Tensor SPC Tool
Tensor Residual Localization
Detection tells us something changed. Localization shows where and how the structured process behavior changed across sensors and time.
Purpose
Move from anomaly detection to structural diagnosis.
A Tensor SPC alarm should not stop at a single Q statistic. Residual localization decomposes the reconstruction error so the user can see which sensor-time region drove the alarm.
Core calculation
The residual tensor compares the observed tensor with the model reconstruction.
Residual energy is then visualized by sensor and time to locate the structural mismatch.
Manufacturing example
Same process, clearer diagnosis.
This demonstration uses a structured manufacturing process with several related features. The fault is intentionally subtle: individual signals remain plausible, but the relationship between vibration and surface finish changes during the middle of the run.
Residual energy heatmap
sensor × time localizationThe heatmap is not raw process data. It shows where the tensor reconstruction error is concentrated.
Top contributing sensors
share of residual energyTime contribution profile
when the anomaly emergedObserved vs reconstructed response
top contributing signalThe tensor model reconstructs the expected structured response from learned sensor-time relationships. The observed response diverges during the same region highlighted by the residual map.
Interpretation
The tensor model detected a localized structural deviation. The largest mismatch occurred in the vibration and surface-finish response during the middle portion of the observation. Individual process values may still appear plausible, but the coordinated behavior no longer matches the learned sensor-time structure.
Practical meaning: Tensor Residual Localization extends the alarm from “something changed” to “this sensor-time region drove the change.”
How to use the result
Localization supports investigation, not automatic conclusion.
The localization output should guide where to investigate. It does not replace engineering review or traditional SPC; it adds a structured diagnostic layer.
| Output | Question answered | Use |
|---|---|---|
| Tensor Q | Is structured behavior abnormal? | Screen for structural process change. |
| Residual heatmap | Where is the mismatch concentrated? | Identify the sensor-time region that drove the alarm. |
| Sensor contributions | Which signals contributed most? | Prioritize investigation. |
| Observed vs reconstructed | How did actual behavior differ from expected behavior? | Explain the anomaly in process terms. |