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Statistical Analysis6 min read

Box Plot Interpretation: Identifying Interquartile Range and Outliers

This article offers practical insights into process control, demonstrating the limitations of relying solely on CPK. It illustrates how Box Plots were instrumental in quickly identifying the root cause of a significant CPK drop on a production line, providing a method to effectively troubleshoot and resolve similar issues.

That Day, the CPK Report Came Out, Everyone Was Silent for Three Seconds, Then I Saw How the Box Plot Saved Us

It was a Friday afternoon, just before quitting time, when a call suddenly came from the production line saying that the CPK of machine L3 had dropped from 1.35 to 1.08, almost breaking 1.0. I thought, "Oh no, my weekend is definitely ruined." The boss's face darkened, and he immediately called everyone involved into the meeting room. Everyone stared at the alarming red CPK report, a profound silence filling the room. Some began checking process parameters, others reviewed machine logs. Frankly, a small drop in CPK might be acceptable, but dropping to almost 1.0 means that the yield could start plummeting.

Where's the Problem? Just Looking at the Mean and Standard Deviation Isn't Enough!

"CPK dropped to 1.08, so obviously the process variation has increased!" a rookie colleague whispered. Yes, that's true, but the problem is that increased variation can have thousands of reasons. It could be a sudden machine malfunction, an abnormal batch of raw material, or even operator trembling. Just looking at a single number like CPK, you only know "there's a problem," but not "where the problem is." This is where the Box Plot becomes incredibly useful. Simply put, it lays out your data for you to see, not just the mean, but also the distribution, especially those "oddball" data points.

So the key takeaway is: A Box Plot allows you to see the data distribution at a glance, including the median, quartiles, and most critically, "outliers."

How Do You Actually Do It? Understanding These Three Lines and A Few Points Is Enough!

When you get a Box Plot, you need to know how to read it. It usually has five "numbers," known as the "five-number summary."

  1. Median: The line in the middle of the box. It divides the data into two halves: half are larger than it, and half are smaller. This is more robust to abnormal values than the mean.
  2. First Quartile (Q1): The bottom of the box. It represents that 25% of the data is smaller than it.
  3. Third Quartile (Q3): The top of the box. It represents that 75% of the data is smaller than it.
  4. Interquartile Range (IQR): The distance between Q3 and Q1. It represents the "width" of the middle 50% of the data. The more concentrated the data, the smaller the IQR. For example, a critical measurement value from our L3 machine that day typically had an IQR of about 0.05 mm, but that day it directly soared to 0.12 mm—a clear red flag!
  5. Whiskers: The "whiskers" extending from the box. These whiskers typically extend to Q1-1.5\*IQR and Q3+1.5\*IQR.

So the key takeaway is: These lines and points can tell you the concentration of the data and whether there are any particularly "prominent" values.

The Most Common Pitfall: Panicking at the Sight of Dots?

That day in the meeting room, I immediately pulled up the Box Plot for machine L3. There were a bunch of dots outside the whiskers, scattered both above and below. These are "Outliers."

"Wow, so many abnormal points!" exclaimed Xiao Zhang, the newcomer.

"Don't panic just yet," I said. "Outliers aren't necessarily a bad thing, but you absolutely must investigate them."

Let me give you an example: Suppose we are measuring the thickness of a wafer.

Under normal circumstances, the thickness distribution should be quite concentrated. However, if the Box Plot shows a cluster of outliers at the upper end, this might indicate that a few wafers are exceptionally thick. The Box Plot for our L3 machine that day showed a cluster of outliers below the lower whisker. This indicated that the measured values for several batches of products suddenly became exceptionally low, increasing the overall variation and causing the CPK to drop. Upon investigation, it turned out that the incoming material parameters for a certain batch had drifted, preventing the process from achieving stability. If you only look at CPK, you'll just see "large variation," but the Box Plot directly tells you: "There are some data points that are very different from the others!"

So the key takeaway is: Outliers are the soul of the Box Plot; they directly point to potential root causes that you might otherwise overlook.

One Thing You Can Do Today

Take your process data and start by plotting a Box Plot to check for outliers.

Want to try it yourself?

Every tool mentioned in this article is available on InsightFab — just upload a CSV to analyze.

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