If you want to build systems that aren't easily hacked, this is a good article with a great presentation embedded in it.
29 December 2011
22 December 2011
Probability Management improves our odds of success with realistic estimates and attainable targets.
How much will it cost?
How long will it take?
This kind of question doesn't have just one answer; it has a whole bunch of answers, each with its own probability of turning out to be right.
When we pluck one number out of the bunch to use as a target, we're also choosing our probability of success - the probability that we can meet or beat that target.
04 December 2011
Ontario's Lotto 649 lottery involves a draw of 7 different numbers between 1 and 49. Each ticket has 6 different numbers from the same range. Prizes are awarded for various coincidences. This is a good excuse to do some 'statistics by simulation.'
Here's the challenge: What's the probability that at least one number on a ticket will match one of the numbers drawn?
25 October 2011
The Project Management Institute Ottawa Chapter held their annual Symposium last week.
I got to give a presentation on Probability Management for Projects to a couple of hundred project managers. That gave me a captive audience and an hour to talk about banishing the Flaw of Averages from project estimates. The feedback I've had makes it clear that there's a lot of interest.
A related paper and Excel model are at smpro.ca/ProbMan.
13 August 2011
09 July 2011
Yesterday, the City of Ottawa's Mayor Jim Watson announced that the Light Rail Project is going ahead at a projected cost of $2.1 Billion. This came as a relief to the people who were certain it would be more than double that, especially taxpayers who would be footing the bill.
08 July 2011
If anyone was wondering how I made the pretty chart in "The Right Way to do a Histogram", this is it. It's also really useful for estimating sample distributions.
10 June 2011
29 May 2011
This is a reprise of an earlier post. Not only was it not up to my usual quality, it was written before we had a good term for the kind of probability distribution that's central to Probability Management and avoiding the Flaw of Averages. "Sample Distribution" captures the key characteristic and fits with the 'sample' and 'sampling' that are an important part of it. Also, Sam Savage likes it; if the guy who invented the discipline approves, I know we have a winner.
A sample distribution quantifies the uncertainty in an uncertain variable. It's always a list of numbers--in programming terms a one-dimensional array or vector. Each element of the vector is a sample value drawn without bias from the possible values of the uncertain variable. For the rest of this article, when I use 'distribution' without qualification, it refers to a sample distribution.
20 February 2011
30 January 2011
"Average" is a simple concept; we measure a bunch of things, add the measurements, divide by the number of measurements.
Averages are not always that simple.
26 January 2011
18 January 2011
No, it's not yet another mythical Japanese productivity scheme; it's the name of a clever way to join four timbers using elegant Japanese joinery--and an example of risk management in plan design.
One carpenter working alone will carve the most intricate part first, then carve the rest, one at a time, fitting each new part in place, sanding and scraping for a perfect fit.
If you’re in a hurry, but don’t want to sacrifice quality, you could assign a part to each of four carpenters. All four carpenters won’t be as capable as the best carpenter; some will work more slowly to maintain the needed quality. You have to give each one very precise instructions; all the dimensions must be accurate (not merely precise) for a sub-millimeter fit on all the faces and edges. Also, when they’re done, it’s unlikely that all four will be perfect, so there’ll be some extra effort going into the final fit. You hope that any flaws involve too much wood; too much can be sanded down, too little means starting over.
Nonetheless, the concurrent approach is likely to finish sooner than the serial approach, but it will involve more carpenters, and more carpenter-hours.
The choice between one carpenter and four (or two) is a risk management decision. If everything goes well, the single carpenter might finish faster than four unlucky carpenters who run into problems at every turn. It’s a matter of probabilities.
A good plan design needs to take those probabilities into account, and give management choices between higher risk, higher cost and longer time scales.