# Multi-Vari Analysis

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 con?rm the results.

Multi-vari Analysis – Tools

Multivariate analysis is concerned with two or more dependent variables Y1, Y2, being simultaneously considered for multiple independent variables, X1, X2, etc. Recent advances in computer software and hardware have made it possible to solve more -problems using multivariate analysis. Some of the software programs available to solve multivariate problems include: SPSS, S-Plus, SAS, and Minitab. Multivariate analysis has found wide usage in the social sciences, psychology or educational ?elds. Applications for multivariate analysis can also be found in the engineering, technology, and scienti?c disciplines.

The highlights of the following multivariate concepts or techniques:

• Discriminant Function Analysis

• Multi-vari Analysis – Discriminant Function Analysis

• Discriminant Function Analysis

If one has a sample with known groups, discriminant analysis can be used to classify the observations or attributes into two or more groups. Discriminant analysis can be used as either a predictive or a descriptive tool. The decisions could involve medical care, college success attributes, car loan credit worthiness or the previous economic development issues. Discriminant analysis can be used as a follow-up to the use of MANOVA. Again, linear combinations of predictors or groups are provided by the researcher. The possible number of linear combinations (discriminant functions) for a study would be- the smaller of the number of groups -1, or the number of variables.

Some assumptions in discriminant analysis are:

The variables are multivariately normally distributed.

The population variances and covariances among the dependent variables are the same, and the samples within the variables are randomly obtained and exhibit independence of scores from the other samples.