Problem 1 An experimenter has conducted a 25-2 fractional factorial experiment. The test matrix and the resulting response observations are shown below. Notice that the first three columns (A, B, and C) are shown in standard order. Block (1 or 2) D E C Std A B 50 -1 -1 -1 1 -1 1 21 1 -1 1 -1 1 2 45 -1 1 -1 3 1 25 1 -1 -1 -1 4 1 43 1 1 1 -1 5 -1 6 33 1 -1 1 1 -1 -1 1 7 1 1 -1 45 34 8 1 1 1 1 1 Answer questions a thru i on the next page. Note: Although this is a small enough problem that you could answer all the questions by hand calculations (ugh!), I suggest you follow the JMP path below (shown on page 1 of the Hints PDF file) to assist you: Analyze> Specialized Modeling> Specialized DOE Models > Fit Two Level Screening a. Write the design generators (for D and E) that have been used to construct this design. Be careful - this may not be the "standard" design for 5 factors in 8 runs. b. What is the complete defining relation? LO c. What is the resolution of this design? d. What is the effect of factor A? Write the aliases for this main effect. e. If this experiment had been run in 2 blocks, confounding the effect of AB with the block effect, fill in the column labeled block in the table with the number of the block (either 1 or 2) for each run. f. Analyze the data from the original design (that is, with no blocking). What are the two factors with the most impact on Y? g. Dropping the other three negligible factors results in a two most important factors. (Fill in the blank with the type of design.) design in the h. Write down a model involving these two factors that you could use to predict the response over the design space. Write this model in the coded factors. C i Use this model to predict the response at the point in the design space where Y is mimimized. Problem 1 An experimenter has conducted a 25-2 fractional factorial experiment. The test matrix and the resulting response observations are shown below. Notice that the first three columns (A, B, and C) are shown in standard order. Block (1 or 2) D E C Std A B 50 -1 -1 -1 1 -1 1 21 1 -1 1 -1 1 2 45 -1 1 -1 3 1 25 1 -1 -1 -1 4 1 43 1 1 1 -1 5 -1 6 33 1 -1 1 1 -1 -1 1 7 1 1 -1 45 34 8 1 1 1 1 1 Answer questions a thru i on the next page. Note: Although this is a small enough problem that you could answer all the questions by hand calculations (ugh!), I suggest you follow the JMP path below (shown on page 1 of the Hints PDF file) to assist you: Analyze> Specialized Modeling> Specialized DOE Models > Fit Two Level Screening a. Write the design generators (for D and E) that have been used to construct this design. Be careful - this may not be the "standard" design for 5 factors in 8 runs. b. What is the complete defining relation? LO c. What is the resolution of this design? d. What is the effect of factor A? Write the aliases for this main effect. e. If this experiment had been run in 2 blocks, confounding the effect of AB with the block effect, fill in the column labeled block in the table with the number of the block (either 1 or 2) for each run. f. Analyze the data from the original design (that is, with no blocking). What are the two factors with the most impact on Y? g. Dropping the other three negligible factors results in a two most important factors. (Fill in the blank with the type of design.) design in the h. Write down a model involving these two factors that you could use to predict the response over the design space. Write this model in the coded factors. C i Use this model to predict the response at the point in the design space where Y is mimimized
