DoE Final_2024(1)
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DoE course. MECH 5750 Final Exam. – Quiz Option (0-9) __________Name___________________
Please answer questions Quiz version that matched your student ID last (end) digit
DoE course. MECH 5750 Final Exam. – Quiz Option (0-9) __________Name___________________
Problem 1. (All Students answer All questions a – k)
½ point each question (6 points total) In an industrial waste treatment plant, metals are precipitated by mixing lime in a tank to produce metal hydroxides. Use only two levels orthogonal arrays
Design an experiment to study 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 _____ Factor Assignments: Flow______, Speed______, LVL______, MIX______, TEMP______
b.
Considering only 2-way interactions only among the five factors and ignoring all other interactions:
Array _____ Factor Assignments: Flow______, Speed______, LVL______, MIX______, TEMP______
c.
Ignore all interactions for the five factors at two levels:
Array _____ Factor Assignments: Flow______, Speed______, LVL______, MIX______, TEMP______
d.
If you added one factor Tank Width, and you decided to have a saturated (screening) experiment for the six factors
Array ___ Factors: Flow____, Speed____, LVL____, MIX____TEMP ____Width ____
e.
If you added one factor Tank Width, and you decided to have a half factorial expt. for the six factors
Array ___ Factors: Flow____, Speed____, LVL____, MIX____TEMP ____Width ____
f.
If you added three factors: Tank Width, Height Depth and considering Flow to be the most important factor and all other seven factors interact to it, while ignoring all other interactions:
Array ___ Factors: Flow____, Speed____, LVL____, MIX____TEMP ____Width ____Height ____Depth____
g.
Please insert the interactions for only one linear graph below, if your last digit is odd, complete the figure to the left, is your last digit is even complete the figure to the right 11
12
5 8 10
6 4
7
8
9 4 2
10 12
MECH 5750 DoE Final 1
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DoE course. MECH 5750 Final Exam. – Quiz Option (0-9) __________Name___________________
Please answer questions Quiz version that matched your student ID last (end) digit
h.
Considering only these two (two–way interactions) for the five factors, and ignoring all other interactions. Answer your versions only (
Please circle or highlight your ID # below
) – (1 point)
ID 0 - FLOW x MIX and FLOW x LVL
ID 1 - MIX x LVL and Mix x TEMP
ID 2 - TEMP x FLOW and TEMP x SPEED
ID 3 - SPEED x TEMP and SPEED x FLOW
ID 4 - TEMP x MIX and TEMP x FLOW
ID 5 - TEMP x MIX and TEMP x FLOW
ID 6 - SPEED x TEMP and SPEED x FLOW
ID 7 - FLOW x MIX and FLOW x LVL
ID 8 - MIX x LVL and Mix x TEMP
ID 9 - TEMP x FLOW and TEMP x SPEED
Array _____ Factor Assignments: FLOW______, SPEED______, LVL______, MIX______, TEMP______
i.
Considering Flow with four levels and the rest of the 4 factors with two levels, ignore all interactions Array _____ Factor Assignments: Flow______, Speed______, LVL______, MIX______, TEMP______
j.
Considering all 5 factors with two levels and you select a non-interacting (Plackett-Burman) array Array _____ Factor Assignments: Flow______, Speed______, LVL______, MIX______, TEMP______
k.
Show division of L8 into two half fraction L4s?
MECH 5750 DoE Final 2
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DoE course. MECH 5750 Final Exam. – Quiz Option (0-9) __________Name___________________
Problem 2. (All Students answer All questions a – f)
. In an industrial waste treatment plant, metals are precipitated by mixing lime in tanks to produce metal hydroxides. Design experiment to study metal precipitation.1
point each question (6 points total)
Five factors at three levels (parts a - f). 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 only 4 factors with three levels (FLOW, SPEED, LVL and MIX) and consider all interactions Array _____ b. Considering all 5 factors with three levels and selecting 2-way interactions only among three selected factors (Flow Speed and LVL), while ignoring all other interactions:
Array _____ Factor Assignments: Flow______, Speed______, LVL______, MIX______, TEMP______ c. Considering all 5 factors with three levels and ignore all interactions: Array _____ Factor Assignments: Flow______, Speed______, LVL______, MIX______, TEMP______
d. Considering only 3 factors with three levels (FLOW, SPEED, and LVL) and ignore all interactions Array _____ Factor Assignments: Flow______, Speed______, LVL______
e. Considering only 4 factors with three levels (FLOW, SPEED, LVL and MIX) and ignore all interactions Array _____ Factor Assignments: Flow______, Speed______, LVL______, MIX________
f. Considering all 5 factors with three levels and you select a non-interacting (Plackett-Burman) array Array _____ Factor Assignments: Flow______, Speed______, LVL______, MIX______, TEMP______
MECH 5750 DoE Final 3
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DoE course. MECH 5750 Final Exam. – Quiz Option (0-9) __________Name___________________
Problem 3. Please only answer the version that matches your UML last Digit
. 2 point each question I/II
For each answer (0-9), We want to repeat an experiment to investigate the effect of different conditions for the repetition of noise factors.
You do not have to show all combinations, just the total # experiments, Example
. I.
Show typical repetition and level of noise factors to test all conditions (example for three factors at two
levels:
three factors: operators (O), shifts (S) and Forman (F) you should show L8 - 8 repetitions
: O1S1F1 O1S1F2 O1S2F1 O1S2F2 O2S1F1 O2S1F2 O2S2F1 O2S2F2 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: for three factors, you can ignore interactions and choose the smaller array to fit three factors: L4- 4
repetitions
- O1S1F1 O1S2F2 O2S1F2 O2S2F1
(4 points total). Be careful if the number of Factor levels are not the same, it does not follow the example above 0.
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
2 Operators (O) - 2 shifts (S) 1.
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:
2 Operators (O) - 2 shifts (S) – 2 Forepersons (F)
2.
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:
2 Operators (O) - 2 shifts (S) – 2 Forepersons (F) – 2 Machines (M)
3.
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) - 2 shifts (S) 4.
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) - 3 shifts (S) 5.
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) - 3 shifts (S)
- 3 foremen (F) 6.
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) - 3 shifts (S) - 3 foremen (F) – 3 Machines (M) 7.
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:
2 Operators (O) - 3 shifts (S) 8.
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:
4 Operators (O) - 2 shifts (S) 9.
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:
4 Operators (O) - 4 shifts (S) MECH 5750 DoE Final 4
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DoE course. MECH 5750 Final Exam. – Quiz Option (0-9) __________Name___________________
Problem 4 Minitab Questions
. All Students answer all Questions
. 3/4 point each question. (9 points total) 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______________, or Most negative level______________
ii.
When you use Minitab plots for Means for selecting the levels, which level would you select to minimize
the outcome: Most positive level______________, or Most negative level______________
iii.
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). iv.
What is the formula and recommended Minitab minimum for R-sq % (R squared %) after ANOVA analysis? Formula__________ ______ %_____
v.
When do you use the Optimizer versus the Predictor in Minitab (one short and concise reason only)?
vi.
How is the CenterPoint design handled in Minitab, and how do you know that you did it correctly (
Please Provide 4 instances
) using the factor plot function? Please be short and concise in your answer. vii.
If an L8 was repeated three times in Minitab, how should you design it and what methods do you use for
model reduction and pooling in ANOVA analysis in Minitab as opposed to single repetition? Please be short and concise in your answer. viii.
Show how Minitab constructs the regression equation
for an L8 if only factors 1 and 2, as well as three-way interaction 1*2*4 were significant using information from coefficients analysis and ANOVA?
ix.
List 3 different instances
to determine from Minitab Analysis that a factor is Significant. x.
If you used the foldover techniques
in Minitab, list the steps you would take to isolate the top two most important factors?
xi.
What two major contribution Taguchi made to DoE regarding interactions, what are the names of two tools
he used?
xii.
What major contribution Taguchi made to DoE regarding variability Analysis, what are the names of two tools he used?
xiii.
What are resolutions III, IV and V designs, give examples of each using orthogonal arrays?
xiv.
What is the symbol 2
7-3
V
means, give an example?
xv.
What is the main difference between Taguchi approach to DoE versus Classical DoE as outlined by Minitab? xvi.
Describe briefly when to use three level Factors versus two level factors in orthogonal experiments, please give two reasons
? MECH 5750 DoE Final 5
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