**The C control chart allows to count the number of faults for constant samples.**

## Introduction

Control chart C is part of the family of cards with attributes. It is used to track the number of faults. In other words, it counts the faults on the contrary of the P and NP control chart, which counts the number of scraps.

It is used when the same product can have many defects without being considered a scrap.

## 1. Calculate the average fault number C_{cross}

By sample, the number of faults is counted. We then calculate the average of the number of faults on all the samples. It is noted that the size of the subgroups must be strictly identical.

We call this variable C_{cross}. It will be the center line of our graph.

## 2. Deduct the Limits

Of the variable C_{cross}, the upper and lower limits of 3 σ are deduced via the formulas, inferred from the Fisher Law:

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

**√**

**C**

_{cross}**LCL = C _{cross} -3 ***

**√**

**C**

_{cross}

## 3. Interpretation

The graph reflects the evolution of the number of faults. So it reads in the same way as any other Control Chart with attributes. In other words, if our criteria are validated ” *from the top* “, then we must act.

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

## Source

D. C. Montgomery (2009) – Statistical quality control

S. G. Amin (2001) – Controls Charts 101: A Guide to health care applications