**This Control Chart counts the same parameter as the C, but transforms it in proportion.**

## Introduction

The Control Chart U is part of the family of Control Chart with attributes. It counts the percentage of the average number of defaults in a sample.

In relation to the **C Control Chart**, which counts the same parameter, it is preferred in cases where having the same large number of samples at each sampling is complex and varies.

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

By sample, the number of faults is counted. The average percentage of the number of defects on all samples is then calculated.

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

## 2. Deduct the limits.

In contrast to the **C Control Chart**, the U-Control Chart has a variable limit because it ” *allows* ” to have variable sample sizes. The limits are calculated using the following formulas, deducted from the fish law:

**UCL _{I} = u_{cross} + 3 ***

**√ (**

**u**

_{cross}/n_{i})**LCL _{I} = u_{cross} -3 ***

**√ (**

**u**

_{cross}/n_{i})

n_{I} being the sample number of I sampling.

## 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