I finally got around to creating a simple shell spreadsheet, showing the combining of PERT distributions (as part of answering Nic’s question below). You can download it at http://tynerblain.com/downloads/Combining-PERT.xlsx

I hope you find it useful. I added some comments, it should be easy to steal from for your own projects.

Everyone else – enjoy :). Math is free.

Thanks for the question. What I’ve learned about correlation between distributions (e.g. the amount of shared-variation) has always been in terms of looking at two distributions, never three. So, you raised an interesting question. I sort of alluded to the answer (when I talked about repeatedly combining pairs of estimates), but definitely didn’t explain it.

I’m assuming that your rho=0.75 is the same between A (2/4/6) and B (3/5/10), as it is between A and C (4/6/12), as it is between B and C.

I couldn’t find any “real math” (e.g. from other people, or otherwise formally proven) to back me up on it, but my suspicion is that you just combine any pair (AB, BC, or AC) to create a new distribution, then combine that resultant distribution with the remaining initial set (C, A, or B, respectively).

The combinations of distributions are combinations that input normal distribution approximations of the beta distributions (represented by the individual PERT estimates) and output normal distributions. So, the math should work for repeated combinations.

I did a quick test, trying the above approach with all three sequences, and got the same result, regardless of the order in which I combined distributions.

My resultant estimate for your example is 7.6/16.2/24.8 (std of 2.9).

My approach was to determine the combined distribution for A+B -> AB (4.3/9.5/14.7) and for B+C -> BC (5.1/12.2/19.2) and C+A -> CA (5.0/10.7/16.3), then combine them again with C, A, and B, respectively. The second combination for ABC yielded 7.6/16.2/24.8 with all three approaches.

That makes me feel confident that the order is independent.

My “sniff test” makes sense too. Combining the distributions causess you to incorporate the first relationship (between A and B, in AB), but does not address the other correlations (between C and either A or B). That correlation is accounted for in the second combination of distributions.

Does that help?

How do I combine 3 or more correlated PERT estimates, e.g. 2/4/6 and 3/5/10 and 4/6/12 with rho=0.75?

Thanks!

/Nic

I don’t have a template-spreadsheet for doing this, I’ve just built them on the fly as projects required them. I’ll put one together for a future article. It will be tricky to come up with a general way to identify related tasks (versus unrelated tasks) – but I have an idea about how to do it. If you subscribe to the blog, you’ll get an email when it shows up.

Thanks again,
Scott

Your articles about PERT are the best ones I have ever read! Very well explained. Your advanced article is great explaining why PERT estimates cannot be added. No other article I have read has mentioned this.

I have looked all over internet to find a spreadsheet that calculates PERT correctly and doesn’t just add the estimates. Despite my efforts I have not been able to find a good one. Do you have a good spreadsheet or can recommend a good PM tool for this?

Thanks!

Kind Regards
Cecilia

Somewhere (or some-when) I wrote up an analysis of agile estimation, based on Mike Cohn’s work. Maybe an old blog article that I can’t find, but I think it was something for a client. The key element was that using velocity to manage / predict “rough estimates” based deliverability distinctly from detailed (PERT) estimates for tasks made sense, because you still get the feedback loop that removes uncertainty from the estimation process. Can’t find the write-up.

Long story short, I think the calculator can come in handy for that ‘planning estimation’ phase.

If you’re doing iterative development you might find interesting the calculators (“Release Calculator” and “Wiggle Room Calculator”) that you can find in the sidebar of my website positiveincline.com. Tweet me (@asplake) if you find them interesting/useful or have suggestions for others.

Mike