Definition

The Multi-vari (Multi-variate) Chart is a useful graphical tool that helps differentiate the sources of variation in a process. It is often employed in the preliminary stages of data analysis to evaluate the behavior of the quality characteristic from process data collected before any interventions are made to the process. The process variation is broken down into three main sources: within unit, Units and temporal (over time) variation. The chart helps to quickly identify the dominant sources of variation prior to using more formal methods such as control charts or analysis of variance.

Examples

Three friends decided to record their running times each day for three weeks. At the end of this duration, they collated their records and put them on a multi-vari chart, to see if there were any large variations among them. The chart is shown (you can obtain this chart from a statistical software package such as Minitab).

The overall trend for running times is downward over the three weeks, as indicated by the dotted line. Within each week, the lines connecting the three dots depict the variation between the runners. Following the trend for each runner across the three weeks, Jan achieved the highest decreases in running times whereas Kim had the slowest times even though they did improve over time. Lisa started off with the lowest running time in the first week, increased it in the second week but decreased it again in the third week. None of the three possible sources of variation (within-runner, between-runner or over time) seem very large in this case.

Application

Multi-Vari charts are the graphical equivalent of the Analysis of Variance (ANOVA) and Variance Components techniques; however, any apparent differences still should be verufied using a formal test.