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A Multi-Vari analysis is a graphical tool, which, through logical subgrouping, analyzes the effects of categorical X’s on continuous Y’s. The graphical results of Multi-Vari Analysis can be quantified using Nested Analysis of Variance. Multivariate analysis is concerned with two or more dependent variables Y1, Y2, being simultaneously considered for multiple independent variables, X1, X2, etc.

In statistical process control, one tracks variables like pressure, temperature or pH by taking measurements at certain intervals. The underlying assumption is that the variables will have approximately one representative value when measured. Frequently, this is not the case. Temperature in the cross section of a furnace will vary and the thickness of a part may also vary depending on where each measurement is taken. Often the variation is within piece and the source of this variation is different from piece-to-piece and time-to-time variation. The multi-vari chart is a very useful tool for analyzing all three types of variation. Multi-vari charts are used to investigate the stability or consistency of a process. The chart consists of a series of vertical lines, or other appropriate schematics, along a time scale. The length of each line or schematic shape represents the range of values found in each sample set.

### Multi-Vari Sampling Plan Design Procedure:

1. Select the process and the characteristic to be investigated.

2. Select the sample size and time frequency.

3. Set up a tabulation sheet to record the time and values from each sample set.

4. Plot the multi-vari chart on graph paper with time along the horizontal scale and the measured values on the vertical scale.

5. Join the observed values with appropriate lines.

6. Analyze the chart for variation both within the sample set, from sample-to- sample, and over time.

7. It may be necessary to conduct additional studies to concentrate on the area(s) of apparent maximum variation.

8. After process improvements, it will be necessary to repeat the multi-vari study to conﬁrm the results.