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In the years 1940, Leonard Seder, classmate at MIT and friend of Shainin, developed the Multi-Vari graph, a graphical method of analyzing variance.

## Introduction

In the years 1940, Leonard Seder, classmate at MIT and friend of Shainin, developed the Multi-Vari graph, a graphical method of analyzing variance. The idea is somewhat the same as that of Taguchi with the plans of Signal/noise experiments.

Among the first followers of this method, Shainin discovered that with the Multi-Vari graphics, one could quickly converge to the root cause of a problem. By comparing the measured data according to different sources of variation, we visualize and measure that it is the most important source of variation.

Shainin suggests to look at variations according to three possible sources:

• Position: variation from one part to another, from one mould to another, from one machine to another, from one person to another, from one site to another.
• Time: change hour after hour, team after team…
• Frequency: variation from one batch to the next.

## 1-Identify what you want to measure

The first step is to identify the value that we want to measure. It must be representative of the problem. For example, if we want to analyze the root cause of the variability of the machining diameter of a tree, it is this data that we will take as a measure.

## 2-Identify the levels of the sources of variability

Along with a plan of experiments, the different levels of the 3 possible sources of variability are identified. These levels will be used to carry out the measurements. These levels will have to be representative of reality and ” sweep ” the possible extremums.

In taking our example, we define the following elements:

• Position: we will take the measurement position we are doing on our tree. This will take 2 measurements to the left and 2 measurements to the right of the tree each of which is 180 ° from each other.
• Time: we will take trees that will be machined at the same time and that on 5 different hours.
• Frequency: three consecutive trees will be taken for each hour.

Most generally, groups of 3 to 5 units produced consecutively spread over hours or different and consecutive teams. On each of these pieces, the measurement will be carried out according to the position chosen beforehand.

## 3-Carry out the measures

Once the entire test process is in place, the measurement is carried out according to the specific protocol. In our case, we perform 4 measurements of the diameter on each of the 3 consecutive trees that we collect each hour on 5 consecutive hours.

This process will be continued in the first step on the initially defined time frame. But in practice, we will do so until we have been able to ” tap” 80% of the variability we are looking for.

## 4-Build the Multi-Vari diagram

Once the measurements are collected, the different points of the diagram are constructed. In order, we put the value of measuring the diameter. In the x-axis, we will represent both time and frequency.

In our example, we get the following graph. Legend :

• At the bottom: each of the 5 hours
• At the top: each of the three trees
• In order: The value of the diameter
• The blue dots: the value of the diameter for each of the 4 measuring positions per shaft.
• In green the average measurement of each of the 5 groups of 3 trees.

## 5-Analyzing the graph

The last step is to analyze the graph. One will research what is the cause among the 3 that is causing the greatest variability in the measure.

In taking our example, we realize that the cause of time is at the origin of the greatest variability. Indeed, the 3rd groupof measurement, therefore took at the 3rd hour of production, is much less than the other 4. When comparing, we identify that:

• The position has a variability of 0.001: the difference between the greatest value and the smallest value of each tree.
• The frequency has a variability of 0.0005: difference between the greatest value of the average of one of the trees taken in the same group of 3.
• Time has a variability of 0.0015: the difference between the largest and the smallest mean of the values of each of the 5 groups.

## Source

K. S. Vinay, P. Gowda, H. Ramakrishna (2014) – Industrial scrap reduction using Shainin technique

J. Garside (1999) – Make it

T. P. Ryan (2007) – Modern Engineering statistics