SPC Extension
Traditional SPC and Tensor SPC on the same data
This page shows why Tensor SPC is best framed as an additional monitoring layer. Traditional SPC remains useful for individual variables; Tensor SPC adds sensitivity to structured relationships across sensors and time.
The monitoring problem
The individual signals are not the whole story.
In this example, a simplified environmental-control process has three coordinated signals. Under normal behavior, increasing light is followed by a temperature increase, and the ventilation response rises afterward. The fault is not a dramatic single-sensor spike. The fault is a breakdown in the expected relationship.
Light Intensity
External driver increases during the cycle.
Temperature
The process warms in response to the light pattern.
Ventilation Response
The control response should increase as temperature rises.
Download the comparison dataset. The data include the observed signals, expected ventilation response, injected fault window, and structural residual.
Layer 1
Traditional SPC view
Traditional control charts are valuable because they ask whether individual variables are stable. In this example, that view gives useful context, but it does not clearly explain the structural failure. The charts show a possible area of concern, yet no single variable alone tells the full story.
Possible concern, limited explanation
The individual charts can draw attention to the time window, but the fault does not appear as a simple single-variable exceedance. The core problem is that ventilation failed to respond to the temperature pattern.
Traditional SPC remains useful
This is not a replacement argument. Traditional SPC is still the correct first layer for monitoring individual signals, stability, and obvious special-cause behavior.
Layer 2
Tensor SPC view
Tensor SPC preserves the observation × sensor × time structure. Instead of asking only whether each signal stayed inside its own limits, it asks whether the process behaved like the structured system learned from normal operation.
Clear structural anomaly
The tensor residual rises sharply because the observed ventilation response no longer matches the expected sensor-time relationship. The issue is localized to the period where the control response decouples from the temperature pattern.
The system stopped behaving coherently
The anomaly is not simply that one value was too high or too low. The anomaly is that the relationship among signals over time changed in a way that deserves attention.
Comparison
Complementary monitoring layers
| Method | What it monitors | What it shows in this example |
|---|---|---|
| Traditional SPC | Individual signal stability and point-wise behavior | Some concern, but no strong single-variable explanation |
| PCA / flattened multivariate monitoring | Overall multivariate variation after the structure is flattened | May detect a change, but sensor-time localization is less direct |
| Tensor SPC | Structured sensor-time relationships and reconstruction residuals | Clear structural anomaly where ventilation fails to follow temperature |