**The NP control chart is the same as P-control chart, appropriate in cases where we have constant samples.**

## Introduction

The NP control chart is part of the attributes control chart. It is based on the same principle as the P-control chart, in the sense that it counts the number of scrap. The difference is based on the fact that we are working on values and not proportions, and that the number of samples taken each time must be the same. Thus, if it is not easy to always control the same number of samples per sample, then we will choose the card P.

## 1. Calculate the average NP_{cross}

The average NP_{cross} is obtained by averaging the number of scraps in each subgroup. Statistically, the card is considered to be fully effective for a n * p > 5 product. n being the total population and p the proportion of scrap. This ensures the convergence to the normal law and a better sensitivity of the Control Chart.

However, the NF X06-032-1 standard recommends a calculation for at least 300 measurements.

## 2. Deduct the Limits

In the case of the NP control chart, the limits are always constant. The formulas are as follows, which are the result of the **Binomial law** :

**UCL = NP _{cross} + 3 ***

**√ (NP**

_{}Bar * (1 – P_{cross}))**LCL = NP _{cross} -3 ***

**√ (NP**

_{}Bar * (1-P_{cross}))With:

- NP
_{cross}: Average number of defective - P
_{cross}: Average of the percentage of defective

In the case where the lower limit calculation gives a negative value, it is set to 0 on the graph.

## Interpretation of the NP control chart

The graph reflects the evolution of the number of scrap. It reads in the same way as a map to the extended or standard deviation. In other words, if our criteria are validated ” *from the top* “, then we must act.

On the other hand, if our defect ratio validates a criterion ” *from the bottom*“, then we are progressing. However, one can investigate why and in particular be sure that the definition of ” *scrap* ” is the same.

## Source

J. De Mast (2003) – Quality improvement from the viewpoint of statistical method