### Little's Inequality

The interesting thing about Little's Law, in spite of its very general applicability, and in certain cases mathematical certainty, there are many cases when it simply does not hold true. In those cases it's not so much Little's Law as Little's Inequality. Could the fact that specific instances of data do not follow Little's Law actually give us useful information about our Kanban and Scrum systems and point to the right kind of interventions to manage and improve their flow? That's what this blog is about.

 Flow Metrics for a Kanban System over time(WiP, TiP, DR, Delivery Bias, Net Flow)

In 1961 John Little published his proof of this general queuing theory equation [litt]:
L=Î»W
L is the average number of items in the queue, Î» is the average arrival rate, and W the average wait time
Since that time Little's Law has found numerous applications in the study of general flow systems from telecommunications to manufacturing, including in Kanban systems. Because throughput or delivery rate is the more significant attribute for management of such systems (and on average it is approximately equal to arrival rate), it is often expressed as follows:
Delivery Rate = WiP / TiP
The overline indicates the arithmetic mean, WiP is the number of items in the system, and TiP the "time in process" from entering to leaving the system under consideration. See this Glossary for further explanation of the meaning of TiP, versus Lead Time or Cycle Time (and why I don't use Cycle Time!).
However when we look at data from actual Kanban systems, where the averages are over relatively short periods (say a week or a month), or where average arrival rate does not equal average delivery rate, it is Little's Inequality that applies, not his Law. Juggling the terms above we can express it in this way:
Delivery Rate  ( WiP / TiP )  0    ("Little's Inequality")
This is because if the system itself is trending in some way (technically the system is not stationary), or if the scope of the averages is not so wide that every item that entered has left the system - usually both these conditions are true for the periods we wish to analyse - then Little's Law does not apply exactly.

That might seem to imply Little's Law is not useful to us. However the degree to which the law is not true is very relevant and does give us important management information:
Delivery Rate  ( WiP / TiP ) < 0    More work is being taken on than is being delivered
Delivery Rate  ( WiP / TiP ) = 0    The system is balanced
Delivery Rate  ( WiP / TiP ) > 0    More is being delivered than new work being taken on
This looks like actionable data for managing flow in Kanban Systems - a number that shows bias in the system towards (or away from) delivering. Let's look at the set of graphs in the figure above that demonstrate this. The data set is from +Troy Magennis's SimResources website and uses his data, spreadsheet and some of the graphs he provides to assist with his forecasting models[mage]. You can find more about Troy's work at FocusedObjective.com and also download these spreadsheets to explore what your data reveals about your Kanban or Scrum systems.

Firstly the figure shows graphs of the 3 main variables in Little's Law: WiP, TiP and Delivery Rate, The next graph is a plot of Little's Inequality - labelled Delivery Bias, showing whether it is greater or less than zero at any point in time. Note that the formula above is normalised relative to the overall average delivery rate for the whole dataset (AvDR) so that the range (in this case between -1 and +1) is comparable with other datasets. The final graph in the set shows Net Flow, the difference between items completed and started - it is one of the metrics included in Troy's spreadsheet and it again provides a view of how balanced the system is.

As expected the graphs show a strong correlation between Net Flow and Little's Inequality for most of the range. Clearly if we're starting more than we're finishing we should expect both the inequality and the Net Flow to be negative. What's interesting is where they don't correspond, and why. Look at weeks 2015-11 and 2015-12. Why in week 11 are we finishing more than starting and yet we still have a negative value for Little's Inequality? The clue is in the TiP for these weeks. In week 11 the average TiP is much lower than in week 12. Perhaps this indicates the items closed that week were smaller in size - or maybe they were "expedited" at the expense of other items in progress. When the items that had been in process longer are closed the following week, Little's Inequality indicates more strongly that balance is being restored.

Little's Inequality as expressed above focuses on Delivery Rate, hence the label Delivery Bias. It could be re-expressed to focus on Time In Process as follows:
TiP  WiP / Delivery Rate
This metric might be labelled Time in Process Bias. We want TiP values to be as low as possible, but a negative value of this metric is likely to indicate an issue to address, since it would indicate that the TiP of the work in progress is likely to be longer than the items recently delivered.

The time an item stays in the process is also the focus of a new metric from +Daniel Vacanti recently published in his Actionable Agile Metrics [vaca] (see also ActionableAgile.com). He also looks at the degree to which a given system follows an ideal flow through a metric he calls "Flow Debt" (roughly translated as delivering more quickly now at the cost of slower times later). Dan prefers the term Cycle Time to Time In Process and so defines Flow Debt as the difference between the "Approximate Average Cycle Time" (AACT) as observed on a Cumulative Flow Diagram and the "Average Cycle Time" (ACT). Comparing these 2 items gives an idea of whether Flow Debt  is being created or not. Flow Debt is accumulating when AACT>ACT. You can calculate AACT by looking at the time since the cumulative arrivals into the system equalled the current cumulative deliveries. ACT is calculated from the arithmetic mean of the actual times for delivered items in the period. Again the degree to which these quantities do not match indicates the degree to which the system is out of balance.

All these metrics - Little's Inequality (or Delivery Bias), Net Flow and Flow Debt - provide insight into the behaviour of Kanban systems based on the degree to which the system follows Little's Law over the period of study. Further experimentation and experience will show the best ways to use them in concert and the best ways to visualise the flow characteristics of the systems and how to intervene to improve them.

If you have data which you would like to analyse using these metrics do let me know. I'm happy to share spreadsheets and advice with anyone who contacts me. Equally check out Troy Magennis's and Dan Vacanti's web sites referenced above for more tools and insights.

References
• [litt] Little, J. D. C. "A Proof of the Queuing Formula: L = Î»W," Operations Research, 9, (3) 383-387. (1961)
• [mage] Magennis, T. "Forecasting and Simulating Software Development Projects: Effective Modeling of Kanban & Scrum Projects using Monte-carlo Simulation", FocusedObjective.com. (2011)
• [vaca] Vacanti, Daniel S. "Actionable Agile Metrics for Predictability: An Introduction". LeanPub. (2015)

### Does your Definition of Done allow known defects?

Is it just me or do you also find it odd that some teams have clauses like this in their definition of done (DoD)?
... the Story will contain defects of level 3 severity or less only ... Of course they don't mean you have to put minor bugs in your code - that really would be mad - but it does mean you can sign the Story off as "Done"if the bugs you discover in it are only minor (like spelling mistakes, graphical misalignment, faults with easy workarounds, etc.). I saw DoDs like this some time ago and was seriously puzzled by the madness of it. I was reminded of it again at a meet-up discussion recently - it's clearly a practice that's not uncommon.

Let's look at the consequences of this policy.

Potentially for every User Story that is signed off as "Done" there could be several additional Defect Stories (of low priority) that will be created. It's possible that finishing a Story (with no additional user requirements) will result in an increase in…

### "Plan of Intent" and "Plan of Record"

Ron Lichty is well known in the Software Engineering community on the West Coast as a practitioner, as a seasoned project manager of many successful ventures and in a number of SIGs and conferences in which he is active. In spite of knowing Ron by correspondence over a long period of time it was only at JavaOne this year that we finally got together and I'm very glad we did.

Ron wrote to me after our meeting:

I told a number of people later at JavaOne, and even later that evening at the Software Engineering Management SIG, about xProcess. It really looks good. A question came up: It's a common technique in large organizations to keep a "Plan of Intent" and a "Plan of Record" - to have two project plans, one for the business partners and boss, one you actually execute to. Any support for that in xProcess?

Good question! Here's my reply...

There is support in xProcess for an arbitrary number of target levels through what we call (in the process definitions) P…

### Understanding Cost of Delay and its Use in Kanban

Cost of Delay (CoD) is a vital concept to understand in product development. It should be a guide to the ordering of work items, even if - as is often the case - estimating it quantitatively may be difficult or even impossible. Analysing Cost of Delay (even if done qualitatively) is important because it focuses on the business value of work items and how that value changes over time. An understanding of Cost of Delay is essential if you want to maximise the flow of value to your customers.

Don Reinertsen in his book Flow [1] has shown that, if you want to deliver the maximum business value with a given size team, you give the highest priority, not to the most valuable work items in your "pool of ideas," not even to the most urgent items (those whose business value decays at the fastest rate), nor to your smallest items. Rather you should prioritise those items with the highest value of urgency (or CoD) divided by the time taken to implement them. Reinertsen called this appro…