Analyze the following 23 full factorial design with 2 replications data using Minitab. Answer: The high-high-high 3-way interaction rules the experiment. To maximize CTQ, set all factors at the high…

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Options

• AThe high-high-high 3-way interaction rules the experiment. To maximize CTQ, set all factors at the high level.

• A
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Explanation

Option A is correct because in a 2³ full factorial design, Minitab's analysis (via ANOVA and Pareto chart of effects) identifies which effects are statistically significant - and when the three-way interaction (ABC) dominates, it means all three factors jointly influence the CTQ (Critical-to-Quality output) more than any individual factor or two-way interaction does. When the high-high-high combination of a 3-way interaction is the dominant effect, the interaction plot confirms that the CTQ response is maximized when all three factors are simultaneously set to their high levels.

Since only option A is presented here, the distractors in the original question likely offered conflicting conclusions - such as setting factors at their low levels, relying on a main effect rather than the interaction, or picking a partial combination (e.g., only two factors at high) - all of which would be wrong because they ignore what the Minitab output explicitly shows: the 3-way interaction term is the ruling effect, and its direction points to the (+,+,+) corner of the design cube.

Memory tip: Think of the design cube - a 2³ experiment has 8 corners. When the 3-way interaction "rules," the winning corner is always the one where all factors go the same direction as the interaction's sign. If the high-high-high interaction is dominant and positive, the peak CTQ lives at that corner. "All high wins when the 3-way interaction drives the game."

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