# Methods and formulas for Multi-Vari Chart

Select the method or formula of your choice.

## Plotted Points of the Average Response with Variation Chart

To calculate the means for each of the factors, sort the response values by Factor 1, Factor 2, Factor 3, etc… Then calculate the means from right to left.

For example, suppose Measurement is the response and the 3 factors are Operator, Part, and Subcomponent.

C1 C2 C3 C4
Measurement Operator Part Subcomponent
0.29 A 1 A
0.41 A 1 A
0.64 A 1 B
0.59 A 1 B
-0.56 A 2 A
-0.58 A 2 A
-0.48 A 2 B
-0.42 B 2 B
1.34 B 3 B
1.17 C 3 A
1.27 C 3 A
1.30 C 3 B
There are a total of 8 cell means defined by the 3 factors:
• Cell mean 1 = (0.29 + 0.41)/2 = 0.35
• Cell mean 2 = (0.64 + 0.59)/2 = 0.615
• Cell mean 3 = (-0.56 - 0.58)/2 = –0.57
• Cell mean 4 = -0.48
• Cell mean 5 = -0.42
• Cell mean 6 = 1.34
• Cell mean 7 = (1.17 + 1.27)/2 = 1.22
• Cell mean 8 = 1.30
There are 5 factor level means for Factor 2 (Part):
• Mean 1 = (0.29 + 0.41 + 0.64+0.59)/4 = 0.4825
• Mean 2 = (-0.56 - 0.58 - 0.48)/3 = –0.54
• Mean 3 = -0.42
• Mean 4 = 1.34
• Mean 5 = (1.17 + 1.27 + 1.30)/3 = 1.246
There are 3 factor level means for Factor 1 (Operator):
• Mean 1 = (0.29+0.41+0.64+0.59-0.56-0.58-0.48)/7 = 0.044
• Mean 2 = (-0.42 + 1.34)/2 = 0.46
• Mean 3 = (1.17 + 1.27 + 1.30)/2 = 1.246

The overall mean = average of all response values.

The range bar within in each cell is produced by connecting the minimum data point with the maximum data point inside the cell. If there is no replicate in a cell, no range bar is produced for the cell.

## Plotted Points of the Standard Deviation Chart

The plotted points are the sample standard deviations within each cell. The mean of the standard deviations equals the average of all standard deviations.

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