# The data was fine. The model was wrong.

Machine class (retold): Process engineering

Fitting parameters that should have been constant refused to be, until the model itself went under investigation.

- Suspected at the start: The data
- Actually wrong: The model
- After the fix: One parameter set

## The issue

A process model was being fitted to experimental data across a family of test structures. In theory the fitted parameters are properties of the process, so they should come out the same for every structure. They did not. Every structure wanted its own numbers, and the data itself looked clean.

## The quiet assumption

When a fit misbehaves, the instinct is to doubt the data, then the experiment, then the operator. The one thing nobody doubts is the model, because the model has been in use for years. That assumption was the entire problem, and it was invisible precisely because everyone shared it.

## What Cala surfaced

Given the setup and the misbehaving fits, Cala reasoned about what could make process constants appear structure-dependent, and asked for the one thing nobody had put on the table: the model implementation itself, to verify against the underlying physics.

The implementation used a quadratic form where the physics calls for an exponential. Close enough to pass for years inside the usual operating range, and wrong enough to bend every fit the moment the structures pushed outside it.

References (retold terms): Model specification note · p. 4

## The check

Refit every structure with the corrected form, changing nothing else.

## The outcome

The parameters collapsed onto a single set across all structures, as the physics said they should. The instrument was fine, the data was fine, the people were fine. The model was the issue, and it took a reasoner with no loyalty to it to say so.

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A real investigation from early testing on production equipment, retold on a different class of machine so the site, the tool and the people cannot be identified. The reasoning is the part that is true.

Canonical page: https://calalayer.com/case-studies/the-model-was-wrong

Cala (calalayer.com): AI root-cause investigator for hardware engineers.