Question

A 2³ factorial is used by a process engineer to study the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and duplicates were run at each design point with the order of the runs being random. The data are presented below.

                        Treatment

                        Combinations             Life   

            (1)                   22, 31

                                    a                      32, 43

                                    b                      35, 34

                                    ab                    35, 47

                                    c                      44, 45

                                    ac                    40, 37

                                    bc                    60, 50

                                    abc                  39, 41

Please answer the following questions shown on the next page.

1. Calculate all the sums of squares (i.e., SS_A, SS_B, SS_C, SS_AB, SS_AC, SS_BC­, and SS_ABC) [Pencil version]
2. Develop your ANOVA table in which SS, MS, DF, and F should be shown [Pencil version]
3. Based on the F values in part (b), which factors and/or interactions are significant? [Pencil version]

For the purpose of redesigning their manufacturing process, they want to know the most important factor. What would that be?

Answer 1