np chart
**np Chart** is a control chart for monitoring the count of defective units in constant-size samples, where each unit is classified as either defective or acceptable.
## What Is an np Chart?
- **Metric**: Number of defective units (np) per sample
- **Requirement**: Constant sample size (n) across all samples
- **Distribution**: Binomial distribution assumption
- **Related**: p-chart tracks proportion defective (variable sample size)
## Why np Charts Matter
For attribute data with pass/fail inspection of fixed sample sizes, np charts provide simpler arithmetic than proportion charts while monitoring process stability.
```
np Chart Example:
Sample size: n = 50 units per lot
Average defective rate: p̄ = 0.04
Center Line: np̄ = 50 × 0.04 = 2.0 defectives
UCL = np̄ + 3√(np̄(1-p̄)) = 2 + 3√(2×0.96) = 6.2
LCL = np̄ - 3√(np̄(1-p̄)) = 2 - 4.2 = 0 (use 0, not negative)
```
**When to Use np vs. p Chart**:
| Condition | Chart |
|-----------|-------|
| Fixed sample size | np chart |
| Variable sample size | p chart |
| Count defects per unit | c or u chart |