Problem 1 (15 pts, group): The following five factors (and their level:) were studied in a fractional factorial experiment in an automotive plant in order to improve pigment dispersion for the production of coloured coatings films: 1: machine type (-) vertical (+) horizontal `pigment type red 3: pigment concentration (9%) 10 15 4: processing temperature ( F) 140 160 5: flow rate (gallhr) 20 30 The design and measured response are showm below. The response is an indicator of quality of 'grind fine:' (0 on the scale denotes a coarse coating, whereas 10 is a fine coating) A B C D Response 6.25 + 6.1 7.7: 6.75 6.25 + 5.25 + + + - + 7.00 + 5.50 + 5.25 + + + 6.50 (2) (1 pt) Determine the column of signs (level:) for flow rate. (1 pt) Determine main and 2-factor interaction effects (C) (1 pt) What does the estimate of factor _ give, ie, what are the aliases of factor 2? What does the estimate of interaction (13) give, ie , aliases of (13)? (1 pt) If you now ignore 3- and higher-order interactions, what do the estimates of factor _ and interaction (13) give? (1 pt) What is the resolution of the design? (f) (1 pt) What is the generator for the other half fraction? (3 pte) Which are the significant effects? State your assumptions, if any. (h) (3 pts) Discuss your conclusions, be., if you were to talk to plant personnel. how would you guide them to run the process, ie, what choices of levels are you going to suggest for the five factors, in order to achieve a higher (better, in this case) response, ie, how would you maximize your response? (Hint: marginal means plote!) (i) (3 pt:) The plant is currently using vertical type machine: Should the plant continue using vertical machines or replace them (at an additional cost) as an external consultant has recently suggested