**According to Dorian Shainin, Isoplot charts can be used to quantify the variation due to method and measuring system.**

## Introduction

According to Dorian Shainin, Isoplot charts can be used to quantify the variation due to method and measuring system. The idea is ” *logical* “: if we perform 2 successive measurements under the same conditions and the 2 measurements are similar, then the measurement system is reliable.

This method is applicable only if we measure quantifiable variables in the same way as for the use of **Gage R & R**.

## 1. Selecting Objects to measure

The tool is used on 30 different parts.

## 2. Perform a first measurement

We will proceed to a first measurement under the standard conditions of use (temperature, tools…).

## 3. Perform a second measurement

Once the parts are first measured, we will perform a second measurement under the same conditions as the first one.

For this reason it is important that the set of 2 measurement series takes place in a shortened period of time to avoid certain type of variability such as the temperature of the room.

## 4. Arrange the dots on a chart

The set of measuring pairs is available on a chart. A correlation graph is developed. We then draw a line at 45 ° which corresponds to the average of the points. It is calculated simply by taking the lowest values and the important value of the 2 series.

Example:

If we have 2 sets of points with values ranging from 5 to 9, then the first point on the right will be (5; 5) and the second (9; 9).

## 5. Perform the graphical analysis

Shainin has developed a simple analysis technique that makes it easy to understand whether the measurement protocol is correct or not. To do this, an ellipse is traced from the farthest points in length and width: This ellipse must contain all the points. Note that this ellipse must be symmetrical in relation to the right.

Next, the ratio of the **ΔM** height (ellipse width) to the **ΔS** length (the length of the ellipse reported on the x-axis) is calculated.

According to Shainin, if the ratio is less than 1/6, then the measurement system will be considered very reliable.

## Measure the R^{2}

With respect to the accuracy level, to determine the size of the ellipse, it is recommended to use the Pearson correlation coefficient as a **linear regression**.

It reads in the following way:

**r**The measurement system is considered reliable^{2}> 64%:**4% < r**The measurement system is considered to be moderately reliable and improvement actions have to be implemented.^{2}< 64%:**r**The measurement system is unreliable and cannot be applied as part of the Shainin method of troubleshooting. And no doubt it cannot be usable at all.^{2}< 4%:

**aberrant**values. This could mean that the Pearson coefficient is weak only because one or more values do not fit into the model that is good.

## Isoplot or Gage R & R?

Even if the Isoplot makes it possible to get a good idea of the variation of measurement, to be more precise and to really measure the source of variability, the **Gage R & R** It is better.

Indeed, the Isoplot method considers only repeatability and not reproducibility. It is therefore only possible to identify the variability that can be in the measurement protocol with a given operator and a given device.

In addition, it is not easy to identify a clear ellipse. The values we take in length and width can have a slight variability which has a significant influence in the calculation of the ratio.

## Source

R. W. Traver (1995) – Manufacturing solutions for consistent quality and reliability

A. Urquhart (1985) – Metrology characterization

P. D. Shainin (1992) – Managing SPC, a critical quality system element