U Chart

u Chart is a control chart for monitoring defects per unit when inspection unit size varies between samples, normalizing counts to a standard basis.

## What Is a u Chart?

• Metric: Defects per unit (u = c/n where c=defects, n=units inspected)
• Flexibility: Handles variable sample sizes
• Distribution: Based on Poisson (defect counts)
• Control Limits: Vary with sample size for each point

## Why u Charts Matter

Production often involves variable lot sizes. The u chart normalizes defect rates, enabling fair comparison across different sample sizes.

u Chart Example (Defects per wafer):
Sample 1: 15 defects in 5 wafers → u₁ = 3.0
Sample 2: 24 defects in 10 wafers → u₂ = 2.4
Sample 3: 8 defects in 4 wafers → u₃ = 2.0

Overall: ū = (15+24+8)/(5+10+4) = 47/19 = 2.47

Control limits for sample i with nᵢ units:
UCLᵢ = ū + 3√(ū/nᵢ)
LCLᵢ = ū - 3√(ū/nᵢ)

u vs. c Chart Selection:
| Scenario | Chart |
|----------|-------|
| Fixed inspection quantity | c chart |
| Variable inspection quantity | u chart |
| Count defective items | np or p chart |