Orbit charts, and why you should use them



For details, click on the following:

1. What is an “orbit chart”?




Orbit chart of Quality versus Productivity Whack-a-Mole

Orbit chart of Quality versus Productivity Whack-a-Mole



The orbit chart is meaningless if the points are independent

The orbit chart is meaningless if the points are independent

2. Examples of orbit charts


2.1. Minard’s Russia campaign chart


2.2. Unplanned versus planned downtime in nuclear power plants


France versus Japan nuclear plant downtime stats 1979-1989



2.3. GINI index versus GDP in Brazil and the US, 1980-2011




2.4. Populations of predators and preys


Orbit chart - Predator-prey limit cycle

Predator-prey limit cycle


2.5. Parker Hannifin’s “North-by-Northwest” chart


Orbit chart -- Parker Hannifin North-by-Northwest chart




2.6. Orbit charts for spacecraft

Pioneer 10 and 11 flight path

Voyager 1 and 2 flight paths


2.7. Recovery from crisis at Toyota versus GM


GM sales and profits chart

Toyota sales and profits chart 2001-2011


The Toyota chart further shows three distinct periods:


2.8. Janet Yellen’s orbit chart of inflation versus unemployment


Inflation versus unemployment in US 19690-2013

See the articles for animations and explanations of the different segments.



Colgate and P&G inventory turns versus operatings margins

walmart versus target inventory turns versus operating margins





3. How to generate orbit charts in Excel


Selecting scatter chart with straight lines and markers on Excel

Selecting scatter chart with straight lines and markers in Excel


Looping and spiraling chart generated with Excel

Looping and spiraling chart generated with Excel


  1. Labeling every n-th point. 


Orbit chart with date labels affixed by Excel macro

Orbit chart with date labels affixed by Excel macro


4. Orbit charts for multidimensional data







11 comments on “Orbit charts, and why you should use them

    • I have seen this kind of chart in a variety of contexts without a generic name, and I thought they deserved one. I remember hearing the term “orbit” used in the same sense a few decades ago, to designate the path followed by solutions of differential equations. But, if you google “orbit chart,” the only items that come up are related to planets or electrons.

  1. Great article as usual, Mike. We have used these types of charting techniques to demonstrate convolutions and variation in process performance. Great visual charting techniques that help people to see what is going on in their processes.

  2. Comment in the Lean Six Sigma Worldwide discussion group on LinkedIn:

    As the old saying goes, “Few ideas are truly new.” The idea of mapping state information graphically has been used in the field of Chaos Theory for nearly 50 years. Lorenz, for example, used this technique to show graphically how systems behave over time (in that case, his focus was on weather). You can find a lot of information about this form of mapping by searching “phase space” (which refers to the resulting spatial representation of a system’s potential state boundaries), “phase plots” and “phase diagrams” which are basically the same as your “orbit charts.” There is also no limit to the number of dimensions these plots can take on, though it is extremely difficult to visualize more than 3 dimensions. (The Lorenz plot, for example, is 3 dimensional since there are 3 variables in the system.)

    The value of mapping system state information into such a format comes from the understanding of how systems behave over time, and the potential range that system variables may take on during the life of a system. In chaos theory, “orbits” are due to “strange attractors” which represent stable points of the system, and seem to “attract” the system’s state much like a gravity well might attract a planet. These plots also reflect the “dynamics” of a system and show there are critical relationships of variables within the system (that otherwise can’t be seen). In system dynamics, “all things are connected.” It is just a matter of determine WHEN, not IF, these relationships are strong and weak. Such plots help us understand when this happens. Finally, “orbit plots” are helpful to understand how a system responds to “initial conditions.” This means that one “orbit” that “flies near” a previous orbit” may take on a completely different path. A system that is highly susceptible to such conditions may be “chaotic” and is therefore unlikely to be “predictable” from our traditional ways of thinking.

    I have used phase plots to show (for example) the relationship between schedule and cost variations (between planned and actual) on engineering projects (human-intensive systems).

    Thanks for sharing this idea!

    • You are right that it is hardly a new idea, and its origins are in math, which is not a popular subject in manufacturing. My own introduction to this kind of plots was as a summer intern at the Hahn-Meitner Institut in Berlin in the summer of 1976, and it was memorable.

      One of the doctoral students was trying to solve a system of equations governing the population of two types of defects in ionic crystals: interstitials — ions knocked out of position in the crystal lattice — and vacancies — the holes they leave behind. Of course, when an interstitial meets a vacancy, it falls into it and they cancel each other, which is the main factor of complexity. It is a bit like the population dynamics of single versus married men and women.

      At the time, I often used translations of soviet textbooks, because they were cheap. In particular, I was fond of Vladimir Arnold’s treatise on ordinary differential equations, in which he showed how to plot orbits of the solutions of systems of equations on the back of an envelope when you can’t solve them analytically. I applied this technique to the doctoral student’s problem, which gave him the answer he was looking for. After that, we were able to plot a numerical solution, which was the first program I ever wrote, on a tiny Wang machine, in what I didn’t know was assembler.

      Vladimir Arnold later taught at UC Berkeley and died in 2010. The doctoral student, now Dr. Wolf E. Montserrat, later worked on the recycling of spent nuclear fuels.

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  4. Very interesting. I have to see how this may be exploited in software engineering or business analysis or requirements engineering. Surely the shape and direction of paths reveal some “not easy to see” properties of the subject of study. I have added this to my favorites.

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