A 23 factorial is used by an 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 Combination 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
a) Calculate all the sums of squares (i.e., SSA, SSB, SSC, SSAB, SSAC, SSBC, and SSABC)
b) Develop your ANOVA table in which SS, MS, DF, and F should be shown
c) Based on the F values in part (b), which factors and/or interactions are significant?
d) For the purpose of redesigning their manufacturing process, they want to know the most important factor. What would that be?
e) Using Minitab, obtain the ANOVA table
f) Check if the three assumptions are met [ USE Minitab for the plots and write conclusions]
g) Using Minitab, obtain the Pareto chart. What are your conclusions from the Pareto chart?