[11] A process engineer is trving to improve the life of a cutting tool. He ran a 23 experiment using cutting speed {A}, metal hardness [B], and cutting angle {C} as the factors. The data from two replicates are shown in Table below: Replicate | || (1} 221 311 a 325 435 b 354 348 ab 552 472 c 440 453 ac 406 377' 95; 605 SOD gig/g 392 419 Run {D Do any of the three factors affect tool life? b. What combination of factor levels produces the longest tool life? c. Is there a combination of cutting speed and cutting angle that always gives good results regardless of metal hardness? [12) Four factors are thought to possiblyr influence the taste of a softdrink beverage: type of sweetener {A}, ratio of syrup to water {B}, carbonation level {C}, and temperature {D}. Each factor can be run at two levels, producing a 24 design. At each run in the design, samples of the beverage are given to a test panel consisting of 20 people. Each tester assigns a point score from 1 to 10 to the beverage. Total score is the response variable, and the objective is to find a formulation that maximized total score. Two replicates of this design are run, and the results are shown in Table below. Analyze the data and draw conclusions. \"1* Treatment REPl lCtE Combination | || {1} 188 195 a 172 180 b 179 187 oh 185 178 c 175 180 DC 183 178 89? 190 180 93:29 175 168 d 200 193 ad 17!] 178 bd 189 181 9112);}: 183 188 Cd 201 188 95:53 181 173 @533! 189 182 $39,911 178 182 Q3) An engineer has performed an experiment to study the effect of four factors on the surface roughness of a machined part. The factors (and their levels) are A = tool angle (12, 15), B = cutting fluid viscosity (300, 400), C = feed rate (10, 15 in/min), and D = cutting fluid cooler used (no, yes). The data from this experiment (with the factors coded to the usual +1, -1 levels) are shown in Table below: Surface Run A B C D Roughness 0.00340 N 0.00362 3 0.00301 4 X 0.00182 0.00280 X 0.00290 0.00252 0.00160 4 0.00336 10 0.00344 11 0.00308 12 0.00184 13 0.00269 14 0.00284 15 0.00253 16 + + 0.00163 a. Estimate the factor effects. Plot the effect estimates on a normal probability plot and select a tentative model. You can assume that the high order interaction (4way) is negligible and use it towards the estimation of error - The Sparsity of effect principle b. Fit the model identified in part (a) and analyze the residuals. Is there any indication of model inadequacy