This past weekend I ran a session at Agile Coach Camp Canada on this subject of lead time distributions, and their role in guiding the improvement of your delivery process. This article provides a brief summary, and additional resources to learn more about the topic.
TL;DR
Lead Time is essentially a measurement of the time that it takes to go from "We promise" to "Here it is", and what's important to understand about it is that it's not a number, but a probability distribution.
The next thing to know is that this distribution is not a symmetrical, "normal" (or "Gaussian") distribution. Instead, it is asymmetric, with a "hump" to the left and a "tail" to the right. The implication of this is that "best case" scenarios and "worst case" scenarios will not compensate for each other and cause the average to "come out of the wash" at the end. Moreover, the "worst case" scenarios can be several (or even "many several") times away from the average; this means that if we want to establish service level expectations based on them, they will most likely be so far distant from the average that our customers will find them simply unacceptable.
The good news is that we know the "forces of nature" that cause that shape: it's all about delays. And those delays can be seen as the risks we are exposed to as part of our process, which means we can use classic risk management approaches to deal with them (in addition to more exotic and sophisticated techniques that have been uncovered in recent years.)
So, the bottom line is: your Lead Time is made of risks. If you identify and understand what those risks are (their likelihood and impact in terms of delay), you will get important clues about how to better manage and improve your process.
Where to Find more Details
My colleague Alexei Zheglov has done extensive study of this topic, and is the source of most of the material that I presented during this session.
From Alexei's production, the following links are the most relevant:
"Lead Time: Learning from Real and Fake Charts, Traffic Lights, and Coconuts": this is the talk that inspired my Coach Camp session, and it goes in great detail about the nature of delay as a risk.
"Lead Time Webinar": an earlier presentation that discusses the concept of Lead Time and Kanban Systems. (slides)
"Analyzing the Lead Time Distribution Chart": this article discusses how to measure lead time, and how to analyze results.
"Inside a Lead Time Distribution": this article describes the structure of the lead time distribution, in terms of it's several points of interest (mean, mode, median, control limits, etc.)
"Forecasting Cards": during the session, I showed some cards depicting rainbow coloured distributions, with factors to calculate several points in the curve based on knowing the average. They can be found in this link.
Other relevant resources include:
Troy Magennis' collection of spreadsheets to calculate flow metrics and do probabilistic forecasting.
"What We Know About Duration: Individual Activities", by David J. Anderson: this is part 1 of a series of articles describing the probabilistic nature of the "how long will it take?", and the implications. Make sure to follow the links towards the end of the article to find the other parts.