# Estimating Interaction Effects using a Combined-Array Design in Robust Parameter Experiments

This posting presents another example illustrating the advantage of combined-array experiments in Robust Parameter Designs over the Taguchi crossed-array designs.  Kilgo (1988)  presents an example of a 25-1 fractional factorial experiment providing data to construct a model for estimating the mean response.  We modify the use of the experiment to make it relevant to a Robust Parameter Design experiment.

The purpose of the study implementing the experiment was provide relationships among factors affecting the recovery of peanut oil from peanut particles.   These relationships would guide the design of oil extraction equipment (Goodrum and Kilgo, 1987).   Carbon dioxide (CO2) at very high pressures was to be used to extract the oil from peanuts.   The oil would dissolve in the CO2.   Previous research indicated five factors that would affect the amount of oil that would dissolve in the CO2.   These factors are A = CO2 pressure, B = CO2 temperature, C = peanut moisture, D = CO2 flow rate, and E = peanut particle size.   The experimental design as described by Kilgo (1988) did not consider that a factor might be a noise factor.  So the analysis did not include the Robust Parameter Design viewpoint.   We will assume that factor E, peanut particle size, is a noise or uncontrollable factor in the actual operation of the machine.

The 25-1 fractional factorial design can be a resolution V design where every main effect is aliased with a four-factor interaction and every two-factor interaction is aliased with a three-factor interaction.   Hicks and Turner (1999) in Example 13.2 analyzed the resolution of this design by Kilgo (1988) and came to the same conclusion.   Thus, assuming the three and four factor interactions are negligible, we can estimate main effects and two-factor interactions among the controllable and noise factors using data produced by this design.

Contract this capability with the Taguchi crossed-array approach.  Assume that both the crossed-array and combined-array designs have the same number of runs, i.e., 16.   For four controllable factors, the inner array of the four controllable factors could be a 24-1 fractional factorial design with 8 runs.    Montgomery (2005) in Example 8-1 shows that the highest possible resolution for a 24-1 design is IV.  That means, no main effect is aliased with another main effect or with any two-factor interactions; however, the two-factor interactions are aliased with each other.    Thus, the crossed-array approach can’t estimate two-factor interactions among controllable factors.

The next posting will present the results for a Robust Parameter Analysis of the data produced by the Kilgo fractional factorial experiment.

References

1. Goodrum, J. W. and M. B. Kilgo (1987). “Peanut Oil Extraction with SC-CO2: Solubility and Kinetic Functions.” Transactions of the ASAE 30(6): 1865-1868.
2. Charles R. Hicks and Kenneth V. Turner, Jr. (1999). Fundamental Concepts in the Design of Experiments, Fifth Edition, Oxford University Press, New York.
3. Kilgo, M. (1988). “An Application of Fractional Factorial Experimental Designs.” Quality Engineering 1(1): 45-54.
4. Montgomery, D. (2005). Design and Analysis of Experiments, 6th Edition, John Wiley & Sons, Inc., New York.