Design of Experiments is a topic that is difficult for many Six Sigma certificate applicants to master. Not to worry, we’ve got you covered with a comprehensive study guide.

The objective of Design of Experiments (DOE) is to Establish optimal process performance by finding the right settings for key process input variables. Design of Experiments is a way to intelligently form frameworks to decide which course of action you might take. This is helpful when you are trying to sort out what factors impact a process.

Basic Flow for Design of Experiments

The overall process of a Designed experiment is as follows:

  • Define objective(s)
  • Gather knowledge about the process
  • Develop a list and select your variables
  • Assign levels to variables
  • Conduct experiments
  • Data analysis and conclusions

Learning Design of Experiments

Factors in an Experiment

In most experiments, you’ll have a number of factors to deal with. These are elements that affect the outcomes of your experiment. They fall into a few basic categories:

  • Experimental factors are those that you can specify and set yourself. For example, the maximum temperature to which a solution is heated.
  • Classification factors can’t be specified or set, but they can be recognised and your samples selected accordingly. For example, a person’s age or gender.
  • Treatment factors are those which are of interest to you in your experiment, and that you’ll want to manipulate in order to test your hypothesis.
  • Nuisance factors aren’t of interest to you for the experiment, but might affect your results regardless.

There are two basic types of treatment factors that you’ll use:

  • Quantitative factors can be set to any specific level required – for example, pH levels.
  • Qualitative factors contain a number of categories – for example, different plant species or a person’s gender.

Example

A popular example in explaining factors is the simple-sounding task of baking cookies. Most people would simply follow a recipe – or, let’s face it, buy the cookie dough pre-made and bake whatever we don’t eat raw. But how did the recipe come to be in the first place? Someone had to experiment with ingredients and baking method to get just the right combination.

  • Flour: The ratios of flour to liquid and flour to fat are crucial to the texture of a cookie. Too much flour, and you end up with a dry, crumbly cookie. Too little, and you end up with an overly flat, crispy cookie.
  • Sugar: The type of sugar used can change the way a cookie reacts to the baking process. Using granulated (white) sugar usually creates a crisper, flatter cookie. Using brown sugar creates a moister, chewier cookie.
  • Fat: Rubbing the fat into the flour creates a softer cookie. Using butter creates a flatter cookie than using margarine.
  • Eggs: Eggs create a less crumbly, chewier cookie.
  • Baking powder: Using baking powder causes a cookie to rise or spread, creating a ‘cakey’ texture or a more crisp cookie.
  • Temperature: Low temperature baking gives a cookie more time to spread out while cooking, meaning it’s more likely to be flatter and crisper.

Think of each of these ingredients and the baking temperature as factors in an experiment. You can’t test each factor on its own – you need to have all ingredients to produce the cookies. But you can modify the amount and type of ingredient, and the temperature at which they’re baked, to find the combination that yields your perfect cookie.

Other Terminology

Review the common terminology used in Design of Experiments Factorial Design.

Planning and Organizing Designed Experiments

Determine the Factors

Next, we must understand the type of factors that can affect an outcome so we can create the appropriate design to determine how to structure our experiment.

It’s also helpful to see an example of the kinds of Factors that are in an Experiment. These are our variables to the possible and desired outcomes.

Determine the Appropriate Design for the Experiment (Full Factorial or Partial)

Here we want to define the interactions that will be in the experiment and understand how to analyze those interactions.

One Factor at a Time (OFAT)

The (OFAT) approach is to doggedly explore each single factor independently. This is a brute force technique that you can get by with when you have just a few variables or interactions. The downside is that with large variable (factor) sets you will spend a lot of resources doing this and you may miss the complicated interactions other more sophisticated designed experiments will give you.

One Factor at a time vs Full Factorial.

OFAT- One Factor at a Time
OFAT- One Factor at a Time

Factorial Design

I’ve included a quick overview of different types of factorial design. For a full description, see this overview of Full Factorial Design and see an overview of Partial or Fractional Factorial Design here.

Full Factorial Design

Full Factorial Design is a thorough an exhaustive way of determining how each factor or combination of factors affects the outcome of an experiment. At least one trial for all possible combinations of factors and levels.

2^5-2 means that there are 5 factors at 2 levels and 2 generators. The generator determines what effects are confounded or combined with one another.

We would call this example an 1/L^g fractional factorial.

Thus, 2^5-2 is a 2 level, 5-factor, 1/4th fractional design.

Partial Factorial Design

Finally there is Partial (or Fractional) Factorial Design. Often doing a full factorial design analysis is impossible or impractical. Here’s how you can optimize your resources and still achieve a rigorously-supported decision.

Other Designed Experiment Types

You can find notes on other design of experiment types here.

Items to Avoid When Conducting a Designed Experiment:

  1. Unwarranted assumptions of the process.
  2. Undesirable combinations of the factors.
  3. Violation of known laws of physics.
  4. Too large or small design sizes.
  5. Inappropriate confounding.
  6. Imprecise measurement.
  7. Unacceptable prediction error (Type 1 & type 2 errors).
  8. Undesirable run order.

Additional notes on designing experiments:

  • http://www.statsoft.com/Textbook/Experimental-Design

Design of Experiments Video

Introduction to Design of Experiments Video

Full Lecture here:

Six Sigma Black Belt Certification Design of Experiments Questions:


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Questions, comments, issues, concerns? Please leave a note in the comments below!


Question: In comparison to a full-factorial design of experiment (DOE), a traditional, one-at-a-time approach will: (Taken from ASQ sample Black Belt exam.)

(A) miss interactions
(B) gain efficiencies
(C) save time
(D) cost less

Comments (5)

Hi Ahmed,

That’s a good question for the IASSC. I would assume not, but organizations have been known to put items not necessarily on their BOK on their exams.

10.15.2020 Very true… in my Green Belt IASSC exam, there were questions I know now were from the Black Belt level.

The wording of the test questions also is a bit challenging… or unclear …or confusing. Isn’t the test difficult enough already?

Dude… I’m hooked now that you applied Design of Experiment to creating a cookie recipe. As a cookie connoisseur myself, I can’t wait to apply DoE in the kitchen!

But really! DoE has been a hard topic for me to swallow until now.

I’m glad!

I do end up using many cooking analogies in my descriptions (Hypothesis Testing overview being another prime example).

While we’re all in different industries and will see different applications of the material, we all have to eat and many of us cook. It’s a helpful shared experience to draw from.

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