and what each technique is actually able to answer
- 02
The stated advantages, including usefulness where there is little or no previous schedule data
- 03
The stated disadvantages, including subjective time analysis and the cost of maintaining the diagram
- 04
Why the beta distribution is assumed at activity level and a normal distribution at path level
- 05
The three estimates, and the one in a hundred rule that stops the range collapsing
- 06
Why the most likely value is not the mean, and what the weighting in the formula is doing
- 07
The expected duration formula, and how it behaves on symmetric against skewed estimates
- 08
The standard deviation as the range divided by six, and why only the gap between the extremes matters
- 09
The three step procedure, computing expected values for every activity rather than the obvious ones
- 10
Expected project duration as a sum along the critical path, and the independence assumption behind it
Expected durations across a network, and a path that moves
- +2Work one row in full to show the method. For wireframes the expected duration is 4 plus four times 6 plus 11, all over 6, which is 39 over 6, or 6.5 days. The standard deviation is 11 minus 4 over 6, which is 1.167, so the variance is 1.362.
- +2Complete the table. Expected durations are 4.0, 6.5, 7.0, 11.0, 6.0 and 3.0; standard deviations are 0.333, 1.167, 0.667, 1.667, 1.333 and 0.333; variances are 0.111, 1.362, 0.445, 2.779, 1.778 and 0.111.
- +1Notice what the weighting did. Wireframes were estimated most likely at 6 and come out at 6.5, and build at 10 comes out at 11, because both have long pessimistic tails. The three activities with symmetric estimates come out exactly at their most likely values.
- +1Enumerate the paths using expected durations. P, Q, R, S, U gives 4 plus 6.5 plus 7 plus 11 plus 3, which is 31.5 days. P, T, S, U gives 4 plus 6 plus 11 plus 3, which is 24 days.
- +1Identify the path and state the duration. The longer chain governs, so the critical path is P, Q, R, S, U with content migration carrying 7.5 days of float, and the expected project duration is 31.5 working days.
Key terms
- Optimistic estimate
- The shortest time interval an activity might be completed in, equivalent to roughly a one in a hundred chance that things go this well. It is a near extreme rather than a comfortable best case.
- Most likely estimate
- The duration an activity is most likely to take. It is not necessarily the mean, and it is the same number the deterministic critical path method would have used.
- Pessimistic estimate
- The longest time interval an activity might take, equivalent to roughly a one in a hundred chance that things go this badly. The gap between it and the optimistic estimate is what drives the standard deviation.
- Beta distribution
- The skewed probability distribution generally assumed for a single activity duration, chosen because there is a floor on how fast work can go and no ceiling on how slow.
- Activity variance
- The square of an activity's standard deviation. Variances add along a path while standard deviations do not, which is why the variance is carried rather than the deviation.
- Independence assumption
- The assumption that one activity running long tells you nothing about whether the next will. It underpins the summation of durations along the critical path and is the assumption most often violated in practice.
Three Point Estimating and Expected Duration FAQ
Why is the most likely value multiplied by four?
Because the formula is a weighted average over six shares in which the middle estimate carries most of the information and the two extremes still pull the answer towards whichever side has the longer tail.
On a symmetric set of estimates the formula returns the most likely value exactly; on a skewed set it returns something between the most likely and the pessimistic value, which is the behaviour you want when work can run late by more than it can run early.
Can I set the extremes as a fixed percentage either side of the most likely value?
You can, and the result carries no information about the activity. A symmetric range forces the expected duration back onto the most likely value and makes the standard deviation a function of nothing but the percentage you chose, so the whole calculation becomes an elaborate way of restating a single point estimate.
Estimate the extremes from what could actually happen to that particular piece of work, and use the one in a hundred framing to stop the range collapsing to something comfortable.
Do I need expected durations for activities I know are not critical?
Yes, because you do not yet know which path will govern. The critical path found with most likely durations is not guaranteed to be the one found with expected durations: an activity with a long pessimistic tail gains time under the weighted mean, and a chain containing several such activities can overtake a chain that looked longer.
Compute the table for every activity and rerun the passes on the expected values rather than assuming the earlier path still holds.
Where does the independence assumption break down?
Wherever a single cause stretches several activities at once, which is common: bad weather, a shortage of a trade, an underestimated specification. When that happens the true project variance is larger than the sum of the individual variances, so the method is optimistic about certainty rather than about duration. Saying so in an answer shows you understand what the assumption is buying rather than merely that it exists.
Assessment move
Build the table the same way every time and the arithmetic stops being where marks go. Six columns: activity, optimistic, most likely, pessimistic, expected duration, standard deviation and variance. Fill every row before looking at the network, carry three decimals on the deviations and squares, and only then run the passes on the expected values.
The four errors worth drilling against are computing expected durations only for the activities on the old critical path, forgetting the factor of four in the numerator, dividing the range by something other than six, and rounding a deviation to one decimal before squaring it. Each produces a plausible number.
Practise the interpretation as well as the calculation: look at the column of pessimistic minus optimistic values and say which activity is carrying most of the uncertainty, because that is the question the next chapter turns into a decision, and it is answered by reading a column rather than by any further arithmetic.
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