In general, we are sadly missing an intuitive understanding of random processes. Several authors wrote about this blind spots in the last years – Taleb in Fooled by Randomness



or Sam L. Savage in the Flaw of Averages – just to name a few.


To my mind, the basic problem is that we rarely have the opportunity to experience long stretches of random phenomena. Of course we all saw dice being thrown and the stock market fluctuate – but this is not enough to develop an intuition about random events. To do this, we would need to observe and record long stretches of the phenomenon – and I would have yet  to see the person, who spent hours and hours throwing a balanced die and recording the results – not to say, analyzing the them as well . (Well, there was a truly renaissance personality called Cardano, who did this in the XVIth century, and wrote a book about it, but this was more then unusual).


Studying and improving processes is a field where we really miss an intuitive understanding of how random variations influence the behavior of the system. In principle Six Sigma acknowledged the role of random variations but, sadly, not when looking at process mappings. Lean followed in the same steps, simply formulating the request to reduce the variation as far as possible in order to achieve a uniform flow. So, in the end, some practical questions are left unanswered in both methodologies, like: How much variation is acceptable? What are precisely the negative effects of randomness in our concrete process? How could we make a cost-benefit analysis of the variation reduction?

To answer these questions, we would need to understand the effects of randomness on a process. To my knowledge there is one discipline that really attempted to do this: Factory Physics  (  . In this theory we apply queuing theory to the manufacturing processes and the result is that we can come up with a formula that will precisely describe the effects of random variations on a manufacturing operation., the (in)famous Pollaczek-Khinchine equation eventually combined with Little’s Law.

Now, if you are the type of person, who was trained in reading and interpreting equations (like physicists are, no surprise here) then all you would need is to look at this equation to understand the effects of variation on a value stream. Unfortunately, very few people can do that, so, for the rest of us the equations provide a tantalizing hint of what is going on, but fail to deliver the kind of intuitive understanding we would find useful. To achieve that we would need to be able to observe and track processes with random variations over a long period of time to see what is going on.

This is generally not feasible in real life, due to constraints of costs and time. The processes are rarely constant over a long enough period, so that we could observe their behavior at leisure. Changing some parameters, like the average processing times, or the standard deviation of the processing time at a given step, just to be able to observe the effects of a such a change, is of course impossible. So, we need a random system that is cheap and fast to change and  also easy to observe.

This is why in the 80-ties Goldratt invented the Dice Game – an abstract model of a processing line, where the only influencing factor was the randomness of the processing times. The game is played as follows: 5-8 people sit at a table, each with a six sided die. There are matchsticks to the right and to the left of each person, one person’s right matchstick heap being the left heap of the next person. There is also a “feeder” – someone who is providing new matchsticks at the input of the process. At the sign of the moderator, each person throws the die and moves as many matchsticks from their left to the right as the count of points on their die. If they do not have as many sticks to their left, (say they have 3 sticks and the die says 5) they move as many sticks as they can.  The feeder will input regularly 3 then 4 then 3 again to the process at the beginning of each cycle.


The operation is then repeated, for as many times as the moderator sees fit – generally not more than 20 cycles to avoid boring people to death.  Then the exercise will be repeated, but instead of a die a coin is tossed. The rule is that heads mean moving 3 sticks, tails mean moving 4.


Now, consider the following: in both cases the average performance of each workstation will be 3.5 sticks per cycle, that is, the line is perfectly balanced in both cases. Before reading on, think about the following questions:

  1. Would you expect a difference in these two cases (die vs. coin).
  2. Do you expect a difference in the throughput (finished products per cycle) between the two cases?
  3. Where do you expect to see the bottleneck?
  4. If each step can still move 3.5 pieces on the average, how would you improve the process?


As we are missing the intuitive understanding of random processes, it is not easy to answer these questions. Getting enough people together to play the dice game is not as easy either, especially if we want to see the longer term effects – no one will waste time to play this for several hundreds of cycles, right? Still, understanding the behaviot´r of the Dice Game is an important step towards understanding random variation in a value stream.


The solution is to write a computer simulation with a comfy user interface and let people simulate the system. In this case the individual steps are fairly simple so writing this simulation is not a complicated job, adding a user interface is also pretty much a standard using R and the Shiny interface. This way we can play several thousands of rounds, without getting bored, we can measure the results, change the parameters or simply repeat the runs several times, to see how the system behaves. There is no better way to develop our intuition, and in my experience, there wasn’t a singleperson who was not surprised by some aspects of what they saw.


As is happens, we, at ifss,  developed a such a simulation and it can be accessed by anyone via the Internet. It is not up all the time, but if anybody would like to figure out the answers to the above questions, we would be happy to start the simulation. Just send a message, some time in advance, and we shall find an opportunity to run activate the simulation,

So, feel free to explore and to start developing your intuition about random processes. We would be happy to hear from you, and if you try the simulated VSM Game, sharing what you experienced would be even nicer.