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 |