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Where is my variation coming from?

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Let’s say that you want to investigate the roundness of a manufactured part. It has been reported that the capability of the process that makes the round part is very poor. It has been determined that the variation in the process is very high resulting in poor capability. You have been tasked to find out the root cause of the high variation and fix it. How would you attack this problem? One possibility is to use the multi-vari chart. To analyze where the variation is coming from, we would collect data for a period of time from this process and plot it using the multi-vari chart to understand where the problem is coming from. Let’ say that we want to determine if the roundness is dependent on the location we perform the measurement, so we can indicate four places on the part where we can measure roundness. Second, we want to find out if the roundness problem is always there or changes from one batch of production to the next, so we can collect data every few hours to see if the variation is due to changes in the process in the short-term. Finally, we may want to collect the data over a long period of time say a week or longer to see if there are any patterns in roundness variation over the long term. The data collected for this exercise is shown in the table below.

Multi Vari Inputs
A multi-vari chart is a graphical chart which visually shows where the major variation in the data set is coming from. It is called a multi-vari chart because usually multiple variables are plotted on the same chart. Variation in data can come from multiple sources. On a multi-vari chart, the source of variation is typically represented as variation within a part/product, variation in the short term, and variation in the long term. Once the major source of the variation is determined, then corrective actions can be taken to attack and reduce the source of variation.

How to create multi-vari chart?

We will use the Sigma Magic software to create the multi-vari chart. The first step is to add the multi-vari chart template to the excel workbook. You can do this by clicking on Graph and then Multi-Vari chart. Specify the number of variables and the order you want to use the variables to create the plot. In our example, we have 3 variables (positional, short-term and long-term). Specify which variable you want to plot for each axis. You can specify the variable to use for the panels, the horizontal x-axis and for the legend. Enter the data into the excel template and then click on Compute Outputs. The analysis results and graph is created as shown below. In this example, the short-term variable is the batch data and the panel variable is the day and the legend variable is the position where the roundness is measured.

Multi Vari Ouputs
The legend variable is plotted as-is in black. From this chart we can see that the difference between the maximum and minimum values has a maximum value of about 10 units. The short-term variable is plotted as the average for all positions and is shown in red. For example, for the first panel (day 1), the average values shown in each batch varies from 15 to 16 (range of 1.3). Overall, looking at all the days, the batch to batch variation has a maximum value of 1.72. The green dots show the average of all the values for each day. This value ranges from 15 to 19.3 with a range of 4.3. In this example, it can be seen that the positional variation is larger than the other types of variation. You may want to check out why this is so and what actions you can take to ensure that the roundness values are pretty comparable at all locations. You may also want to plot the mult-vari chart with different combination of variables for legend, horizontal axis, and the panel variable. This will provide other views of the data and will help you understand the variation in the data better.

Since a multi-vari chart is a graphical way of looking at the variation and it gives us important clues as to the source of variation in our data. However, being a visual chart, the results can be subjective as different people may interpret the chart differently. If statistical proof of the source of variation is required, we can either use the ANOVA or Mood’s Median test to analyze the same data set.

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