## One factor at a time (OFAT) Versus Factorial Designs

Posted on May 25, 2011 Comments (2)

Guest post by Bradley Jones

Almost a hundred years ago R. A. Fisher‘s boss published an article espousing OFAT (one factor at a time). Fisher responded with an article of his own laying out his justification for factorial design. I admire the courage it took to contradict his boss in print!

Fisher’s argument was mainly about efficiency – that you could learn as much about many factors as you learned about one in the same number of trials. Saving money and effort is a powerful and positive motivator.

The most common argument I read against OFAT these days has to do with inability to detect interactions and the possibility of finding suboptimal factor settings at the end of the investigation. I admit to using these arguments myself in print.

I don’t think these arguments are as effective as Fisher’s original argument.

To play the devil’s advocate for a moment consider this thought experiment. You have to climb a hill that runs on a line going from southwest to northeast but you are only allowed to make steps that are due north or south or due east or west. Though you will have to make many zig zags you will eventually make it to the top. If you noted your altitude at each step, you would have enough data to fit a response surface.

Obviously this approach is very inefficient but it is not impossible. Don’t mistake my intent here. I am definitely not an advocate of OFAT. Rather I would like to find more convincing arguments to persuade experimenters to move to multi-factor design.

Related: The Purpose of Factorial Designed Experiments – Using Design of Experiments – articles by R.A. Fisher – articles on using factorial design of experiments – Does good experimental design require changing only one factor at a time (OFAT)? – Statistics for Experimenters

Categories: Data, Design of Experiments, Quality tools, Science, Six sigma, Statistics

Tags: Design of Experiments, guest post, Quality tools, Science, Six sigma, Statistics

2 Responses to “One factor at a time (OFAT) Versus Factorial Designs”

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May 25th, 2011 @ 12:24 pm

I think it depends on what is trying to be understood.

For example, if the purpose is trying to understand a new tool or process than a factorial design could be beneficial. Receiving a new molding tool can be set in a molding press and a factorial design setup to understand the settings to run the tool for the best results.

If a person is problem solving, then I believe one factor at a time is best. My problem solving mentor taught me that if you have to design a factorial with more than 3 factors then you haven’t done due diligence in truly understanding the problem.

I know that 2 or 3 factors is a factorial design but the number of trials are small enough to be easily managed. I consider a factorial design when the number of trials starts to explode or you have to do substitutions so you can’t see all the factors because some are buried in together.

May 26th, 2011 @ 2:31 pm

I push for both efficiency and for interaction detection. For non-stat people, the interaction argument is easier for them to understand. In fact, Brad, I use the mountain example (but mine rising ridge goes from SE to NW ) to show that the 1FAT (OFAT looks like zero FAT to me…) approach leads to what LOOKS like a optimum but is not –the worst kind of information gathering because it effectively precludes more experiments.

The efficiency is really from two angles. The abstract one is the s.d. of the effects for DOE vs 1FAT, especially for FF’s in the same number of runs. However, to me much more traction is gained when people begin to see that they really can study 5 or 10 factors AS A SYSTEM rather than 1 or 2 at a time. This encourages experimenters to collaborate (more factors get considered) instead of hiding in a corner and deciding what small number to study on their own.

In fact, it was just earlier today that a “client” (student at a corporation) presented the results of a 4 factor experiment. The “last” factor, machine, contributed almost all of the variation–the 3 “engineering factors” contributed far less. A big surprise to the company.