Using Multi-Vari Charts to Analyze Families of Variations

Bruno Scibilia 15 August, 2013

When trying to solve complex problems, you should first list all the suspected variables identify the few critical factors and separate them from the trivial many, which are not essential to understanding the cause.




Many statistical tools enable you to efficiently identify the effects that are statistically significant in order to converge on the root cause of a problem (for example ANOVA, regression, or even designed experiments (DOEs)). In this post though, I am going to focus on a very simple graphical tool, one that is very intuitive, can be used by virtually anyone, and does not require any prior statistical knowledge: the multi-vari chart.

What Is a Multi-Vari Chart?

Multi-vari charts are a way of presenting analysis of variance data in a graphical form, providing a "visual" alternative to analysis of variance.

They can help you carry out an investigation and study patterns of variation from many possible causes on a single chart. They allow you to display positional or cyclical variations in processes. They can also be used to study variations within a subgroup, between subgroups, etc.

A multi-vari chart is an excellent tool to use particularly in the early stages of a search for a root cause. Its main strength is that it enables you to visualize many diverse sources of variations in a single diagram while providing an overall view of the factor effects.

To create a multi-vari chart in Minitab Statistical Software, choose Stat > Quality Tools > Multi-Vari Chart...  Then select your response variable and up to four factors in the dialog box.

Interpreting Multi-Vari Charts

Suppose that you need to analyze waiting times from several call centers that are part of a large financial services company. Customers and potential customers call to open new accounts, get information about credit cards, ask for technical support, and access other services.

Since waiting for a long time while trying to reach an operator may become a very unpleasant experience, making sure callers get a quick response is crucial in building a trusting relationship with your customers. Your customer database has data about customer categories, types of requests, and the time of each phone call. You can use multi-vari graphs to analyze these queuing times.

The multi-vari chart below displays differences between the two call centers (Montpellier and Saint-Quentin: red points on the graph), the weekdays (green points on the graph) and the day hours (several black and white symbols). It suggests that waiting times are longer on Mondays (Mon: in the first part of the graph).


In the following multi-vari graph, the type of requests has been introduced. Notice that the types of request (black and white symbols) generate a large amount of variability. Again it suggests that waiting times are longer on Mondays (the first panel in this plot).

Multivari 2

In the third multi-vari graph, customer categories have been introduced (black and white symbols in the graph). Notice that for request types (the red points in the graph), technical support questions seem to require more time. Again, the queuing times tend to get longer on Mondays.

Multivari 3

In the fourth multi-vari chart, the call centers (the red points), the customer categories (the green points) and the types of requests (black and white symbols) are all displayed. Waiting times seem to be larger at the Montpellier call center. Note that each call center focuses on specific types of requests. For example, technical support calls are only processed at the Montpellier call center. Obviously, the technical support calls (represented by circles with a dot in this plot) are the main issue in this situation. 

Multivari 4

Next Steps After the Multi-Vari Chart

This financial services company needs to better understand why queuing times last longer on Mondays, also longer waiting times for technical support calls need to be dealt with. This conclusion is correct only if the full range of the potential sources of variations, has been considered.

A multi-vari chart provides an excellent visual display of the components of variation associated with each family. However, when there is no obvious dominant factor, or when the “signals” from the process are too “weak” to be detected easily, it is useful to augment the multi-vari graph with more powerful statistical techniques (such as an ANOVA or a regression analysis) to numerically estimate the effects due to each factor.