“In everyday life, the Flaw of Averages ensures that plans based on average customer demand, average completion time, average interest rate, and other uncertainties are below projection, behind schedule, and beyond budget.” – Sam L. Savage, 2009 – The Flaw of Averages
“Variation is the hard reality, not a set of imperfect measures for a central tendency. Means and medians are the abstractions.” – Stephen Jay Gould, 1985 – “The Median Isn’t the Message”
“Essentially, all models are wrong, but some are useful” – George E. P. Box, “Empirical Model Building and Response Surfaces”, (1919 – 2013)
“Remember that a model is not the truth. It is a lie to help you get your point across.” – Sam L. Savage, “The Flaw of Averages”, 2009
“You are allowed to lie a little, but you must never mislead.” – Paul Halmos, mathematician, (1916 – 2006)
Last week I read an article about yet another tool showing the ability to produce CFDs (cumulative flow diagrams). Maybe you’re already a user of one of these tools that help you visualize your workflow, and generate them for you automatically (or “auto-magically”) as part of reports they provide. Or, perhaps like me, you still generate them mostly using MS-Excel. Either way, have you wondered just a little about how a CFD works?
As most do, this article displayed a line extending vertically between “stages” on the CFD (or workflow processes, as I often call them) and identified this distance as the WIP (work-in-progress) on a specific date for the respective stage (or stages) of interest. There was also a description of another distance, a line extending horizontally between stages of interest on the CFD and identifying it as the “average lead time” for the requests (workitems) arriving on a specific date. That is, the average time for a request (workitem) to “flow” through (arrive into and depart out of) one or more stages of interest. Lastly, there was a description of a sloped line, as a mean delivery rate of requests (workitems) flowing into or out of a stage (workflow process) depending on viewing the workflow upstream or downstream. Note: for more on the basics on reading a CFD, see this earlier post here.
A Difference Is Not An Average, Right?
It is easy to understand that WIP is simply a “difference” between two counts on the CFD and represents the number of requests (workitems) at a point in time. Similarly, seeing the slope as a simple rise over run calculation of a number of requests per unit of time (a rate over a period of time of interest) is not a complex concept to accept. But, what about the notion of the “average lead time” derived from the CFD? How is it a “difference” between two points in time read from the CFD (ex. calendar dates) can represent an “average” unit of time for a request (workitem) to flow through a stage (workflow process)? A “difference” that represents N numbers summed up and divided by N. Yes, really! But how can this be?