I don't understand the sensitivity plots in DesignXplorer. They are displayed using positive and negative numbers in both bar and pie charts. What is the significance of the sign and the number?
The sensitivities essentially indicate the effect on a given output that a single parameter variation will have. There is a slight difference in how the numbers associated with sensitivities are calculated depending on the type of graph that they originate in. DX has 2 types of sensitivity,
Single Parameter Sensitivity
The value in the bar chart is basically indicating the percentage that the current value of the output will change based on changing the input.
P: (LB, UB)
X: (9, 11)
Y: (9, 11)
Z: (9, 11)
Sum: X + Y + Z
Sum: (27, 33)
Now, let`s say we`re looking for the single parameter sensitivity when X = 10, Y = 10, Z = 10. The current value of Sum is 30. Changing X from 9 to 11 will change Sum from 29 to 31 (2 units of change from the current value of 30) or 6.67% (2.0/30.0), hence the single parameter sensitivity value of 0.0667. Similarly, the sensitivity for Y and Z should be 0.0667.
The value in the bar chart is the Spearman rank-order correlation coefficient. This is a bit more complex to calculate, and is based on the formula shown in the DX help under "Six Sigma Analysis > Postprocessing Six Sigma Analysis Results > Theory". A value of 1 means perfect correlation ` A change in the input accounts for all of the change in the output. These values can be positive (increasing the input increases the output) or negative (increasing the input decreases the output.) A value of 0 means no correlation ` A change in the input will not change the output at all. The values are relative to each other, but not to the values of the parameters themselves. For instance, in the simple example above, DX will calculate Global Sensitivities of about 0.57 for X, Y, and Z. This means that each parameter equally affects the output, and that the correlation between input and output is positive.
For global sensitivities, we use a significance level to eliminate the insignificant parameters from the sensitivities. You can read more about that in the documentation (DesignXplorer Help | Six Sigma Analysis | Postprocessing Six Sigma Analysis Results).
In both cases, the pie charts are formed by normalizing the sensitivity values on a scale of 0 to 1. Basically, this means that we sum all of the sensitivity values and then divide each sensitivity value by this sum to determine the percentage in the pie chart. The labels within the pie chart snapshots are meant to convey the information in the bar chart (the value of the sensitivity itself is the label) and the pie chart together.