Process behaviour charts are the key to understanding your business

Written By Caidyrn Roder

All processes exhibit variation. It’s inescapable. Each part that comes off a production line is slightly different. The revenue your business generates varies from month to month. The number of visitors to your website varies day by day. The amount of work your teams complete changes from week to week. 

Variation is as fundamental as gravity. There’s no point fighting it. If you ignore it, you will miss opportunities for continual improvement, waste time taking action where none is warranted, and fail to act when action is required. Once you accept this, you will have taken the first step to understanding variation. 

The good news is that there are some simple tools that help you to understand the variation in your processes. Tools that help you achieve greater stability and predictability. Tools that can guide your continuous improvement efforts to ensure that you take action when it’s warranted. In this post, I’m going to introduce one such tool - the Process Behaviour Chart (also known as a Control Chart*). 

*I’m using the term Process Behaviour Chart (PBC) instead of Control Chart in this article as suggested by Dr. Wheeler in his book Understanding Variation. For those of you who are familiar with the “Control Chart” in Jira, be aware that the PBCs that I describe in this article are very different to the Jira version. As far as I’m aware, that Jira chart is not a Control Chart in the traditional sense. 

Two types of variation

In the 1920s, Walter Shewhart, the creator of the Process Behaviour Chart, realised that variation comes in 2 flavours:

  • Routine variation: The level of variation that we expect from a process based on its past behaviour

  • Exceptional variation: Any variation that is outside the limits of what we would expect from a process based on its past behaviour

To illustrate the difference, let’s take the example of driving to the supermarket. I live reasonably close to my local supermarket, so it takes on average about 5 minutes to drive there. But it doesn’t take me exactly 5 minutes each time. Sometimes it’s a little slower and sometimes it’s a little faster. There are a range of factors that influence that - the time of day, how lucky I am with the traffic lights, how many other people have decided to go to the supermarket at that time, etc. The point is that we expect this level of variation. It’s routine. 

Occasionally, however, the trip takes significantly longer. A few weeks ago, I set off for the supermarket as usual, only to find that a set of traffic lights was out and traffic had backed up. I happened to get to the intersection just as a police officer was getting set up to direct traffic, so it took a while for things to start flowing. That trip took me 25 mins instead of 5. This level of variation is outside of what I expect for my trip to the supermarket. It’s exceptional. 

This same principle applies to processes in organisations. The trouble is, it’s not always so easy to tell which variation is routine and which is exceptional. This is in part because the traditional methods of reporting don’t distinguish between these 2 types of variation. 

For example, a common type of management report compares the current month’s financial performance to a target. Or to an average. Or to the same month last year. In fact, it’s often some combination of these. 

The problem with this kind of comparison is that you only have 3 options: up, down or the same. And what does that really tell you? Are you up or down compared to the target / average because of something you did, or is that just the routine variation in your system? 

Comparing 2 values gives you no insight into the level of routine variation that you should expect from your system. This means that you are liable to overreact, making adjustments to your process, strategy or organisation when none are warranted. W. Edwards Deming refers to this as tampering. At best, tampering is wasted effort. At worst, it will destabilise your entire system. 

“Managing a company by means of the monthly report is like trying to drive a car by watching the yellow line in the rear-view mirror”

This is what Myron Tribus meant when he said “managing a company by means of the monthly report is like trying to drive a car by watching the yellow line in the rear-view mirror”. You might have some idea of where you’ve been, but it’s limited and you have no visibility of where you’re going.  

We need a tool that lets us differentiate between routine and exceptional variation. Something that we can apply to any process, using the data that we already have available. That tool is the Process Behaviour Chart. 

Process Behaviour Charts

In the 1920s, the Western Electric Company was involved in manufacturing equipment for telephone systems. They were experiencing variation in their manufacturing process which was causing quality issues. Unable to solve the problem themselves, they enlisted the help of Dr Walter Shewhart at Bell Laboratories. 

It was while working on the problem that Shewhart identified the 2 types of variation described above. And having identified them, he set about creating a tool to distinguish between them - the Process Behaviour Chart (which he referred to as the Control Chart). 

There are a number of different types of Process Behaviour Charts, but I’m going to focus on one called an XmR chart, which was created by W. J. Jennett in 1942. It is particularly flexible, and works well with the type of process data that we often encounter in knowledge work (“one-at-a-time” data). 

How to construct a Process Behaviour Chart (XmR chart)

Part of the beauty of Process Behaviour Charts (PBCs) is their simplicity. You can plot them with pencil and paper (in fact, this is how they were used in factories for years). But it’s easier with Excel, so that’s what I’ve used for this process and the examples.

To help you get started quickly, I’ve created this Excel file which includes the examples from this article plus a template that you can simply paste some data into. 

Here’s an overview of the steps to create a PBC (don’t worry if the steps don’t make sense yet - all will be explained):

  1. Select your process data

  2. Enter the process data into an Excel spreadsheet (or Google sheet)

  3. Calculate the average

  4. Calculate the moving ranges (mR)

  5. Calculate the average of the moving ranges

  6. Calculate the natural process limits and the upper limit for the range

  7. Create the charts

Note that the XmR chart is actually 2 different charts, displayed together. The X chart is a chart of individual values and the mR chart is a chart of the moving ranges. They are usually shown together, with the X-chart above the mR chart. They look something like this. 

Fig. 1: Example of an XmR chart created in Excel

1. Select your process data

Choose the data that you want to report on. It needs to be a single variable in time order. Some examples of data you could chart are:

  • Revenue by month

  • Number of website visitors by day or week

  • Team throughput by sprint

  • Cycle time of a team’s work items, ordered by date completed (or date started)

To illustrate the process, I’m going to use cycle time data for the last 50 work items completed by a team. 

2. Enter the data into a spreadsheet

Now enter / paste the process data into a column in an excel spreadsheet. It should look something like this.

Fig. 2: Enter process data in column A

While it’s not needed for the PBC, it’s usually a good idea to include additional data about each of the data points - i.e. ticket reference number, summary, etc. This makes it easy to cross reference individual data points once you’ve created the chart. I’ve excluded this additional data from this example for simplicity. 

3. Calculate the average

Use a formula (in Excel, the formula is =AVERAGE()) to calculate the average of the first 25 data points*, then fill this formula down the second column in the spreadsheet so that you can plot it as a horizontal line on the chart.

Fig. 3: Calculate the average

*One of the amazing things about PBCs is how little data they require to work. There is an art to choosing the data to calculate averages and limits that I’m not going to go into here. But just know that you can use as few as 5 data points to calculate the average and the limits (not ideal, but it works ok), and there are diminishing returns after 25 data points (see Exact Answers to the Wrong Questions by Donald J. Wheeler if you want to learn more). 

You might see this average referred to as X̄ (X bar).

4. Calculate the moving ranges

This sounds more complicated than it is. The moving range is simply the absolute value of difference between 2 successive data points. So to calculate the moving ranges, start at the 2nd data point then subtract the one before from it, then take the absolute value of the result. So for my example data, the first few moving ranges are:

  • 15 - 5 = 10

  • 9 - 15 = -6 = 6 (absolute value)

  • 16 - 9 = 7

The Excel formula =ABS() does the trick here for absolute values. 

Fig. 4: Calculate moving ranges (mR)

I leave a gap of 2 columns in my spreadsheet to leave space for the limits that we’ll calculate in a moment (this makes it slightly simpler to construct the chart in step 7).

5. Calculate the average moving range

Use a formula to calculate the average of the moving ranges for the first 25 values*, then fill this formula down the column in the spreadsheet so that you can plot it as a horizontal line on the chart. 

Fig. 5; Add the average moving range (mR Bar)

*24 moving ranges, because the first moving range is on the 2nd line of the data. 

You will often see this average called m̄R̄ (mR Bar).

6. Calculate the limits

Next, we’re going to calculate 3 limits, then fill down the columns in the spreadsheet:

  • Lower Natural Process Limit (LNPL) 

  • Upper Natural Process Limit (LNPL)

  • Upper Range Limit (URL)

These define the limits within which we expect routine variation to fall. In other words, any data point that falls outside these limits is possible exceptional variation. 

The formulae for the 3 limits are:

LNPL = Average - (2.66 x m̄R̄)

UNPL = Average + (2.66 x m̄R̄)

URL = 3.27 x m̄R̄

If you’re anything like me, you may be thinking that this looks too simple to work. And while proving these formulae is outside the scope of this article, just know that people have been using PBCs effectively for over 100 years and we’re yet to find anything better. 

Note that for data where negative values don’t make sense (e.g. cycle time, throughput and website visits can only be positive) we don’t plot the LNPL if it’s negative. In my example, I have set the LNPL to 0 because the formula gave me the result of -2.47.

Fig. 6: Add the limits to the spreadsheet

7. Create the charts

You can use the Excel template that I have provided for this, or you can create the charts from scratch. Either way, you’re going to need some familiarity with Excel charts for this bit. 

Create 2 line charts and position the X Chart above the mR Chart:

  • The X-Chart will have the Cycle Time, Average, LNPL and UNPL

  • The mR-Chart will have mR, mR Bar and URL

When you’re done, it should look something like this.

Fig. 7: The completed XmR chart

Points to note

  • The black line on the X Chart plots cycle time in what is known as a run chart. It displays the values of cycle time in time sequence order (in this case, the order in which work items were completed by the team). 

  • The black line on the mR Chart plots the moving ranges (also as a run chart). 

  • The green line on the X Chart and mR chart is the average of the cycle times and moving ranges respectively

  • The red dashed lines are the limits (UNPL and URL). 

  • The LNPL is not shown on the X Chart because it is less than 0 in this case (which doesn’t make sense for Cycle Time)

Based on this XmR chart, we can conclude that this process only has routine variation for the data that (see detection rules below). 

Using Process Behaviour Charts

Process Behaviour Charts let you visualise the variation in your process and the detection rules (outlined below) help you to identify the 2 types of variation identified by Shewhart - routine and exceptional variation. The idea is that once you have identified what type of variation you’re dealing with, you can take appropriate action. 

At a high level, the key difference between action you should consider:

  • Routine variation is inherent in the system. It is not specific to one event or outcome. If you wish to reduce the level of routine variation, you need to adjust the system rather than reacting to the variation as if it were a one-off occurrence.

  • Exceptional variation is an indication that there was something different (exceptional) about one or more events or outcomes. In this case, it’s worth investigating what was different about this event to identify actions that you can take to prevent recurrence. 

Detection rules

Over the years people have come up with many rules for detecting the presence of exceptional variation in process data. In this article I’m going to cover 3 suggested by Wheeler in his book Understanding Variation. They are easy to use and have plenty of power in detecting instances of exceptional variation. 

Note that while these are referred to as “rules”, you also need to use your understanding of the context. The rules are not infallible. They are meant to guide you on when you should investigate possible exceptional variation and when you should not. You need to use your judgement when applying these rules. 

Rule 1: Any point outside the limits

One or more points outside of the limits on either the X Chart or the mR Chart is a signal that there is possible exceptional variation.

Fig. 8: 3 examples of detection rule 1 - point outside the limits

Rule 2: A run of eight

8 or more successive values on the same side of the average line on the X Chart may be a signal that there is exceptional variation with a weak but sustained effect. This can also be an indication that the process has shifted and that you may need to recalculate the limits moving forward (any recalculation of limits should be based on your understanding of the context). 

Fig. 9: Example of detection rule 2 - run of eight

Rule 3: Runs near the limits

At least 3 out of 4 consecutive values that are closer to one of the limits than they are to the central line may be a signal that there is exceptional variation that has a moderate but sustained effect.

Fig. 10: Example of detection rule 3

Examples

Let’s wrap things up by examining a couple of examples of real data plotted on Process Behaviour Charts. 

Squad cycle time data

The first is a plot of cycle time data from a development team that I worked with a few years back. It was a strong team with a track record of delivering good work. They were running a stable system, which meant they were able to deliver predictably. This predictability is visible in the first portion of the Process Behaviour Chart below. 

But around point 33, something happened. All of a sudden we see multiple signals on the Process Behaviour Chart. 

Fig. 11: XmR Chart of real squad cycle time data with examples of detection rules 1, 2 and 3

Even without knowing the context, you can see that something changed in their process at around data point 33 in the Process Behaviour Chart. Rules 1, 2 and 3 all happen at the same time and the data continues to display increased variation, even after the points that I’ve outlined in the chart. 

The cause? One of their team members had been moved to another team and they had not yet replaced him. This meant that whenever they did work that required his skillset, they had to wait until the other team had capacity to support them. In other words, they had introduced a dependency, which increased the variation in their system. 

Knowing this context, we can be confident that the underlying process has changed and we can recalculate the averages and limits. This lets us quantify the impact of this change in team structure and helps us to understand what level of variation we can expect from this team moving forward (until something else changes in their system). The average cycle time has nearly doubled from 2.8 to 5.4, and the Upper Natural Process limit has increased from 6.79 to 12.1.

Fig. 12: XmR Chart of real squad cycle time data with limits recalculated at point 33

Note that even with these recalculated limits, you can still find examples of the detection rules in this data set. 

ProSocia website visits

The second example is a Process Behaviour Chart of traffic from the ProSocia website over the past 12 months or so. This chart is annotated with blog posts and other LinkedIn activity so that we can better understand the context at a glance. 

Fig. 13: XmR chart of ProSocia website traffic by week, annotated with our marketing activities

This is something that we’ve been using to better understand the effectiveness of our marketing efforts. The beauty of this approach is that it helps us to identify when actions that we’re taking are actually making a difference to our website traffic (i.e. when we see exceptional variation). And while I’ll be the first to admit that the raw traffic numbers are nothing to write home about, I am pleased with the overall trend that is made clear by the Process Behaviour Chart.

Conclusion

For me, understanding variation has been like getting a glimpse of the code behind the matrix. It’s helped me to improve how I work at both a team and an organisation level. It has far-reaching implications for how we design systems, how we forecast work and even how we structure staff appraisals and incentives (Deming has a lot to say on this last topic). 

As might be expected, this article has only scratched the surface. I’m hopeful that I’ve given you enough information to try out Process Behaviour Charts and begin your journey to understanding variation. To be honest, I’m only beginning the journey myself. If you’d like to learn more, check out some of the references below or contact us if you’d like to chat. 

References and further reading

Articles

Books

  • D. J. Wheeler, Understanding Variation: The Key to Managing Chaos (2nd Edition), SPC Press, 2000 (I highly recommend this book - Dr. Wheeler explains the concepts in a very accessible way, supported by real examples)

  • D. Vacanti, Actionable Agile Metrics for Predictability Volume II, LeanPub / ActionableAgilePress, 2023 (this book is also great - it’s only book that I’ve found so far that explores Process Behaviour Charts from the perspective of software teams)

  • D. J. Wheeler, D.S. Chambers, Understanding Statistical Process Control (3rd edition), SPC Press, 2010 (this one is a text book - read it to get a much deeper understanding of Process Behaviour Charts and statistical process control)

Caidyrn Roder
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