5.
Process Improvement
5.6. Case Studies 5.6.1. Eddy Current Probe Sensitivity Case Study


Effects Estimation 
Although the effect estimates were given on the
DOE interaction plot on a previous
page, we also display them in tabular form.
The full model for the 2^{3} factorial design is \( \begin{eqnarray*} Y &=& \mu + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \beta_{12} X_1 X_2 \\ &+& \beta_{13} X_1 X_3 + \beta_{23} X_2 X_3 + \beta_{123} X_1 X_2 X_3 + \epsilon \end{eqnarray*} \) Data from factorial designs with two levels can be analyzed using leastsquares regression. The regresson coefficients represent the change per one unit of the factor variable, the effects shown on the interaction plot represent changes between high and low factor levels so they are twice as large as the regression coefficients. 

Effect Estimates 
The parameter estimates from a leastsquares regression analysis
for the full model are shown below.
Effect Estimate   Mean 2.65875 X1 1.55125 X2 0.43375 X3 0.10625 X1*X2 0.06375 X1*X3 0.12375 X2*X3 0.14875 X1*X2*X3 0.07125Because we fit the full model to the data, there are no degrees of freedom for error and no significance tests are available. If we sort the effects from largest to smallest (excluding the mean), the four most important factors are: X1 (number of turns), X2 (winding distance), X2*X3 (winding distance by wire gauge interaction), and X1*X3 (number of turns by wire gauge interaction). 