Example 3 - Two Level Fractional Factorial Design
[Download DOE++ Example File (*.rdoe)]
Background
Consider a manufacturing process for an integrated circuit.* The objective is to improve the process yield. The five factors that may affect the process are:
It is too expensive to run a full factorial design, which has 25 = 32 runs. Therefore, the engineers decide to run a half fractional factorial design using generator E = ABCD.
Experiment Design
The engineers use DOE++ to design a two level fractional factorial design. The design-specific settings, the factor properties and the response properties used are shown next.
The design matrix and the response data are given in the "Fractional Factorial Design Model 1" Folio.
Analysis Part I
Step 1: After performing the experiment according to the design and recording the results, the engineers enter the data set into the Standard Folio, as shown next.
The data set as entered in the DOE++ Folio.
Step 2: In the Select Effects window, all effects up to two-way interactions are selected for inclusion, as shown next.
Step 3: The data set is analyzed with the default risk (significance) level of 0.1, using individual terms.
Step 4: An Effect Probability plot is created, as shown next.
The Effect Probability plot shows that effects A, B, C and AB are significant.
Analysis Part II
The results for the reduced model are given in the "Fractional Factorial Design Model 2" Folio.
Step 1: The design Folio is duplicated and the copy is named "Fractional Factorial Design Model 2."
Step 2: In the Select Effects window, only the significant effects are selected to calculate the new model, as shown next.
Step 3: The reduced model is calculated. The coefficients for A, B, C and AB, found in the Regression Information table in the Analysis tab, are:
Conclusions
As shown in the Regression Information table in the Analysis tab, each of the effects in the reduced model has a positive effect on the yield. Therefore, in order to increase the yield, the high level setting of factors A, B, and C should be applied.
* Montgomery, D. C. Design and Analysis of Experiments, 5th edition, John Wiley & Sons, New York, 2001.
