Semiconductor manufacturing today includes hundreds of process with precise measurements collected throughout production

Variations with these measurements, can result in a pass or fail during quality control

Research Question

Can analysis of manufacturing measurements identify what is associated with semiconductor failures?

The dataset being used is from SECOM who collects measurements during the manufacturing process

## Number of observations: 1567

## Number of variables: 593

## Pass: 1463

## Fail: 104

This dataset has hundreds of measurements from process that can be compared with the final result at the end of the line.

The goal with this data is to determine which measurements show the highest statistical probability of failure

Before looking at all the individual sensors, we should look at the overall result

• 1,463 observations passed
• 104 observations failed
• Only 6.6% resulted in failure

This results in the dataset being highly unbalance with failures being more rare than successful results

The SECOM dataset contains over five hundred measurements taken during the manufacturing process.

The goal is to find whether some sensors data differ between a product that Passes and one that Fails.

For each sensor, we can check:

• The average measurement on passing sets
• The average measurement on failing sets
• The variation between each group

If a sensor has significant changes between measurements in the two groups, it may be associated with a failure in the process.

Approach

We will compare the average Pass and Fail measurements and use a 2% threshold to identify distinct differences.

We will compare the average measurement of each sensor for Pass and Fail results.

Null Criterion

\(H_0: \text{Percentage Difference} \leq 2\%\)

The Pass and Fail averages are within 2% of each other.

The sensor will be classified as a Non-Distinct Difference.

Alternative Criterion

\(H_A: \text{Percentage Difference} > 2\%\)

The Pass and Fail averages differ by more than 2%.

The sensor will be classified as a Distinct Difference.

This allows us to identify sensors whose measurements show larger differences between Pass and Fail outcomes.

With 590 sensors to go through, and 1567 entries it would be inefficient to manually go through and compare. Instead we will use R to compare all the Pass and Fail.

sensor_col <- grep("^sensor_", names(secom), value = TRUE)

This function allows us to grab only the columns that are sensors, meaning time stamp, label, and result do not show up.

sensor_mean <- secom %>%
  group_by(result) %>%
  summarise(
    across(
      all_of(sensor_col),
      ~ mean(.x, na.rm = TRUE)
    )
  )

This following section is then setup to help determine the average of pass and fail in each dataset, as to help determine the hypothesis

Now that we have the Pass and Fail averages, we can calculate how much they differ.

\[ \text{Percentage Difference} = \frac{|\text{Pass Mean} - \text{Fail Mean}|} {|\text{Fail Mean}|} \times 100 \]

A difference of 2% or less is classified as Non-Distinct.

A difference of greater than 2% is classified as Distinct.

55.1% of the sensors show a Distinct Difference between the Pass and Fail averages.

24.9% show a Non-Distinct Difference, meaning their averages are within the 2% threshold.

The remaining 20.0% do not contain enough usable data to be classified.

In the graph, gold bars represent sensors with a higher average of passing observations while maroon bars representing sensors with high averages in failing. The height of the bar represents the percent difference between the pass and fail average. Therfore, the taller bars will indicate sensors with freater differences between outcomes, making more usefull to determine results.

The goal of this analysis was to determine whether certain sensor measurements are associated with Pass or Fail results in semiconductor manufacturing.

• Using a 2% difference threshold, sensors were classified based on how much their average measurements differed between Pass and Fail data.
• 55.1% of the sensors showed a distinct difference.
• 24.9% showed little difference between the two outcomes.
• The remaining 20.0% did not contain enough usable data to make a comparison.
• Certain distinct sensors showed substantially larger differences than others, suggesting that some process measurements may provide more useful information for distinguishing between Pass and Fail outcomes.

The results suggest that not all measurements are equally associated with the final manufacturing result. This also relates to my own work experience. When a process is not operating correctly, its measurements can become skewed or change noticeably. Other processes may have very little effect on the measurements, causing their sensor readings to remain relatively consistent.

Because of this, sensors that show larger differences between Pass and Fail results may be especially useful for identifying when something in the manufacturing process has gone wrong. While these measurements do not necessarily cause a failure, they can provide valuable information about which parts of the process may require further investigation.

Dataset

SECOM — Semiconductor Manufacturing Process Dataset
UCI Machine Learning Repository

The dataset contains process measurements and Pass/Fail classification data