📚 1.3 – Mechanistic and Empirical Models
Engineering Question:
Can we predict the wire bond pull strength (how strong the wire is attached) based on its length and the die height of the chip?
This is a real-world semiconductor manufacturing problem. We want to model this because we do not know the exact physics behind pull strength — there is no known mechanical formula. But we suspect a pattern can be found from data. This leads us to use an empirical model, which is a statistical regression model based on observed data.
Empirical Model (Regression Equation):
Pull Strength = 2.26 + 2.74 × (Wire Length) + 0.0125 × (Die Height)
This model means:
- Every 1 unit increase in wire length increases pull strength by 2.74 units (strong effect).
- Every 1 unit increase in die height increases pull strength slightly by 0.0125 units.
- There is a base pull strength of 2.26 when both inputs are zero (the intercept).
🔍 Predicted vs. Actual Pull Strength
📋 Sample Data
| # | Wire Length | Die Height | Actual Pull | Predicted Pull |
|---|
Why it matters:
Engineers often face problems where no clear formula exists. Instead of giving up, we build data-driven models (like this one). You’ll see this in material testing, battery life estimation, or machine fault prediction. This is why statistics and modeling are essential skills in engineering!