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This a resolution IV design, because we have four elements in the alias chain AB=CE. For example, in a 16-run, 6 two-level factor design, the AB interaction is confounded with the CE interaction. These designs confound two-factor interactions with other two-factor interactions. The yellow designs in the Available Factorial Designs table are much less risky.
![minitab doe minitab doe](https://i.ytimg.com/vi/Tnc7o5EZGLE/hqdefault.jpg)
Since you cannot separate the effects of A and the other elements of the alias chain, interpreting the true signifiance of that chart is very difficult. Only A is displayed in the Pareto chart, but it is just the first term of a long alias chain: In the Pareto graph of effects, the A factor seems to be significant (above the significance threshold), but A is also confounded with the CE interaction (for example). That's the case for resolution III designs shown in red above. Sometimes the price we pay for a reduction in the number of tests is too high. Choosing an Appropriate Fractional Design This is an unlikely and complex event, so we aren't so worried about these higher-order interactions in a fractional design. Why? A three-factor interaction, for example, would mean that the effect of a factor is modified by the setting of another factor, and that the effect of this two-factor interaction would be modified by the setting of a third factor. The three- and four-factor (higher order) interactions are rarely considered. I + ABD + ACE + BCF + DEF + ABEF + ACDF + BCDEĪ + BD + CE + BEF + CDF + ABCF + ADEF + ABCDEī + AD + CF + AEF + CDE + ABCE + BDEF + ABCDFĬ + AE + BF + ADF + BDE + ABCD + CDEF + ABCEFĭ + AB + EF + ACF + BCE + ACDE + BCDF + ABDEFĮ + AC + DF + ABF + BCD + ABDE + BCEF + ACDEFį + BC + DE + ABE + ACD + ABDF + ACEF + BCDEFĪF + BE + CD + ABC + ADE + BDF + CEF + ABCDEF When you create a fractional factorial design, Minitab tells you which main effects and interactions are confounded with an alias structure and the “alias chains” like these:ĭesign Generators: D = AB, E = AC, F = BC Which Effects and Interactions Are Confounded? An experimenter cannot separate their confounded effects: if the effect of A or BD is significant, you cannot be absolutely sure whether this is due to the A factor or to the BD interaction. We call this a resolution III design since A = BD, which means we have three elements in this alias chain. In an 8-run design with six factors, for example, the A factor is confounded with the BD interaction. In the table, red means that some factors are confounded with two-factor interactions: This is because we pay a price for reducing the number of runs from 64 to 8: aliases (confounded effects) have been generated, so interpreting the results becomes more difficult and riskier. Notice that the 8-run design to study the effects of 6 two-level factors is colored red. and clicking "Display Available Designs." In Minitab, you can quickly access the table of factorial designs shown below by selecting Stat > DOE > Factorial > Create Factorial Design.
#MINITAB DOE FULL#
To study 6 factors, you could use a 32-run design (a half fraction of the full design), a 16-run design (quarter fraction), or even an 8-run design (eighth fraction). Fractional factorial designs are very popular, and doing a half fraction, a quarter fraction, or an eighth fraction of a full factorial design can greatly reduce costs and time needed for an experiment. That is why fractional factorial designs are often used to reduce the number of runs in two-level DOEs. In practice, having six predictive variables is very common, but running 64 tests is very costly and hard to justify. A full factorial design would require no less than 64 runs. Suppose you need to study the effects of 6 two-level factors on a response. The objective of DOE is to reduce experimental costs-the number of tests-as much as possible while studying as many factors as possible to identify the important ones. In science and in business, we need to perform experiments to identify the factors that have a significant effect. Design of experiments (DOEs) is a very effective and powerful statistical tool that can help you understand and improve your processes, and design better products.ĭOE lets you assess the main effects of a process as well as the interaction effects (the effect of factor A, for example, may be much larger when factor B is set at a specific level, leading to an interaction).