---
alias: user-guide-number-defective
description: "This documentation details a binomial chart for monitoring defective numbers in samples"
---

# Number Defective (np)

The following table lists the properties of the Number Defective (np) chart.

| Property                                          | Description                                                       |
|---------------------------------------------------|--------------------------------------------------------------------|
| **Chart**                                         | Number Defective *(np)*                                                                                          |
| **Process observation types**                     | Attributes                                                                                                              |
| **Process observations relationships**            | Independent                                                                                                             |
| **Sample Size**                                   | Constant, usually \>=50                                                                                                 |
| **Distribution type**                             | Binomial                                                                                                                |
| **Size of shift to detect**                       | Large (≥ 1.5σ)                                                                                                          |
| **Number Defective (Indicator 1)**              | $p=number\;of\;rejects$                                                                            |
| **Number Defective (Indicator 2)**              | ***Not applicable***                                                                                                        |
| **Standard Deviation for sample**   | $s = \sqrt{n\overline{p}\left ( 1-\frac{n\overline{p}}{n} \right )}$<br/>Where $n\overline{p}$ is the centerline and $n$ is the sample size which is constant |
| **Number Defective (Indicator 1) Centerline**     | $n\overline{p}=\frac{total\;number\;of\;rejects}{number\;of\;samples}$ |
| **Number Defective (Indicator 1) Control Limits** | $UCL = n\overline{p} + 3s$<br/>$LCL = max(n\overline{p}-3s;0)$|
| **Indicator 2 Centerline**                        | ***Not applicable***                                                                                                        |
| **Indicator 2 Control Limits**                    | ***Not applicable***                                                                                                        |

Table: Number Defective chart properties