IE563_HW4

IE 563: Experimental Design Homework #4 Problem 1 An experiment is conducted to determine the service time (in minutes) at two different banking companies. Factors considered are: day of the week (Monday through Saturday), teller [fixed] (1 or 2), and Bank (A or B). The data is shown in the randomized run order below. (Nested Slide 3) Bank Teller Weekday Service Time (min) Bank Teller Weekday Service Time (min) A 1 Monday 2.793 B 1 Monday 4.9266 A 1 Tuesday 0.987 B 1 Tuesday 3.3894 A 1 Wednesday 1.722 B 1 Wednesday 1.9152 A 1 Thursday 3.066 B 1 Thursday 4.0824 A 1 Friday 6.174 B 1 Friday 4.0572 A 1 Saturday 5.754 B 1 Saturday 5.229 A 2 Monday 6.951 B 2 Monday 2.7594 A 2 Tuesday 2.016 B 2 Tuesday 0.63 A 2 Wednesday 1.47 B 2 Wednesday 0.5796 A 2 Thursday 4.851 B 2 Thursday 1.0962 A 2 Friday 3.066 B 2 Friday 1.0836 A 2 Saturday 4.053 B 2 Saturday 1.1592 A 1 Monday 3.36 B 1 Monday 5.985 A 1 Tuesday 4.746 B 1 Tuesday 2.4192 A 1 Wednesday 5.334 B 1 Wednesday 2.9358 A 1 Thursday 1.659 B 1 Thursday 3.402 A 1 Friday 10.227 B 1 Friday 5.3172 A 1 Saturday 9.765 B 1 Saturday 4.3848 A 2 Monday 9.219 B 2 Monday 2.5578 A 2 Tuesday 4.263 B 2 Tuesday 2.583 A 2 Wednesday 4.242 B 2 Wednesday 2.5326 A 2 Thursday 2.268 B 2 Thursday 3.7926 A 2 Friday 6.069 B 2 Friday 3.2004 A 2 Saturday 9.345 B 2 Saturday 4.1076 a) Analyze the data using the appropriate model.

This is the output for the GLM on a nested model. b) Draw conclusions based on your analysis; including selection of levels appropriate for the application. Bank, Weekday have a significant effect on service time, but the tellers nested at each bank do not. (similar service by tellers at the same bank, but not between the banks themselves). Residual graphs look good. Based on the Tukey test to minimize service time I would go to Bank B and a Wednesday.

Problem 2 A researcher is interested in the hardness of steel bars treated with four coatings (1, 2, 3, and 4) at four furnace temperatures 350 o F, 375 o F, 400 o F, and 425 o F . The furnace is set to a temperature and four steel bars (one with each coating type) are put in the furnace and heated. The following data are shown in the actual run order. Temperatur e Coating Corrosion Resistanc e Temperatur e Coating Corrosion Resistanc e 350 2 192 400 4 232 350 3 177 400 3 215 350 1 148 400 2 222 350 4 178 400 1 251 375 1 145 375 4 302 375 3 184 375 1 182 375 4 182 375 3 186 375 2 191 375 2 208 400 3 142 425 3 482 400 1 148 425 2 451 400 2 124 425 4 398 400 4 189 425 1 458 425 1 530 350 1 163 425 4 482 350 4 196 425 3 516 350 2 219 425 2 445 350 3 169 a) Analyze the data using the appropriate model. Since this is not a CRD since 4 bars are put into the furnace at a given temperature at the same time, but factors are not nested within each other we use a split plot model.

b) Draw conclusions based on your analysis; i.e. do temperature and/or coating type have a significant effect on hardness? Since the residual plots look good we go back to the analysis of variance and see that only Temperature is the only significant factor in determining corrosion resistance. c) Which temperature and coating would you choose to maximize hardness? Since it’s a split plot we can use the means to determine the levels to use. Coat 4 combined with 425-degree furnace temperature produces the best corrosion resistance

Problem 3 An experiment is designed to study pigment reflectance in paint. We are interested in the effect of mixing technique and paint application method on the percentage reflectance of pigment. Three different mixing techniques (A, B, C) and three application methods (brushing, spraying, rolling) of a particular pigment are studied. The procedure consists of preparing the paint using a particular mixing technique and then applying that mix to a panel using the three application methods. The experiment is conducted over 4 days and the data (% reflectance) obtained follow. Day Method Mix Tech. Reflect. Day Method Mix Tech. Reflect. 1 Spray B 43.6 3 Brush C 31.6 1 Roll A 56.1 3 Roll B 32.2 1 Roll C 46 3 Spray A 39.3 1 Spray C 44 3 Spray C 33 1 Brush B 41.2 3 Brush B 29.5 1 Roll B 45.4 3 Spray B 30.6 1 Spray A 54.5 3 Roll A 39.8 1 Brush C 42.3 3 Brush A 38.6 1 Brush A 52 3 Roll C 34.8 2 Brush C 38.5 4 Brush C 38.7 2 Spray C 41.2 4 Spray B 37.5 2 Brush B 38.6 4 Roll B 39.4 2 Spray B 40.5 4 Spray A 48.1 2 Roll C 43.1 4 Brush A 47.3 2 Roll B 41.7 4 Roll A 48.8 2 Spray A 52 4 Spray C 40.5 2 Brush A 48.4 4 Roll C 42.6 2 Roll A 53.1 4 Brush B 36.2 a) Analyze the data using the appropriate model. This model is a split plot with a block on Day.