Mistake Proofing (also known as Poka-Yoke) is the correct Lean tool because it involves creating mechanisms that prevent errors or defects, and these mechanisms are designed to be automatic so that no particular understanding is required to use them.

A Level 2 Design for a factorial experiment means each factor has 2 levels. With 6 factors, the number of runs required is calculated as 2^6, which equals 64. Therefore, it is false that 16 runs are required to fully assess the interactions.

In a Full Factorial experiment, the total number of treatment combinations is calculated by raising the number of levels to the power of the number of factors. In this case, with 3 levels and 3 factors, the calculation is 3 raised to the power of 3, which equals 27.

Based on the DOE factorial plot provided, three correct statements can be identified: B, D, and E. Firstly, the highest tool age was achieved with metal hardness at a high level while keeping cutting speed at a low level, which corresponds to statement B. Secondly, the least tool age achieved when both cutting speed and cutting angle are at the low level, aligning with statement D. Lastly, all factors, as visualized in the plot, had 2 levels in the experiment (-1 and 1), which corresponds to statement E. Two factors being operated at 3 levels each and a 32 factorial design are incorrect because the graph indicates two levels for each factor.

Statement C is incorrect because only two variables are statistically significant at a 0.05 significance level. The P-values for Air-Fuel Ratio and SteamExitTemp are less than 0.05, but not for % methane, which is greater than 0.05 (0.84), indicating it is not statistically significant. Statement E is incorrect because, based on the provided Seq SS (Sequential Sum of Squares), the SteamExitTemp explains the least amount of variation in the TurbineOutput.