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


Identify Important Factors  The two problems discussed in the previous section (important factors and a parsimonious model) will be handled in parallel since determination of one yields the other. In regard to the "important factors", our immediate goal is to take the full subset of seven main effects and interactions and extract a subset that we will declare as "important", with the complementary subset being "unimportant". Seven criteria are discussed in detail in section 1.3.5.18.2 in Chapter 1. The relevant criteria will be applied here. These criteria are not all equally important, nor will they yield identical subsets, in which case a consensus subset or a weighted consensus subset must be extracted.  
Criteria for Including Terms in the Model 
The criteria that we can use in determining whether to
keep a factor in the model can be summarized as follows.
The last section summarizes the conclusions based on all of the criteria. 

Effects: Engineering Significance 
The
minimum
engineering significant difference is defined as
Based on this minimum engineeringsignificantdifference criterion, we conclude to keep two terms: X1 (1.55125) and X2 (0.43375). 

Effects: 90 % Numerical Significance 
The 90 %
numerical
significance criterion is defined as
Based on the 90 % numerical criterion, we would keep two terms: X1 (1.55125) and X2 (0.43375). The X2*X3 term, (0.14875), is just under the cutoff. 

Effects: Statistical Significance 
Statistical
significance is defined as
For the eddy current case study, ignoring threefactor and higher interactions leads to an estimate of σ based on omitting only a single term: the X1*X2*X3 interaction. Thus for our example, if one assumes that the threefactor interaction is nil and hence represents a single drawing from a population centered at zero, an estimate of the standard deviation of an effect is simply the estimate of the interaction effect (0.07125). Two such effect standard deviations is 0.1425. This rule becomes to keep all \( \hat{\beta_{i}} \) > 0.1425. This results in keeping three terms: X1 (1.55125), X2 (0.43375), and X1*X2 (0.14875). 

Effects: Probability Plot 
The normal probability
plot can be used to identify important factors.
The following graph shows the normal probability plot of
the effects.
The normal probablity plot clearly shows two factors displaced off the line, and we see that those two factors are X1 and X2. Thus, we would keep X1 (1.55125) and X2 (0.43375). 

Effects: Youden Plot 
A DOE Youden plot can
be used in the following way. A factor is "important" if it
is displaced away from the centraltendency bunch in a Youden
plot of high and low averages.
For our example, the Youden plot clearly shows a cluster of points near the grand average (2.65875) with two displaced points above (X1) and below (X2). Based on the Youden plot, we keep two factors: X1 (1.55125) and X2 (0.43375). 

Conclusions 
In summary, the criterion for specifying "important" factors
yielded the following:
All the criteria select X1 and X2. One also includes the X2*X3 interaction term (and it is borderline for another criteria). We thus declare the following consensus:
