Saturday, October 19, 2013

RMS anyone?



RMS
I wonder if there is anyone around who remembers RMS -- or more importantly: how it's used in PM? If this sounds a bit technical, but don't bail yet. It's a lot simpler and more actionable than the much more complex Six Sigma idea.

In the Sixer world, defined process control was the major outcome, and we were told that it was practical to obtain the data to drive the statistics.

Nonsense, for the most part, in PM. Projects don't usually have the historical data in reliable form to drive process control limits to anywhere like six sigma; most projects live in the "one sigma" world.

And that reality, one sigma, brings us to RMS! "Root of the Mean of the Squared-error"

Application
It's really not that bad, and: It's actionable by PMs! Here's a question you could answer with RMS analysis:
If it costs the project $100 to discover/fix a page error in a deliverable document, what's your risk exposure if you plan your project anticipating finding 1000 errors at an average discovery/fix of 3 per page? Your budget is: $100 * 1000 errors = $100K; or 333 pages * $300/page = $100K
Example
To answer that question, here's an example of  how RMS analysis works:
Let's say you have a team working on documents, and you've based the budget on a reasonable number of errors/fixes in the documents: say 3 errors per page. In effect, 3 errors/page is the mean error rate that drives your project estimates for time and labor to discover and fix the errors.
Now, suppose you get a monthly report from your work package manager that gives the following four observed errors per page in various documents in process: 1,2,5,4
The errors, relative to planning mean, are the difference between the actual observed error and the planning mean. For the first one we compute (1-3) = -2; for the others, applying the same protocol: -1,2,1.  (It actually doesn't matter if you adopt the opposite protocol: 3-1 = 2, if you are consistent)
The squared errors are: -2 * -2 = 4; and 1,4,1. The mean-squared error is average of the squared-errors, computed as: (1/4)(4+1+4+1) = 2.5 errors-squared.
Now, as a practical matter we can't work with something dimensioned as errors-squared, so we just take the square root to get the dimension back where we can use it. 
And (drum roll goes here), the RMS is the sqrt (2.5) = 1.59 error/page (Call it 1.6 or even 1.5, since we're only talking planning stuff here, not trying to navigate to the moon)
So can we answer the question about risk exposure?
Yes: By virtue of a couple of statistical theories, we can say:
Expect any similar document page errors to be more likely within +/-1.6 error/page of the planning mean than elsewhere.
Thus, anywhere from about (3 - 1.6) = 1.4 to about (3 + 1.6) = 4.6 is where most of the results are expected to be.
In short-hand, our expectation is: Planning mean +/- RMS.

Exposure:
Now, calculate the exposure: The best approach is to use the figure of 333 pages. Most of the cost (not budget) to discover/fix errors will likely be between:
  • 333 * 1.4 * $100 = $47K, and
  • 333 * 4.6 * $100 = $153K 
Since you have a budget of $100K, you are exposed to a risk of $53K -- of course, there's an opportunity to come in at $47K, thus saving $43K!

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