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DOE6 min read

DOE Results Analysis: Interpreting Main Effect Plots and Interaction Plots

The author recounts a critical production line incident where Cpk plummeted and DPMO surged, leading to a deep dive into problem-solving using Design of Experiments (DOE). This article details how to accurately interpret Main Effect Plots and Interaction Plots, moving beyond a superficial understanding to precisely identify root causes and enhance troubleshooting efficiency.

That Day, the CPK Report Came Out, and the Room Fell Silent for Three Seconds

Do you remember the last batch on the production line, where the Cpk suddenly dropped from 1.3 to 1.08? The atmosphere in the entire Fab was tense then, as DPMO skyrocketed from a few hundred to over six thousand, which would surely infuriate the customer. In the meeting room, everyone stared at that dreadful chart, and I thought, "Oh no, it's time for DOE again." Fortunately, this time I worked with a senior colleague and truly understood how to interpret the Main Effect Plot and Interaction Plot to quickly and accurately identify problems.

Where's the Problem?

Simply put, DOE is a systematic experimental method that helps us identify key variables affecting product yield or performance. After completing the experiment and obtaining the data, the most common outputs are the Main Effect Plot and Interaction Plot. Honestly, at first, I only looked at the Main Effect Plot, and if the line was sloped, I'd think, "Oh, there's a difference!" But this perspective is often incomplete, can be misleading, and fails to identify the true culprit.

  1. Main Effect Plot: This plot tells you what impact changing a single factor (e.g., temperature from 200°C to 220°C) will have on the result (e.g., Cpk value). The steeper the line, the greater the impact of this factor.
  2. Interaction Plot: This plot is what I later found to be the most critical. It tells you whether the combination of two or more factors, when changed "together," will produce an additional, non-linear effect. In other words, it's not simply that if A performs well, B also performs well; sometimes A performs well at one level of B, but poorly at another level of B.

How Was It Actually Done?

When our Cpk dropped that time, we found that two factors, A (process temperature) and B (etching time), had a significant impact.

  1. First, look at the Main Effect Plot:

* Factor A: Higher temperature resulted in better Cpk, while lower temperature resulted in worse Cpk. The line looked very steep, as if high temperature was the only solution.

* Factor B: Longer etching time resulted in better Cpk, while shorter etching time resulted in worse Cpk. The line was also steep, seemingly indicating that longer was better.

* At this point, you might instinctively conclude: "Okay, increasing the temperature and extending the etching time is the way to go!" But don't rush, don't jump to conclusions yet.

  1. Next, look at the Interaction Plot:

* Assume the Interaction Plot shows: when Factor A is at a low temperature, Factor B (regardless of its duration) results in very poor Cpk; but when Factor A is at a high temperature, Factor B only pushes Cpk above 1.5 when the "etching time is long." If high temperature is paired with "short etching time," Cpk is only 1.1.

* The key takeaway is: If you only look at the Main Effect Plot, you might assume that both temperature and etching time should be as high as possible. But in reality, high temperature is only effective when paired with "long etching time." Simply increasing the temperature alone might not be effective, or even lead to no improvement if paired with the wrong etching time. This is the power of interaction! The more the two lines cross or are non-parallel, the more significant the interaction.

The Most Common Pitfall

My most common mistake in the past was to only look at the Main Effect Plot and rush to adjust parameters. One time, to improve the stability of a certain parameter, I looked at the Main Effect Plot and felt that Factor C had the biggest impact, so I asked the production line to adjust C in a certain direction. As a result, parameter stability improved slightly, but another unrelated yield suddenly plummeted! Later, my senior colleague found out that while Factor C had a significant impact when viewed alone, it had a strong interaction with another Factor D. When C was at a low level, combining it with a high level of D led to a yield collapse. That time, I truly learned a lesson: one cannot just look at individual effects; one must view the overall performance "systematically."

One Thing You Can Do Today

Next time you look at a DOE report, first look at the Interaction Plot, then go back and interpret the Main Effect Plot.

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