by Manikandan Jayakumar, guest bloggerWe use Design of Experiments (DOE) to optimize the value of a response (Y) by simultaneously changing the values of several factors (X’s). The response will often be a continuous variable, but in some scenarios you need to optimize an attribute or categorical response (Pass/Fail, Accept/Reject, etc.).
- Position of catapult on the launch ramp
- Angle of catapult
- Number of rubber band windings
- Position of gummi bear on the catapult
- Position of fulcrum in the catapult
What Is an Effect in DOE?
In DOE, we're trying to detect the effect of changing each variable from the low to high level. Usually, the way to make the difference most obvious is to make the levels as far apart as possible. Let me borrow some data from Carly Barry to...
Last time, we talked about center points and replicates in design of experiments. It turns out that both are tools that you can use to increase the probability of finding a statistically significant difference. But what we really want to know is, how many center points and replicates should be in the gummi bear experiment? To answer that question, we have to estimate the standard deviation of the distances the gummi bears go.
Estimating the Standard Deviation When You Do Design of Experiments
I do have an old data set from some students launching gummi bears that I can use. Historical data is a...
Last time, we talked about what resolution means in design of experiments (DOE). After you choose your resolution in Minitab Statistical Software, you need to choose the number of center points and the number of replicates for corner points. We can consider these two questions together because they’ll help determine the total size of the experiment.
Using center points to check your model
I alluded to center points when we talked about 2-level designs previously. Center points are experimental runs with the all of the continuous factor settings set halfway between the low level and the high...
Now that we’ve settled on a 2-level factorial design, we’ll take a look at some of the different 2-level designs that we can run with 5 factors. Minitab gives us 3 options in design of experiments: a full factorial, a half fraction and a quarter fraction. In the statistical world of DOE, we say these designs offer different "resolutions" to an experiment.
You can think of choosing a statistical resolution in DOE as similar to choosing between cameras with 10 or 20 megapixels. In both designed experiments and with cameras, higher resolution is generally better. However, depending on your goal,...
Now that we’ve learned enough about design of experiments to understand the experimental designs that Minitab offers, it’s time to consider which we should use to study the gummi bears. We'll consider the designs in the same order that we did in the earlier blog posts:
What Type of Design do I Need?
Here's a series of questions to ask:
1. Is it reasonable to assume there is a linear relationship between the factors and the response?
If you answer "yes" to that question, a factorial design is probably a good choice.
Design of experiments (DOEs) is a very effective and powerful statistical tool that can help you understand and improve your processes, and design better products.
DOE lets you assess the main effects of a process as well as the interaction effects (the effect of factor A, for example, may be much larger when factor B is set at a specific level, leading to an interaction). In science and in business, we need to perform experiments to identify the factors that have a significant effect. The objective of DOE is to reduce experimental costs—the number of tests—as much as possible while studying as...
Suppose that on your way to a summer holiday resort (a very distant place), your car breaks down. You might just call the roadside assistance and wait for your car to be towed to a repair shop. But suppose that you think you are smarter than that, and you would like to solve the issue by yourself—or at least evaluate the repair cost. Vehicle breakdowns can occur for a large number of reasons.
Intuitively, when facing a complex problem, we tend to test different solutions as soon as they come to our mind. When we understand that one solution will not work, we will then look for the next...
In previous posts on design of experiments, or DOE, we’ve covered:
Next on the list are split-plot experiments.
Split-plot designs are extremely popular in design of experiments because they cover a common case in the real world: when you have a factor that you want to study but can’t change as often as your other factors.
If you have an agricultural mind, as many scientists did back when they were inventing the name of this method, you’ll appreciate the language about "splitting a plot." Suppose that you wanted to study a...
Last time, we talked about why to use designs with just two levels. Now it’s time to discuss the two-level options in design of experiments, starting with Plackett-Burman designs.
Plackett-Burman designs exist so that you can quickly evaluate lots of factors to see which ones are important. Plackett-Burman designs are often called “screening designs” because they help you screen out unimportant factors.
This fits in with our previously-stated goal for design of experiments: learn as much as possible from the smallest amount of data. If we’re not sure a factor is important, we don’t want...
In the last post, we discussed how general full factorial designs let you study factors at more than two levels. The remaining 4 options that Minitab offers for factorial design of experiments are all 2-level designs, including the Plackett-Burman design.
Because there are 4 different kinds of 2-level designs, one of which is selected by default, you can probably guess that 2-level designs are quite popular. So what’s special about a 2-level design, and why would we use one?
One of the benefits of using design of experiments to plan data collection is to learn as much as possible from the...
Having spent some time figuring out what to do with the different variables for our gummi bear experiment, it’s time to get into Design of Experiments with Minitab. Opening Stat > DOE > Factorial > Create Factorial Design presents you with 5 options to choose from immediately:
The dialog box is helpfully explaining that some of these designs are for different numbers of factors. For example, if you want to create an experiment to study more than 15 factors in Minitab Statistical Software, you’re directed to a Plackett-Burman design.
This is somewhat helpful if you know what a factor is....
Do you prefer ketchup or soy sauce?
If someone asked you this question, your answer would likely depend upon what you were eating. You probably wouldn't dunk your spicy tuna roll in ketchup. And most people (pregnant moms-to-be excluded) don't seem to fancy eating soy sauce with hot French fries.
A Common Error When Using ANOVA or DOE to Assess Factors
Modeling techniques such as ANOVA or Design of Experiments (DOE) can determine if factors of interest impact a process. For example, you may want to evaluate how various time and temperature settings affect product quality. Or you may want to...
If you pay close attention to this series on using gummi bears to understand design of experiments, you noticed that in my last post I mentioned pressure as a variable for the first time. Pressure wasn’t on the fishbone diagram that I used when planning variables, even though it’s just as obvious as temperature and humidity.
I’ve been referring to the fishbone diagram quite a bit, but I didn’t spend much time creating it nor did I gather anyone else’s input. Therefore, there are probably lots of unconsidered variables that could make a difference in how far the gummi bears traveled. I can...
"There is a fifth dimension,beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of man's fears and the summit of his knowledge. This is the dimension of imagination. It is an area which we call...The Twilight Zone."
In my last entry, I told you that I don’t have a thermometer or a hygrometer in my office. That means that I have to treat the temperature and humidty of the location where I collect data as variables that I can neither...
After I promised an introduction to blocking in design of experiments last time, one of our Minitab statisticians came to see me. He pointed out that it would be unusual to use blocks in design of experiments as a way to check for the need for further experimentation. The reason is that, so far, I’ve been considering only variables that we can measure and manipulate.
The most typical reason for dealing with blocks is to handle variables that you cannot manipulate.
So I decided to look back at the fishbone diagram to find some new variables to consider, ones that I cannot manipulate. The most...
Of the 24 variables from the fishbone diagram that I made up earlier, I picked 5 last time to intentionally manipulate as factors in my study. That means that there are 19 other variables (plus ones that you thought of on your own) that we still have to consider to do design of experiments. What should we do about these variables? It depends.
We’ll talk about the easiest strategy in design of experiments this week, using the orientation of the bear on the popsicle stick as an example.
Leaving a Variable the Same
Leaving orientation the same while we change the other factors guarantees that...
In recent posts, we’ve reviewed a number of Measurement Systems Analysis (MSA) studies: Type I Gage Studies, Linearity and Bias Studies, and Gage R&R Studies. Before that, we took a look at a cause and effect diagram, also called a fishbone diagram. And we did all this because we were getting ready to practice a designed experiment.
Remember the fishbone diagram?
On the fishbone diagram, I came up with 24 variables that might affect how far the gummi bears go. I’d like to study as many of these factors as possible, but first need to decide which ones I can both manipulate and measure. Here...
When you think of design of experiments (DOE), what types
of applications come to mind? Do visions of camshafts,
widgets, capacitors, resistors, and other industrial
thingamabobs dance in your head?
If so, that's probably because DOE has such powerful and successful applications in manufacturing. Those experiments often involve changing levels of physical factors, such as temperature or pressure or speed or material, and then identifying the settings that produce the optimal effect.
So a designed experiment can raise the spectre of Dr. Victor Frankenstein in the laBORatory, madly pulling...
In my last post, I shared some helpful advice for
performing DOE from Minitab trainers Lou Johnson and Eduardo
Read on for four more tips for making sure your design of experiments project isn't dead on arrival:
1. Fractionate to save runs focusing on Resolution V designs.
In many cases, it's beneficial to choose a design with ½ or ¼ of the runs of a full factorial. Even though effects could be confounded or confused with each other, Resolution V designs minimize the impact of this confounding which allows you to estimate all main effects and two-way interactions. Conducting fewer runs...