THE MULTI-VARI CHART: A SYSTEMATIC APPROACH

Abstract

Prior to setting up a designed experiment or setting up a monitoring system for a process most experimenters perform an exploratory study to investigate thestructure of the process' variation. Tools that are frequently used for such a study are predominantly graphical in nature.The multi-vari chart is a useful tool to analyse measurements from a process in which several variance components can be discerned. The chart differentiatesbetween various sources of variation, related to, e.g., time and streams of products. Visually from the chart it can be estimated whether the error variance is consistent over time and whether the other sources of variation are significant compared to the error variation.Instead of making inferences from the chart purely intuitively, this paper establishes more formal statistical tests for the analysis of multi-varicharts. For this purpose, we state a number of hypotheses that emerge frequently in multi-vari studies. To decide on these hypotheses we constructtests based on control charting methodology. Some of the hypotheses and tests are based on a random effects model whereas others are based on a mixed effectsmodel. We study both models seperately.Augmented with these tests, the multi-vari chart turns out to be a powerful extension of the regular control chart.

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