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The P Control Chart is used to track the proportion of scraps in variable size samples.

## Introduction

It is also called the percentages graph. It’s part of the attributes Control Chart. It is used to track the proportion of non-compliant products (scrap) in subgroups of varying dimensions.

It is generally used when it is too difficult or too costly to carry out physical measures or when one wants to combine several faults in the same overall percentage (in this case we lose as an interpretation).

## 1. Calculate the average Pcross

The average P-cross is obtained by averaging the scrap percentages in each sub-group. 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 defect. 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

Of the P value, the upper and lower limits are deduced according to the following formulae derived from the binomial low :

UCL: Upper limit = Pcross + 3 * (P Bar * (1 – Pcross)/ni)

LCL: Lower limit = Pcross -3 * (P Bar * (1 – Pcross)/ni)

With:

• nI : the number of samples per sub-group.
• Pcross : being the average proportion

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

It is noted that if the sample size varies, then the limits also vary. This is the only difference NP Control Chart, which she, having subgroups of the same size, has constant limits.

## Interpretation of the P Control Chart

The graph reflects the evolution of a proportion. 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. S. Oakland (2003) – Statistical Process Control