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Take-home exam questions for a statistics course focusing on fractional factorial experiments and design generators. Students are expected to analyze an experiment with six factors, determine the defining relation, resolution, estimated effects, and statistically significant effects. They are also asked to compare different design choices and write an essay on the importance of experimental design principles.
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Factor Low Level (–) High Level (+) A: Cutting speed (sf/min) 2000 2500 B: Tool Geometry Negative Positive C: Machine American Monarch D: Cutting Fluid Absent Present E: Feedrate (in/rev) 0.005 0. F: Depth of cut (in) 0.050 0.
The experiment uses the two design generators: E=ABC and F=BCD to get the plus/minus levels for the last two factors. The data are given below.
A B C D E=BCD F=ABD Force
You should analyze this experiment and be prepared to answer questions on the design and analysis during the final exam. Some things you should think about are: What is the defining relation for this experiment? What is the resolution of this experiment? What are values for the estimated effects? According to a normal plot, what effects appear to be large? Can you project this experiment into a smaller experiment and pick up pseudo-replication? What effects are statistically significant? What recom- mendations can you make to produce the lowest cutting force? What is the predicted cutting force for a specific combination of factor levels?
Choice 1: E=ABCD, F=ACD, G=BCD Choice 2: E=ABC, F=BCD, G=ACD
On the attached sheet;
Turn in the sheet at the beginning of the final exam.
(a) Choice 1: A single replicate of a full 2^4 factorial. (b) Choice 2: Two replicates of a 12 fraction of a 2^4 , a 2^4 IV− 1. (c) Choice 3: A 12 fraction of a 2^4 , a 2^4 IV− 1 , with 8 center points
(a) Briefly explain why each principle is important. (b) At the end of the semester we have discussed single and fractional replication experiments (violations of the principle of Replication). What difficulties does this violation create.