Factorial experiment

Imagine you are trying to find the best way to make a product work well. Most people test only one change at a time. This is called an OFAT experiment. However, there is a more powerful way to learn. It is called a factorial experiment.

This method looks at many different factors all at once. A factor is something you can change to see a result. A level is a specific setting for that factor. By testing every possible mix of these levels, you get a full picture. This helps you see how things truly work in the real world.

How does this work step by step? You start by picking your factors and their levels. If you have two factors with two levels each, you have four unique combinations. These different mixes are often called runs, points, or cells.

A full factorial design tests every single possible combination. If the job becomes too huge, researchers use a fractional factorial design. This method strategically leaves out some combinations to save time. It makes a very large experiment much more manageable to finish.

People have used these ideas for a long time. In the 19th century, John Bennet Lawes and Joseph Henry Gilbert used these designs. They worked at the Rothamsted Experimental Station. Later, Ronald Fisher argued that these designs were very efficient. He said they were better than testing one factor at a time. In 1926, Fisher showed they could find many effects at once. He even used the term "factorial" in his 1935 book. Frank Yates also helped by improving how we analyze these designs.

These experiments are very useful for engineers. For example, engineers at a company called SKF wanted to study bearing life.

They used a 2x2x2 factorial design to test three factors. They looked at heat treatment, outer ring osculation, and cage design. Each factor had two levels, creating eight total combinations. They discovered that two factors working together increased bearing life fivefold! This was an extraordinary finding that they might have missed otherwise. They found the best settings much faster than before.

Factorial experiments connect to how we see the world. We often see that things change based on their surroundings. For instance, a motor's power depends on its speed and its type. In a 2x2 experiment, you might test two motors at two different speeds.

This creates four different test units to measure. You can think of these combinations as the corners of a cube. This helps us understand how different parts of a system interact. It turns a simple list of facts into a map of connections.