Posts Tagged ‘process variability’

Can Simulations Model Chaos?

Sunday, January 11th, 2009

Can chaotic systems be predicted? I guess we first need to agree on exactly what a chaotic system is.

BusinessDictionary.com defines it as a
“Complex system that shows sensitivity to initial conditions, such as an economy, a stockmarket, or weather. In such systems any uncertainty (no matter how small) in the beginning will produce rapidly escalating and compounding errors in the prediction of the system’s future behavior.”

It is hard to imagine a complex system that does not show sensitivity to initial conditions. If the follow-on statement is true, then there is little point to ever trying to model or predict the behavior of such a system because it is not predictable. But it is not hard to find counter-examples, even to the examples they provided. Meteorologists do a reasonable job predicting the weather; it depends on your standards of accuracy. Certainly they can predict fairly accurately the likelihood of a 90 degree day in January in Canada or anticipating the path of a tropical storm for the next 12 hours.

A less technical but perhaps more useful definition comes from membrane.com:
“A chaotic system is one in which a tiny change can have a huge effect.”
That leads us toward a more practical definition for our purposes.

For the types of systems we normally model, I would propose yet another definition.
A chaotic system is one in which it is likely that seemingly trivial changes in the initial conditions would cause significant changes in the predicted results, over the time frame being considered.

This definition, while not technically rigorous, acknowledges that most of us rarely have the opportunity or the need to deal in absolutes. We live in a world where the majority of decisions are made subjectively (“Joe has 20 years experience and he says…”) or with gross simplification (“Of course I can model that in a spreadsheet…”). In this world, being able to base a decision on a simulation model with better accuracy and objectivity can help realize tremendous savings, even if it is still only an approximation and only useful within specified parameters.

Can we accurately predict true chaotic systems? By strict definition clearly not. And even by my definition, there will be some systems that are just too chaotic to allow any predictions to be useful.

But can we provide useful predictions of most common systems, even those with some chaotic aspects? Absolutely yes. Every model is an approximation of a real or intended system. Part of our job as modelers is to ensure that the model is close enough to provide useful insight. A touch of chaos just makes that more interesting. :-)

Dave Sturrock
VP Products – Simio LLC

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Posted in Applications, General | 5 Comments »

Predicting Process Variability

Monday, November 3rd, 2008

Systems rarely perform exactly as predicted. A person doing a task may take six minutes one time and eight minutes the next. Sometimes variability is due to outside forces, like materials that behave differently based on ambient humidity. Some variability is fairly predictable such as tool that cuts slower as it gets dull with use. Others seem much more random, such as a machine that fails every now and then. Collectively we will refer to these as process variability.

How good are you are predicting the impact of process variability? Most people feel that they are fairly good at it.

For example, if someone asked you what is the probability of rolling a three in one role of a common six-sided die, you could probably correctly answer one in six (17%). Likewise, you could probably answer the likelihood of flipping a coin twice and having it come up heads both times, one in four (25%).

But what about even slightly more complex systems? Say you have a single teller at a bank who always serves customers in exactly 55 seconds and customers come in exactly 60 seconds apart. Can you predict the average customer waiting time? I am always surprised at how many professionals get even this simple prediction wrong. (If you want to check your answer, look to the comment attached to this article.)

But let’s say that those times above are variable as they might be in a more typical system. Assume that they are average processing times (using exponential distributions for simplicity). Does that make a difference? Does that change your answer? Do you think the average customer would wait at all? Would he wait less than a minute? Less than 2 minutes? Less than 5 minutes? Less than 10 minutes? I have posed this problem many times to many groups and in an average group of 40 professionals, it is rare for even one person to answer these questions correctly.

This is not a tough problem. In fact this problem is trivial compared to even the smallest, simplest manufacturing system. And yet those same people will look at a work group or line containing five machines and feel confident that they can predict how a random downtime will impact overall system performance. Now extend that out to a typical system with all its variability in processing times, equipment failures, repair times, material arrivals, and all the other common variability. Can anyone predict its performance? Can anyone predict the impact of a change?

With the help of simulation, you can.

This simple problem can be easily solved with either queuing theory or a simple model in your favorite simulation program. More complex problems will require simulation. After using your intuition to guess the answer, I’d suggest that you determine the correct answer for yourself. If you want to check your answer look at the comment attached to this article.

And the next time you or someone you know is tempted to predict system performance, I hope you will remember how well you did at predicting performance of a trivial system. Then use simulation for an accurate answer.

Dave Sturrock
VP Products – Simio LLC

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Posted in Applications, Expertise, General | 8 Comments »