Taguchi or DOE?
This article originally appeared in the November 2001 issue of IIE Solutions. Yes, that was a long time ago, but the information is still valid and, I hope, useful.
by John Cesarone, Ph.D., P.E.

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Most engineers have heard of Design of Experiments (DOE) and of Taguchi Methods, but how many of us can really say we understand the difference between them?  Or that we can correctly decide when to use which technique?  In this article, we will examine the relative strengths and weaknesses of each approach, and develop some guidelines for selecting the best approach for solving our specific problems.

First of all, what are these techniques?  In a general sense, they can both be thought of as techniques for optimizing some process which has controllable inputs and measurable outputs.  In a manufacturing situation, the inputs might be settings in some production process, such as temperature of a heat treatment furnace or speeds and feeds on a milling machine.  The outputs are generally quality or productivity oriented, such as process yield or units produced per hour by our production line.  We might be trying to maximize some output (as in throughput or process yield) or minimize some other output (as in failure rate or scrap).

In a design situation, the inputs might be design decisions, and the outputs would then be performance oriented metrics.  For example, inputs might be the number of supports in a structural design, the type of material to be used, or a qualitative decision such as a drum clutch vs. a face clutch.  In these cases, outputs to be measured might be load carried, torque transferred, etc.  In either type of analysis, production scenario or design situation, we are making decisions on how to do something that will affect what we get as an output.

What do DOE and Taguchi have in common?  Besides the inputs and outputs described above, they both deal with multiple inputs.  That is, we might have two, three, five, or a dozen or more input decisions to make, all affecting some measurable output.  It would be nice if we could experiment with these inputs one at a time, optimizing our output for each input in turn, until we've selected ideal values for all input parameters.  Unfortunately, this doesn't usually work, because the inputs generally interact with each other to some extent.  For example, imagine that you are running a carburization process.  You cannot set furnace temperature to optimize yield while ignoring carbon potential, and then experiment with carbon potentials after fixing the temperature; they interact with each other and affect the levels of output together.  What DOE and Taguchi primarily have in common, then, is that they deal with multiple inputs and how they interact with each other.

How do DOE and Taguchi differ?  We will get into this soon, but the primary difference lies in how they handle the interactions between inputs.  When you remember that DOE was invented by scientists for scientists, and Taguchi methods were invented by engineers for engineers, the differences begin to make sense.  Let's look at them each in turn.


The main thing to know about DOE is that it was developed primarily within the scary world of statistics.  Okay, come back out from under your desk; we won't dwell on that part.  Just remember that the theory behind the technique comes from the classical world of pure math.  Using it, however, requires only that small amount of math that you probably remember from your college days.

DOE theory starts with the assumption that all inputs might be interacting with all other inputs.  This is a powerful statement.  The technique makes no assumptions about some inputs being independent, and therefore can handle any interactions that might be lurking somewhere in your process.  When you have no idea what interactions you need to be worrying about, DOE might be the choice for you.  Of course this power comes at a price, and that price is lots of experimental runs and lots of calculations.

One of the first applications of DOE was in ancient agricultural sciences.  Early farming experimenters were starting to understand things like irrigation, fertilization, crop rotation, etc.  These are multiple inputs.  You can also see how they interact with each other:  What is the best irrigation method?  Well, that might depend on your fertilization approach.  What is the best fertilization process?  Well, that could easily depend on your irrigation techniques, and what crop you grew in that field last year.  Since any and all inputs could interact with all other inputs, a technique was needed which would model all of these inputs, and how they all relate to each other.  Thus DOE was born.

Another peculiarity of these early agricultural experiments was that they wanted to get it right the first time.  One experimental run took an entire growing season; a whole year!  You absolutely did not want to collect a year's worth of data, stroke your beard a few times, and then do Phase 2 the next year before you had an answer; your village could starve to death before you were finished.  This leads to another characteristic of the DOE approach: not only are all interactions studied, but they are all studied at the same time in one big round of tests.

These considerations can lead us to an assessment of the strengths and weaknesses of the DOE approach.  The strength is that we can investigate all possible interactions between inputs at the same time; we don't need any innate knowledge of how the process works.  The weakness is that we have no way to make use of any a priori process knowledge that we might happen to have; there is no way to make the experiment more efficient by thinking about how the inputs really do interact.  If you think about it, the strength and the weakness are really the same thing!

Other areas, besides agriculture, where DOE makes perfect sense are any complex sciences with many highly coupled inputs where practitioners have little innate understanding of the fundamental processes involved.  Biology, virology, and meteorology come to mind.  In all of these fields, DOE is a powerful and logical method to optimize process and predict outcomes.

To be fair, not all DOE-based investigations look at all possible interactions.  Those that do are called "full factorial" DOEs.  "Fractional factorial" DOEs can eliminate some interactions, and therefore slim down the amount of work that needs to be done.  But they are still based on the idea of full modeling, and then whittled down to improve efficiency.  The savings are generally fairly meager, such as a factor of two or four, and there is still no way to inject understanding of the fundamental process into the mix.

The details of performing a DOE can be found in many textbooks, and we won't duplicate them here.  But in a nutshell, in a full factorial, all-interaction DOE, tests are performed for all possible combinations of all inputs.  If you have three inputs, each with two possible settings (known as levels), you would need to perform eight tests (that is, two raised to the third power).  You can see how the number of tests can get really large really fast.  Then, the outputs are averaged for all tests where a particular input was set to a particular level, and compared to the average output for all tests where that particular input was set to its other levels.  This comparison gives an insight into the overall affect of that input on the output.  Similar calculations can show the affects of the interactions between the inputs.  After a bit of number crunching, many useful chunks of knowledge can be derived on how the inputs interact and how they affect the process output.