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Dec 6, 2023

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DoE Online course. MECH 5750 Final Exam. – Quiz Option (A-E). Name_________________ Please answer questions Quiz version A, B, C, D or E depending on your student ID last (end) digit 1, 2 answer Quiz A | 3 answer Quiz B | 4, 5, 6 answer Quiz C | 7, 8 answer Quiz D | 9, 0 answer Quiz E 1. If you start with the bicycle hill climb problem in week 9 assignment, factor 6 was folded over to remove the confounding of other factors to factor 6, as shown in the notes. Note you do not have to calculate any values just note down the resulting interactions. Problem 1, Part 1. Please only answer one version depending on your last student ID digit (use right chart above showing the isolated interaction[s]). Please only write down the confounding interactions (no calculations values are required). A. If the DoE was folded with two factors at the same time (2 and 6), what is the confounding (aliasing) table? Average (1+1’) = Average (1-1’) = ______________ Average (2+2’) = Average (2-2’) = ______________ Average (3+3’) = Average (3-3’) = _______________ Average (4 +4’) = Average (4-4’) = _______________ Average (5+5’) = Average (5-5’) = _______________ Average (6+6’) = Average (6-6’) = ________________ Average (7+7’) = Average (7-7’) = ________________

Problem 1 Part 2 . All students Please answer this question for all versions (A, B, C, D, E) . If the DoE design team folded all factors at the same time (1-7), what is the confounding (aliasing) table? Show all factors and all interactions confounding (aliasing). Average (1+1’) = (2*3), (4*5), (6*7) Average (1-1’) = No confounding Average (2+2’) = (1*3), (4*6), (5*7) Average (2-2’) = No confounding Average (3+3’) = (1*2), (4*7), (5*6) Average (3-3’) = No confounding Average (4 +4’) = (1*5), (2*6), (3*7) Average (4-4’) = No confounding Average (5+5’) = (1*4), (2*7), (3*6) Average (5-5’) = No confounding Average (6+6’) = (1*7), (2*4), (3*5) Average (6-6’) = No confounding Average (7+7’) = (1*6), (2*5), (3*4) Average (7-7’) = No confounding Problem 2. (All Students answer All questions a – j) In an industrial waste treatment plant, metals are precipitated by mixing lime in a tank to produce metal hydroxides. Design an experiment to maximize the metal precipitation @Five factors at two levels 2 lime flows [FLOW] (10, 20 L/m) 2 mixing speeds [SPEED] (20 or 25 rpm) 2 tank levels [LVL] (50% or 100%) 2 mixing Times [MIX] (10, 20 rpm) 2 Effluent Temperatures [TEMP] (ambient, 50’F) Select best fit/smallest orthogonal array experiments and show column assignments (in numbers) only: a. Considering all interactions for the five factors at two levels: Array: L32 , Factor Assignments: Flow 1 , Speed 2 , LVL 4 , MIX 8 , TEMP 16 b. Ignore all interactions for the five factors at two levels: Array: L8 , Factor Assignments: Flow 1 , Speed 2 , LVL 4 , MIX 5 , TEMP 3 c. Considering 2 way interactions only among the five factors and ignoring all other interactions: Array: L16 Factor Assignments: Flow 1 , Speed 2 , LVL 4 , MIX 8 , TEMP 15 d. Considering only these two (two–way interactions) for the five factors, and ignoring all other interactions. Answer your versions only (A, B C D or E – Please circle your letter below ) A. [TEMP] x [MIX] and [TEMP] x [FLOW] B. SPEED x TEMP and SPEED x FLOW C. FLOW x MIX and FLOW x LVL D. MIX x LVL and Mix x TEMP E. TEMP x FLOW and TEMP x SPEED Array: L8 Factor Assignments: Flow: 4 , Speed: 1 , LVL: 6 , MIX: 7 , TEMP: 2

e. Considering only four factors at two levels: Flow, Speed, LVL and MIX, and consider all interactions Array: L16 , Factor Assignments: Flow: 1 , Speed: 2 , LVL: 4 , MIX: 8 f. Considering only four factors at two levels Flow, Speed, LVL and MIX, and ignore all interactions Array: L8 Factor Assignments: Flow 1 , Speed 2 , LVL 3 , MIX 4 g. Considering only four factors at two levels: Flow, Speed, LVL and MIX, and consider only two-way interactions while ignoring all others Array: L12 Factor Assignments: Flow 1 , Speed 2 , LVL 4 , MIX 7 h. Considering only three factors at two levels: Flow, Speed and LVL, and consider all interactions Array: L8 Factor Assignments: Flow 1 , Speed 2 , LVL 4 i. Considering only three factors at two levels: Flow, Speed and LVL, and ignore all interactions Array: L4 Factor Assignments: Flow 1 , Speed 2 , LVL 3 j. Considering only three factors at two levels: Flow, Speed and LVL, and consider only two- way interactions while ignoring all others Array: L8 Factor Assignments: Flow 1 , Speed 2 , LVL 4 Problem 3. (All Students answer All questions a – k). In an industrial waste treatment plant, metals are precipitated by mixing lime in a tank to produce metal hydroxides. Design an experiment to maximize the metal precipitation: Five factors at three levels. 3 lime flows [FLOW] (10, 20 or 30 L/m) 3 mixing speeds [SPEED] (20 or 25 or 35 rpm) 3 tank levels [LVL] (50% 75% or 100%) 3 mixing Times [MIX] (10, 20 or 30rpm) 3 Effluent Temperatures [TEMP] (ambient, 25 or 50’F) Select best fit/smallest orthogonal array experiments and show column assignments (in numbers) only: a Considering all 5 factors have three levels and ignore all interactions: Array: L27 Factor Assignments: Flow 1 , Speed 2 , LVL 3 , MIX 7 , TEMP 5 b. Considering all five factors with three levels and selecting 2 way interactions only among three selected factors (Flow Speed and LVL), while ignoring all other interactions: Array: L27 Factor Assignments: Flow 1 , Speed 2 , LVL 3 , MIX 7 , TEMP 8

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c. Considering only 3 factors with three levels (FLOW, SPEED, and LVL) and ignore all interactions Array: L9 Factor Assignments: Flow 1 , Speed 2 , LVL 3 d. Considering only 4 factors with three levels (FLOW, SPEED, LVL and MIX) and ignore all interactions Array: L9 Factor Assignments: Flow 1 , Speed 2 , LVL 3 , MIX 4 e. Considering only 4 factors with three levels (FLOW, SPEED, LVL and MIX) and consider all interactions. Array L81 f. Considering all 5 factors and you wanted to select a non-interacting array to reduce confusion Array: L12 Factor Assignments: Flow 1 , Speed 2 , LVL 3 , MIX 4 , TEMP 5 g. If all five factors had 4 levels, and ignore all interactions ( please select a two levels array only) Array: L16 Factor Assignments: Flow 1 , Speed 2 , LVL 3 , MIX 4 , TEMP 5 h. If two factors (Flow and Speed) had 4 levels and three factors (LVL, Mix and TEMP) had two levels and ignore all interactions ( please select a two levels array only) Array: L16 Factor Assignments: Flow 1 , Speed 2 , LVL 3 , MIX 4 , TEMP 5 i. If one factor (Flow) had 4 levels, the rest of the 4 factors at two levels, considering only 2-way interactions ( Please select a two levels array only) Array: L27 Factor Assignments: Flow 1 , Speed 2 , LVL 4 , MIX 7 , TEMP 15 j. If one factor (Flow) had 8 levels, the rest of the four factors at two levels, and ignore all interactions ( Please select a two levels array only) Array: L16 Factor Assignments: Flow 1 , Speed 2 , LVL 3 , MIX 7 , TEMP 5 k. If two factors (Flow and Speed) had 8 levels and three factors (LVL, Mix and TEMP) had two levels and ignore all interactions ( please select a two levels array only) Array: L8 Factor Assignments: Flow______, Speed______, LVL______, MIX______, TEMP______ Problem 4. In a waste treatment plant that precipitates metals by adding/mixing lime in a tank to the effluent stream to produce metal hydroxides. Design an experiment to minimize the metal precipitation. 2 lime flows [FLOW] (10, 20 L/m) 2 mixing speeds [SPEED] (20 or 25 rpm) 2 tank levels [LVL] (50% or 100%) 2 mixing Times [MIX] (10, 20 rpm) 2 Effluent Temperatures [TEMP] (ambient, 50’F]

For each answer (A, B, C, D or E), We want to repeat the experiment to investigate the effect of different conditions for the repetition noise factors I. Show typical repetition and level of noise factors to test all conditions (example O1S1F1 O1S1F2 etc….) II. For the preceding question I above, show a minimum set of repetitions (if possible) and levels of noise factors. If not possible, indicate no change. A. Use the following conditions (noise factors) as a guide for selecting the number of repetitions, since these noise factors are not under the control experiment design team: 3 Operators (O) - (Mike, Tim or Jim); 3 shifts (S) – Shift (day, night, graveyard) I. O1S1F1, O1S1F2, O1S2F1, O1S2F2, O2S1F1, O2S1F2, O2S2F1, O2S2F2 II. O1S1F1, O1S2F2, O2S1F2, O2S2F1

Problem 5. Please answer the questions below depending on your version (A – E). Design an experiment to study the best material for conformal coating. Select best fit/smallest orthogonal array experiments and show column assignments: Use 2 or 3 level arrays and you might assign more than one column to a factor with multiple levels Version A. 3 Material Types [M] 3M1, 3M2, GE1 3 Material mixing speeds [SP] (10, 20 or 25 rpm) 2 polymer specific gravities [SG] (.9 or 1.1) 1. (State your version here____) If you used the 3 factors at the levels chosen with two repetitions , fill in the blanks: Total # of Experiments (including two repetitions) _____, DoF of all Factors (M, SP, SG) _____, DoF of Error____, Total DoF_______ DoF of M_____; DoF of SP______, DoF of SG___, DoF of ALL Interactions ___________, 2. (State your version here___) Ignoring all interactions: Array ____ Factor Assignments: M____, SP____, SG__ 3. (State your version here____) Considering all interactions: Array _____ 4. (State your version here____) Considering 2 way interactions only Array _____ Factor Assignments: M_____, SP______, SG______ 5. (State your version here____) Considering the interaction of Material [M] x [SG] only and ignoring all other interactions between factors: Array _____ Factor Assignments: M_____, SP______, SG____ Problem 6. Minitab Questions. All Students answer all Questions. Please be brief and to the point, with one concise sentence answer. i. When you use Minitab plots for S/N for selecting the levels, which level would you select to minimize the outcome: Most positive level ii. How many formula choices does Minitab have in order to compute the S/N values? Please list all choices by name only (no formulas required). There are four formula choices listed as follows- a) Larger is better (maximizes the response) b) Nominal is best (based on standard deviations only) c) Nominal is best (based on means and standard deviations) d) Smaller is better (minimizes the response)

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iii. Describe the way Minitab allows for repetitions of the experiment, describe how it creates the experiment matrix based on the repetition types? Repetition of experiment is the measurements on the same item produced under a given set of conditions. If you have three factors with two levels each and you test all combinations of factor levels (full factorial design), one replicate of the entire design would have 8 runs (2 3 ). You can choose to do the design one time or have multiple repetitions with same levels iv. Describe the way Minitab allows for repetitions of the centerpoint, describe how it creates the experiment matrix based on the repetition types? a) When all factors are numeric and the design does not have blocks, Minitab adds the specified number of center points to the design. When it has blocks, Minitab adds the specified number of center points to each block. b) When all the factors in a design are text, center points cannot be added. c) When a combination of numeric and text factors is present and there is no true center to the design. Here when the center does not have blocks, Minitab adds the specified number of center points for each combination of the levels of the text factors. In total, for X text factors, Minitab adds 2X times as many center points. When the center has blocks, Minitab adds the specified number of center points for each combination of the levels of the text factors to each block. In each block, for X text factors, Minitab adds 2X times as many center points. v. When would you use the Optimizer in Minitab, and what does it provide for an output? (List the single most important output, no formulas please) vi. What is the meaning of the regression equation in Minitab (no formulas required)? Regression generates an equation that describes the relationship between one or more predictor variables and the response variable. Linear regression usually uses the ordinary least squares estimation method which derives the equation by minimizing the sum of the squared residuals. vii. What is the meaning of the fit in Minitab (no formulas required)? After responses and a model can be fit to the data means to generate graphs to assess the effects. The results from the fitted model and graphs determine which of the factors are important. viii. How does Minitab compute predicted values (in Mean and S/N) in the Taguchi analysis (describe how it does, no formulas or examples), and how do you use the data provided from the predicted values for analyzing the experiment?

ix. What is the Minitab maximum P-Value for a factor to be significant in the analysis of Coefficient P = 67% x. What is the Minitab maximum P-Value for a factor to be significant in the ANOVA analysis P = 0.05 xi. What is the recommended Minitab minimum for R-sq (R squared) after the ANOVA analys 95% xii. What is the purpose for R-sq (pred) = R squared predicted - after the ANOVA analysis Predictive R 2 helps to determine how well the model predicts responses for new observations. xiii. What is the difference between R-sq (R squared) and R –sq (adj = adjusted) R 2 adjusted is the percentage of response variable variation explained by its relationship with predictor variables, adjusted for the number of predictors in the model. Adjustment is important because the R 2 for any model will always increase when a new term is added. A model with more terms seems to have a better fit because it has more terms.