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How Tensor SPC Works
Move from concept to the actual Tensor SPC monitoring workflow.
Continue →Fundamentals
What Tensor SPC Does Differently
Tensor SPC extends process monitoring by preserving multiway structure across observations, sensors, and time instead of forcing the data into a single flattened vector.
Tensor SPC keeps the data shape meaningful
A typical structured monitoring object can be represented as:
Run × Sensor × Time
This structure lets the monitoring method evaluate not only whether values changed, but whether coordinated behavior across sensors and time still matches the learned baseline structure.
Low-rank reconstruction creates an expected process pattern
Tensor SPC learns a structured representation from normal baseline behavior. A new observation is reconstructed using that learned structure.
𝓔 = 𝓧 − 𝓧̂
The residual tensor captures what the structured model could not explain. Large residual energy indicates behavior outside the learned normal structure.
Tensor Q measures structured reconstruction mismatch
Tensor Q summarizes the residual energy across the structured observation.
Q = ∑s ∑t (Xs,t − X̂s,t)²
A high Tensor Q result indicates that the observation does not match the expected sensor-time structure learned from baseline behavior.
Detection becomes more interpretable
Tensor SPC can support a progression of questions:
| Question | Tensor SPC tool |
|---|---|
| Did structured behavior become abnormal? | Tensor Q / Tensor T² monitoring |
| Where did the mismatch occur? | Tensor Residual Localization |
| What drove the Tensor Q result? | Tensor Contribution Decomposition |
Next step
The next step is to review the Tensor SPC workflow and then explore residual localization and contribution decomposition.
Continue: How Tensor SPC works →Related concepts