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
Answers to the questions.
In a system where every customer arrives exactly 60 seconds apart and every customer requires exactly 55 seconds of service, customers will never have to wait. The answer is zero because every customer will be done, 5 seconds before the next customer arrives.
In a system where customers arrive an average of 60 seconds apart and customers require an average of 55 seconds of service (both following exponential distributions), an average customer will wait about 10 minutes! If you do short simulation runs, you may see different answers, but if you do a statistically valid simulation run of a non-terminating system, you should be able to confirm this answer.
[...] rarely perform exactly as predicted” was the starting line for the blog Predicting Process Variability and is the driving force behind most improvement projects. As stated, variability is inherent in [...]
Simulation is a important tool to predicting process variability. Using simulated data to develop and study for data analysis is very beneficial. In mathematics area, people can gain insight about what happens when assumptions are needed to be proved by simulating models. And we should pay attention that simulated data related to process variability is a reasonable representation of what one would usually expect in the real world.
Simulation is an important tool to predicting process variability. Using simulated data to develop and study for data analysis is very beneficial. In mathematics area, people can gain insight about what happens when assumptions are needed to be proved by simulating models. And we should pay attention that simulated data related to process variability is a reasonable representation of what one would usually expect in the real world.
By using simulation we have an idea about process variability. I also agree that many complex systems can be modeled by using simulation easily (easier than the other methods).
On the other hand, simulation does not give us exact answers, it gives us estimates. Moreover, the number of replications, and/or run-lenght should be taken into account to conclude.
It is important to predict the variability in any project, simulation helps to do that
[...] you haven’t read it, I’d suggest you pause now and read the blog on Predicting Process Variability. Did you pass the test? Don’t feel bad, almost no one does. My facility is much more complicated [...]
[...] is the opening line from a Predicting Process Variability blog. It is also, according to the blog, “the driving force behind most improvement [...]