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Used most often in small-series or very high-value-added production, it applies only for quantitative data and unit samples.

## Introduction

The control chart individual and Moving range can be used to visualize the variation in the average and the extent of the data collected. It is used in cases where each sample is controlled only by a quantitative parameter.

This is the case for example when there are very low cadences, products with very high values added or when controlling at 100% of the products.

## 1. Calculate the Moving Range

For the control chart of range, one starts by calculating the average of the range mRcross. It corresponds to the average of the absolute value of the difference between 2 successive values.

mRi + 1 = i xi+ 1 – xi i

Example:

We have the results of five samples. We get the following table:

Prélèvement
1
Prélèvement
2
Prélèvement
3
Prélèvement
4
Prélèvement
5
Echantillon1110,59,110,111,1
Etendu mobile-0,51,411

We obtain the mobile range mR, by averaging the extents of each group, or in our example 0.975.

## 2. Calculation of limits and construction of the mR control chart

In the particular case of I-MR cards, the coefficients for deducing the high and low limits are always the same (since we still have 1 unit). The calculation is as follows:

• UCL: Upper limit = mRcross * D4 = mRcross * 3.268
• LCL: Lower limit = mRcross * D3 = 0

With the data from the previous table, we get:

• UCL = 3.1863
• LCL = 0

## 3. Calculate the average and deduct the control chart to individuals

### 3.1 Calculation of individuals

The control chart to individuals represents each of the points of our readings over time. There is no specific calculation.

### 3.2 Calculation of limits

The average of our readings is calculated first, then the high and low limits at 3 σ are deduced. With only one data per sample, the standard deviation is estimated from the mobile spread via the formulas:

• UCL: Upper limit = Icross + A2* mRcross
• LCL: Lower limit = Icross -A2* mRcross

The subgroups are always a unit in the case of an I-MR control chart. A2 is therefore constant, and always equal to 2.66.

Example:

The previous example follows:

The average of each sample is calculated. We get in our example, Icross = 10.36.

We deduce the high and low limits, which gives us:

• UCL = 12.95
• LCL = 7.77

## Interpretation of the I-MR control chart

For a reliable evaluation, the practice shows that it takes at least a hundred points to have a reliable judgement on the reality of our process. We understand that at the beginning you have to have a high frequency of sampling. In which case it will take several weeks or months to make a good interpretation.

### Control chart to individuals

The map to individuals detects a centering drift of the process. If one of the decision criteria is validated, a setting must be done to center the process with the value of deviance.

### Control chart to range

The control chart to range detects the degradation of the process dispersion. There are two ways to interpret it:

• If one of the criteria is validated against the upper limit, then the process has a dispersion that degrades and actions are probably necessary.
• If one of the criteria is validated against the low limit, then the process has a dispersion that improves. There is no need to act, but we can investigate why we are improving.

## Source

R. F. Rhyder (1997) – Manufacturing process and design optimization

C. E. Cordy (2006) – Champion practical Six Sigma Summary