1. Why Traditional SPC Struggles
Understand why flattening structured sensor-time data can weaken interpretability and dilute structured anomalies.
Start here →Learning Path
Tensor SPC Fundamentals
Learn the concepts, mathematics, visualizations, and engineering interpretation behind Tensor-Structured Statistical Process Control.
This section organizes the Tensor SPC material into a clear path: why structure matters, how Tensor SPC preserves that structure, how Tensor Q detects structured mismatch, and how residual localization and contribution decomposition support investigation.
Recommended Pathways
Choose a Tensor SPC learning pathway
Different visitors approach Tensor SPC with different goals. These suggested pathways organize the material into a more coherent progression.
Conceptual Foundations Pathway
Recommended for first-time visitors and engineering overview reading.
- Why Traditional SPC Struggles
- What Tensor SPC Does Differently
- How Tensor SPC Works
- SPC vs Tensor SPC
- Interactive Demonstrations
Mathematical / Technical Pathway
Recommended for researchers and technically-oriented users.
- How Tensor SPC Works
- Tensor Q Concepts
- Residual Localization
- Contribution Decomposition
- Research Monograph
Engineering Applications Pathway
Recommended for manufacturing and industrial monitoring applications.
- Structured Process Monitoring
- Residual Localization
- Contribution Decomposition
- Interactive Examples
Interactive Exploration Pathway
Recommended for visual exploration and demonstrations.
- Interactive Demonstrations
- Residual Localization
- Contribution Decomposition
- SPC vs Tensor SPC
Recommended learning path
2. What Tensor SPC Does Differently
See how Tensor SPC preserves multiway process structure across runs, sensors, and time.
Learn the difference →3. How Tensor SPC Works
Review the monitoring workflow, including tensor reconstruction, Tensor Q, and Tensor T².
Open workflow →4. Tensor Residual Localization
Identify where reconstruction error is concentrated across sensor-time structure.
View localization →5. Tensor Contribution Decomposition
Determine which sensors, time regions, and sensor-time cells drive the Tensor Q result.
View decomposition →6. Traditional SPC vs Tensor SPC
Compare conventional SPC monitoring with Tensor SPC as a complementary extension.
Compare methods →Core idea
Traditional SPC is valuable for monitoring individual variables and process stability. Tensor SPC extends that logic to structured data by preserving relationships across sensors, time, and process observations.
Detection tells us something changed. Localization and contribution analysis help explain where it changed and what drove the result.
Next step
Why Traditional SPC Struggles with Structured Data
Start with the core problem Tensor SPC is designed to address.
Continue →Related concepts