Normal Distribution
Last updated 2026.02.13Definition
Normal Distribution or Gaussian Distribution is a type of continuous probability distribution characterized by a symmetric bell-shaped curve centered around the mean (μ). The variance (σ²) and standard deviation (σ) represent the spread of data, and it is the most commonly observed statistical distribution in natural phenomena and manufacturing processes.
Applications in Manufacturing
Quality Control and Process Management
Normal distribution plays a crucial role in manufacturing quality control. Six Sigma quality management is based on normal distribution and serves as the foundation for calculating process capability indices (Cp, Cpk).
- Dimension Control: Assuming measurements like product length, weight, and thickness follow normal distribution for control chart operations
- Defect Rate Prediction: Calculating probability of exceeding specification limits (USL, LSL) using normal distribution
- Process Anomaly Detection: Identifying abnormal signals when process data deviates from normal distribution
Application in Manufacturing AI
In Anomaly Detection algorithms, normal distribution is used to establish baselines. Data points deviating more than 3σ (three standard deviations) from the mean are flagged as anomalies. In predictive maintenance, normal distribution models the acceptable ranges for equipment vibration, temperature, and other parameters.
Key Points
- 68-95-99.7 Rule: 68% of data falls within ±1σ, 95% within ±2σ, and 99.7% within ±3σ of the mean
- Practical Example: For semiconductor wafer thickness with mean 100μm and standard deviation 2μm following normal distribution, 95% falls within 96~104μm range
- Caution: Real manufacturing data may not perfectly follow normal distribution, requiring normality tests