IE604_Project_Brier_Golla

2014

Margaret G. Brier

Anjaneya Ravi Teja Golla

IE 604, Spring’14

DOE on Time of Flight of Paper Airplanes


1 | P a g e

Contents

Objective of the Project ................................................................................................................................ 3

Factors and Levels ........................................................................................................................................ 3

The Response Variable ................................................................................................................................. 3

Literature Review .......................................................................................................................................... 3

Design of Experiment ................................................................................................................................... 4

Experimental Procedure ............................................................................................................................ 5

Probability Test ....................................................................................................................................... 10

First Run Results ..................................................................................................................................... 10

Attainment of the Maximum R-Square (Adjusted) ................................................................................. 15

Normal Distribution ................................................................................................................................ 16

Run Results with Maximum R-square .................................................................................................... 17

Power Curve................................................................................................................................................ 22

Analysis of Results ..................................................................................................................................... 23

Main Effects Plot .................................................................................................................................... 23

Interactions Plot: ..................................................................................................................................... 24

Contour and Surface Plots: ..................................................................................................................... 25

Conclusions and Recommendations ........................................................................................................... 26

Regression Equation ................................................................................................................................... 26

References ................................................................................................................................................... 27

Figures

Figure 1: Random Distribution of the Data ................................................................................................ 10

Figure 2: Half Normal Plot for Original Data ............................................................................................. 11

Figure 3: Pareto Chart for Original Data .................................................................................................... 11

Figure 4: Residual Plots for Original Data .................................................................................................. 12

Figure 5: Residuals vs. Angle Thrown ........................................................................................................ 12

Figure 6: Residuals vs. Person Throwing ................................................................................................... 13

Figure 7: Residuals vs. Type of Fold .......................................................................................................... 13

Figure 8: Residuals vs. Size of Paper .......................................................................................................... 14

Figure 9: Residuals vs. Type of Paper ........................................................................................................ 14

Figure 10: Normal Plots for Original Data ................................................................................................. 15

Figure 11 Varying R-Square (Adjusted) values .......................................................................................... 16

Figure 12: Residual Plots of the Data for Maximum R-squared ................................................................. 17


2 | P a g e

Figure 13: Half Normal Plot for the Data with Maximum R-squared ........................................................ 18

Figure 14: Pareto Chart for the Data with Maximum R-squared ................................................................ 18

Figure 15: Residual Plots for Data with Maximum R-squared ................................................................... 19

Figure 16: Residuals vs. Angle For Maximum R-Squared ......................................................................... 19

Figure 17: Residuals vs. Person Throwing for Maximum R-Squared ........................................................ 20

Figure 18: Residuals vs. Type of Fold for Maximum R-Squared ............................................................... 20

Figure 19: Residuals vs. Size of Paper for Maximum R-Squared .............................................................. 21

Figure 20: Residuals vs. Type of Paper for Maximum R-Squared ............................................................. 21

Figure 21: Estimated Effects and Coefficients for Time ............................................................................ 22

Figure 22 Power Curve ............................................................................................................................... 23

Figure 23: Main Effects Plot ....................................................................................................................... 24

Figure 24: Interaction plot for Response - Time ......................................................................................... 24

Figure 25 Contour Plot of Time .................................................................................................................. 25

Figure 26 Surface Plot of Time ................................................................................................................... 26


3 | P a g e

Objective of the Project

To estimate and analyze the factors effecting time of flight of a paper airplane.

To make a clear recommendation regarding the most favorable settings that will maximize the

time of flight.

Factors and Levels Below are listed the factors and their levels. They were chosen because we think they may play vital role

in the time of flight of paper airplanes. There are 5 factors and 2 levels for each factor.

a. The type of paper

i. Letter paper

ii. Résumé Paper

b. The size of paper

i. Large - 8.5 in x 11 in

ii. Medium - 7.2 in x 9.7

c. The type of fold

i. Fold A – Pointy Nose

ii. Fold B – Flat Nose

d. Person throwing airplane

i. Person A

ii. Person B

e. Angle thrown

i. 00 Parallel to ground

ii. 45° above Parallel

It is possible that other crucial factors may impact the time of flight of paper airplanes. For our purposes,

we have assumed that the effects of temperature, wind, wear of the paper, energy levels of the individuals,

and reaction time of individuals pressing start and stop on the timer are negligible. To reduce the effects

of these factors we did all testing indoors and utilized a standard countdown before throwing the

airplanes.

The Response Variable As stated before, the objective of the study is to determine the desired settings for each factor in order to

achieve the maximum time of flight of paper airplanes. Hence, the response variable is time represented

by the variable Z (in Contour and Surface Plots) and expressed in units of seconds.

Literature Review The experiment which we conduct will be based on the research made by Daniel Z. Meyer and Allison

Antink Meyer in their work “Two Paper Airplane Design Challenges: Customizing for Different

Learning Objectives.” We are looking at factors the factors they did not consider, like the type of paper

used, type of fold and also the length of the wings, as we conduct Design of Experiments and also

perform ANOVA and regression.


4 | P a g e

Design of Experiment There are 5 factors with 2 levels, so we have a 2

5 factorial design, which translates into a full factorial

experiment with 32 responses. To ensure that the data is good we took 2 replications each and did the

experiments in a random order to eliminate any bias. The following is a table showing the experiments

conducted and the random order they were conducted in.

Standard Run

Order

Random Run

Order

Type of

Paper

Size of

Paper

Type of

Fold

Person

throwing

airplane

Angle

thrown

1 1 Letter Large A A 0

2 28 Letter Large A A 45°

3 4 Letter Large A A 0

4 41 Letter Large A A 45°

5 24 Letter Large A B 0

6 14 Letter Large A B 45°

7 33 Letter Large A B 0

8 21 Letter Large A B 45°

9 35 Letter Large B A 0

10 56 Letter Large B A 45°

11 64 Letter Large B A 0

12 10 Letter Large B A 45°

13 46 Letter Large B B 0

14 20 Letter Large B B 45°

15 52 Letter Large B B 0

16 16 Letter Large B B 45°

17 2 Letter Medium A A 0

18 29 Letter Medium A A 45°

19 45 Letter Medium A A 0

20 25 Letter Medium A A 45°

21 12 Letter Medium A B 0

22 39 Letter Medium A B 45°

23 32 Letter Medium A B 0

24 18 Letter Medium A B 45°

25 38 Letter Medium B A 0

26 50 Letter Medium B A 45°

27 58 Letter Medium B A 0

28 63 Letter Medium B A 45°

29 7 Letter Medium B B 0

30 36 Letter Medium B B 45°

31 23 Letter Medium B B 0

32 15 Letter Medium B B 45°

33 62 Résumé Large A A 0

34 11 Résumé Large A A 45°

35 9 Résumé Large A A 0

36 6 Résumé Large A A 45°

37 43 Résumé Large A B 0

38 34 Résumé Large A B 45°


5 | P a g e

39 60 Résumé Large A B 0

40 37 Résumé Large A B 45°

41 48 Résumé Large B A 0

42 47 Résumé Large B A 45°

43 57 Résumé Large B A 0

44 3 Résumé Large B A 45°

45 42 Résumé Large B B 0

46 17 Résumé Large B B 45°

47 31 Résumé Large B B 0

48 51 Résumé Large B B 45°

49 44 Résumé Medium A A 0

50 55 Résumé Medium A A 45°

51 53 Résumé Medium A A 0

52 40 Résumé Medium A A 45°

53 30 Résumé Medium A B 0

54 19 Résumé Medium A B 45°

55 13 Résumé Medium A B 0

56 61 Résumé Medium A B 45°

57 8 Résumé Medium B A 0

58 27 Résumé Medium B A 45°

59 5 Résumé Medium B A 0

60 22 Résumé Medium B A 45°

61 49 Résumé Medium B B 0

62 54 Résumé Medium B B 45°

63 26 Résumé Medium B B 0

64 59 Résumé Medium B B 45°

Table 1: Order of Experiments

Experimental Procedure

To conduct the experiment we first selected the factors and made the airplanes.


6 | P a g e

Fold A was found from http://www.youtube.com/watch?v=i8qxExknDSw.

Fold B was found from http://www.youtube.com/watch?v=JiqjxgBQH_Y.

http://www.youtube.com/watch?v=i8qxExknDSw

http://www.youtube.com/watch?v=JiqjxgBQH_Y


7 | P a g e

After our planes were ready to fly, we brought them to the Campus Centre Atrium to test and successfully

conducted the experiments as per the random run order generated. After running the experiments we

entered our data into Minitab and did an analysis of a 2-factorial DOE. The following is a table showing

the results from the experiments conducted.

Standard

Run Order

Random

Run Order

Type of

Paper

Size of

Paper

Type of

Fold

Person

throwing

airplane

Angle

thrown

Time in

the Air

(sec)

1 1 Letter Large A A 0 1.56

17 2 Letter Medium A A 0 1.13

44 3 Résumé Large B A 45° 1.53

3 4 Letter Large A A 0 1.63

59 5 Résumé Medium B A 0 0.52

36 6 Résumé Large A A 45° 1.89

29 7 Letter Medium B B 0 0.91

57 8 Résumé Medium B A 0 0.76

35 9 Résumé Large A A 0 1.56

12 10 Letter Large B A 45° 1.42

34 11 Résumé Large A A 45° 1.45

21 12 Letter Medium A B 0 1.72

55 13 Résumé Medium A B 0 1.8

6 14 Letter Large A B 45° 1.42

32 15 Letter Medium B B 45° 2.3

16 16 Letter Large B B 45° 1.8

46 17 Résumé Large B B 45° 2

24 18 Letter Medium A B 45° 1.8

54 19 Résumé Medium A B 45° 1.3

14 20 Letter Large B B 45° 1.53


8 | P a g e

8 21 Letter Large A B 45° 1.93

60 22 Résumé Medium B A 45° 0.75

31 23 Letter Medium B B 0 2.28

5 24 Letter Large A B 0 2.33

20 25 Letter Medium A A 45° 2

63 26 Résumé Medium B B 0 2.02

58 27 Résumé Medium B A 45° 1.23

2 28 Letter Large A A 45° 0.99

18 29 Letter Medium A A 45° 0.99

53 30 Résumé Medium A B 0 1.39

47 31 Résumé Large B B 0 1.84

23 32 Letter Medium A B 0 1.34

7 33 Letter Large A B 0 2.25

38 34 Résumé Large A B 45° 2.1

9 35 Letter Large B A 0 1.15

30 36 Letter Medium B B 45° 2.21

40 37 Résumé Large A B 45° 2

25 38 Letter Medium B A 0 0.79

22 39 Letter Medium A B 45° 1.72

52 40 Résumé Medium A A 45° 0.91

4 41 Letter Large A A 45° 1.4

45 42 Résumé Large B B 0 1.93

37 43 Résumé Large A B 0 2.03

49 44 Résumé Medium A A 0 0.8

19 45 Letter Medium A A 0 1.12


9 | P a g e

13 46 Letter Large B B 0 1.53

42 47 Résumé Large B A 45° 1.48

41 48 Résumé Large B A 0 1.39

61 49 Résumé Medium B B 0 1.34

26 50 Letter Medium B A 45° 0.84

48 51 Résumé Large B B 45° 1.93

15 52 Letter Large B B 0 1.93

51 53 Résumé Medium A A 0 1.03

62 54 Résumé Medium B B 45° 2.36

50 55 Résumé Medium A A 45° 0.92

10 56 Letter Large B A 45° 1.2

43 57 Résumé Large B A 0 1.42

27 58 Letter Medium B A 0 0.85

64 59 Résumé Medium B B 45° 2.04

39 60 Résumé Large A B 0 1.75

56 61 Résumé Medium A B 45° 1.5

33 62 Résumé Large A A 0 1.63

28 63 Letter Medium B A 45° 1.53

11 64 Letter Large B A 0 0.99

Table 2: Experimental Results

To conduct the DOE successfully we have converted the levels of the factors into their respective numeric

terms by assigning the following values.

Factor Levels

Numeric

Levels

Type of Paper Letter Paper 1

Resume

Paper -1

Size of Paper Large 1

Medium -1


10 | P a g e

Type of Fold A 1

B -1

Person

Throwing

A 1

B -1

Angle thrown 0° 0°

45° 45°

Table 3: Numeric Values Assigned

Probability Test

Before running the experiments in MINITAB 15 we conducted the probability test, just to make sure that

our Data is randomly distributed. It was confirmed by the following graph, with shows that the P-Value is

0.244, which clearly means that the data is Normally Distributed.

Figure 1: Random Distribution of the Data

First Run Results

The following are plots generated in the first run, which included all the factors and their interactions

without any of them removed.


11 | P a g e

Figure 2: Half Normal Plot for Original Data

Figure 3: Pareto Chart for Original Data

9876543210

98

95

90

85

80

70

60

50

40

30

20

10

0

Absolute Standardized Effect

Pe

rce

nt

A Ty pe of Paper

B Size of Paper

C Ty pe of Fold

D Person Throw ing

E A ngle

Factor Name

Not Significant

Significant

Effect Type

CE

BE

AB

D

B

Half Normal Plot of the Standardized Effects(response is Time (s), Alpha = 0.05)

ABCDEACDE

ABCAEADDE

ACDBCEADE

ABCDBDECDEACE

ABDEC

BCDEAC

ABDE

ABCEBCBD

BCDABECDCEBEAB

BD

9876543210

Te

rm

Standardized Effect

2.037

A Ty pe of Paper

B Size of Paper

C Ty pe of Fold

D Person Throw ing

E A ngle

Factor Name

Pareto Chart of the Standardized Effects(response is Time (s), Alpha = 0.05, only 30 largest effects shown)


12 | P a g e

Figure 4: Residual Plots for Original Data

Figure 5: Residuals vs. Angle Thrown

0.80.40.0-0.4-0.8

99.9

99

90

50

10

1

0.1

Residual

Pe

rce

nt

2.52.01.51.00.5

0.8

0.4

0.0

-0.4

-0.8

Fitted Value

Re

sid

ua

l

0.60.40.20.0-0.2-0.4-0.6

24

18

12

6

0

Residual

Fre

qu

en

cy

605550454035302520151051

0.8

0.4

0.0

-0.4

-0.8

Observation Order

Re

sid

ua

l

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Time (s)

50403020100

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

Angle

Re

sid

ua

l

Residuals Versus Angle(response is Time (s))


13 | P a g e

Figure 6: Residuals vs. Person Throwing

Figure 7: Residuals vs. Type of Fold

1.00.50.0-0.5-1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

Person Throwing

Re

sid

ua

l

Residuals Versus Person Throwing(response is Time (s))

1.00.50.0-0.5-1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

Type of Fold

Re

sid

ua

l

Residuals Versus Type of Fold(response is Time (s))


14 | P a g e

Figure 8: Residuals vs. Size of Paper

Figure 9: Residuals vs. Type of Paper

1.00.50.0-0.5-1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

Size of Paper

Re

sid

ua

l

Residuals Versus Size of Paper(response is Time (s))

1.00.50.0-0.5-1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

Type of Paper

Re

sid

ua

l

Residuals Versus Type of Paper(response is Time (s))


15 | P a g e

Figure 10: Normal Plots for Original Data

Attainment of the Maximum R-Square (Adjusted)

After removing the interactions one by one in the order of the least value, and continuously running the

DOE and observing the variations of the R-Square Adjusted values, which was increasing as we proceed.

We finally got the maximum R-Square Adjusted value and which can be observed from the results shown

below.

5.02.50.0-2.5-5.0-7.5

99

95

90

80

70

60

50

40

30

20

10

5

1

Standardized Effect

Pe

rce

nt

A Ty pe of Paper

B Size of Paper

C Ty pe of Fold

D Person Throw ing

E A ngle

Factor Name

Not Significant

Significant

Effect Type

CEBE

AB

D

B

Normal Plot of the Standardized Effects(response is Time (s), Alpha = 0.05)


16 | P a g e

Figure 11 Varying R-Square (Adjusted) values

Normal Distribution

After maximizing the R-squared we needed to check that our data was still normally distributed. We did

this by looking at the 4-in-1 Residual Plots for Time(s), Figure 12. The bottom left plot shows the

histogram of the residuals. Because the plot is a bell curve, the data is normally distributed.

Terms

DeletedS Press R-squared R-squared (predicted) R-squared (adjusted)

0.298415 11.3986 79.39 17.56 59.42

ABCDE 0.293869 10.719 79.39 22.47 60.65

ACDE 0.289538 10.0993 79.38 26.96 61.8

ABC 0.285503 9.53922 79.37 31.01 62.86

AE 0.281796 9.035 79.32 34.65 63.82

DE 0.278283 8.57298 79.28 37.99 64.71

AD 0.274913 8.14643 79.23 41.08 65.56

ACD 0.271697 7.75291 79.18 43.93 66.36

BCE 0.268646 7.39027 79.12 46.55 67.11

ADE 0.26582 7.05915 79.05 48.94 67.8

ABCD 0.263387 6.76549 78.93 51.07 68.39

BDE 0.26126 6.50186 78.77 52.97 68.9

CDE 0.259279 6.25808 78.61 54.74 69.37

ACE 0.257371 6.0293 78.44 56.39 69.82

ABDE 0.256115 5.84081 78.18 57.76 70.11

BCDE 0.255961 5.70964 77.73 58.7 70.15

AC 0.257425 5.65484 76.99 59.1 69.8

ABD 0.260174 5.65836 76.01 59.08 69.16

ABCE 0.266041 5.79814 74.4 58.06 67.75

BC 0.273067 5.98864 72.5 56.69 66.02

BD 0.280284 6.18803 70.45 55.24 64.2

BCD 0.287321 6.37996 68.35 53.86 62.38

ABD 0.294367 6.5727 66.16 52.46 60.52


17 | P a g e

Figure 12: Residual Plots of the Data for Maximum R-squared

Run Results with Maximum R-square

The following are plots describing the data after removing the non-significant effects, resulting in the

maximum R-squared (adjusted) value.

0.50.0-0.5-1.0

99.9

99

90

50

10

1

0.1

Residual

Pe

rce

nt

2.01.51.00.5

0.5

0.0

-0.5

Fitted Value

Re

sid

ua

l0.60.40.20.0-0.2-0.4-0.6-0.8

20

15

10

5

0

Residual

Fre

qu

en

cy

605550454035302520151051

0.5

0.0

-0.5

Observation Order

Re

sid

ua

l

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Time (s)


18 | P a g e

Figure 13: Half Normal Plot for the Data with Maximum R-squared

Figure 14: Pareto Chart for the Data with Maximum R-squared

1086420

98

95

90

85

80

70

60

50

40

30

20

10

0

Absolute Standardized Effect

Pe

rce

nt

A Ty pe of Paper

B Size of Paper

C Ty pe of Fold

D Person Throw ing

E A ngle

Factor Name

Not Significant

Significant

Effect Type

BCDABE

CE

CD

BE

BD

AB

D

B

Half Normal Plot of the Standardized Effects(response is Time (s), Alpha = 0.05)

A

C

AC

ABD

E

ABCE

BC

BD

BCD

ABE

CD

CE

BE

AB

B

D

1086420

Te

rm

Standardized Effect

2.01

A Ty pe of Paper

B Size of Paper

C Ty pe of Fold

D Person Throw ing

E A ngle

Factor Name

Pareto Chart of the Standardized Effects(response is Time (s), Alpha = 0.05)


19 | P a g e

Figure 15: Residual Plots for Data with Maximum R-squared

Figure 16: Residuals vs. Angle For Maximum R-Squared

50403020100

0.50

0.25

0.00

-0.25

-0.50

-0.75

Angle

Re

sid

ua

l

Residuals Versus Angle(response is Time (s))


20 | P a g e

Figure 17: Residuals vs. Person Throwing for Maximum R-Squared

Figure 18: Residuals vs. Type of Fold for Maximum R-Squared

1.00.50.0-0.5-1.0

0.50

0.25

0.00

-0.25

-0.50

-0.75

Person Throwing

Re

sid

ua

l

Residuals Versus Person Throwing(response is Time (s))

1.00.50.0-0.5-1.0

0.50

0.25

0.00

-0.25

-0.50

-0.75

Type of Fold

Re

sid

ua

l

Residuals Versus Type of Fold(response is Time (s))


21 | P a g e

Figure 19: Residuals vs. Size of Paper for Maximum R-Squared

Figure 20: Residuals vs. Type of Paper for Maximum R-Squared

1.00.50.0-0.5-1.0

0.50

0.25

0.00

-0.25

-0.50

-0.75

Size of Paper

Re

sid

ua

l

Residuals Versus Size of Paper(response is Time (s))

1.00.50.0-0.5-1.0

0.50

0.25

0.00

-0.25

-0.50

-0.75

Type of Paper

Re

sid

ua

l

Residuals Versus Type of Paper(response is Time (s))


22 | P a g e

Figure 21: Estimated Effects and Coefficients for Time

Power Curve In order to determine the power of the experiment conducted we have run the Power curve test. The

following is the result of our power curve test.

Power and Sample Size 2-Level Factorial Design

Alpha = 0.05 Assumed standard deviation = 0.255961

Factors: 5 Base Design: 5, 8

Blocks: none

Number of terms omitted from model: 6

Including a term for center points in model.

Center Total

Points Reps Runs Power Effect

1 2 17 0.95 0.496886


23 | P a g e

0.500.250.00-0.25-0.50

1.0

0.8

0.6

0.4

0.2

0.0

Effect

Po

we

r

A lpha 0.05

StDev 0.255961

# Factors 5

# C orner P ts 8

# Blocks none

# Terms O mitted 6

C enter Points Yes

Terms Included In Model

A ssumptions

2, 1

Ctr Pts Per Blk

Reps,

Power Curve for 2-Level Factorial Design

Figure 22 Power Curve

Analysis of Results

Main Effects Plot

In order to analyze the impact of the factors on the response, we have run the Main Effects Plot and have

got the following results. It can be clearly interpreted that the factors Size of Paper and Person throwing

have a significant impact on the response, time of flight, whereas type of Paper and Type of Fold have no

effect on it.


24 | P a g e

Figure 23: Main Effects Plot

Interactions Plot:

As we have observed the presence of interactions while running the DOE, we wanted to know how the

factors interacted with each other and so we ran the interactions test. We have observed that the Type of

Paper and Person throwing had the strongest interactions. Also, Type of Paper made relatively strong

interactions with all the factors.

Figure 24: Interaction plot for Response - Time

1-1

1.80

1.65

1.50

1.35

1.20

1-1 1-1

1-1

1.80

1.65

1.50

1.35

1.20

450

Type of Paper

Mea

n

Size of Paper Type of Fold

Person Throwing Angle

Main Effects Plot for Time (s)Data Means

1-1 1-1 1-1 450

2.0

1.5

1.02.0

1.5

1.02.0

1.5

1.02.0

1.5

1.0

Type of Paper

Size of Paper

Type of Fold

Person Throwing

Angle

-1

1

Paper

Type of

-1

1

Paper

Size of

-1

1

of Fold

Type

-1

1

Throwing

Person

Interaction Plot for Time (s)Data Means


25 | P a g e

Contour and Surface Plots: In order to maximize the response, i.e., the time of flight of the paper airplanes, we have to find the

optimum settings of the significant factors, which can be obtained by the following Contour and Surface

Plot Graphs. From both the graphs, we can interpret that the response is maximum when Person B is

throwing an airplane made of a large paper.

Figure 25 Contour Plot of Time

Person Throwing

Siz

e o

f P

ap

er

1.00.50.0-0.5-1.0

1.0

0.5

0.0

-0.5

-1.0

>

–

–

–

–

–

< 0.6

0.6 0.9

0.9 1.2

1.2 1.5

1.5 1.8

1.8 2.1

2.1

Time (s)

Contour Plot of Time (s) vs Size of Paper, Person Throwing


26 | P a g e

Figure 26 Surface Plot of Time

Conclusions and Recommendations From the above tests, we can now conclude that the factors which are crucial for the maximum time of

flight are Person B throwing a large paper airplane. It can also be observed that other factors such as Type

of Paper, Type of fold and Angle Thrown are not as significant as we thought at the beginning of the

experiment.

Regression Equation The final part of the experiment is to generate a valid equation for the response involving all the

significant factors and their interactions. For doing so, we use the coefficients of the significant terms

obtained from the run results of maximum R-square (adjusted) values, which can be observed in the

Figure 20, which shows the values of estimated effects and coefficients for time. All the terms which have

p-value less than 0.05 are considered significant and are used in generating the regression equation.

The Coded equation is

X1 : Type of Paper

X2 : Size of Paper

1

0.5 0

1.0

1.5

2.0

-10 -1

1

Time (s)

Size of Paper

Person Throwing

Surface Plot of Time (s) vs Size of Paper, Person Throwing


27 | P a g e

X3 : Type of Fold

X4 : Person Throwing

X5 : Angle Thrown.

The un-coded equation is

( ) ( )

( ) ( )

( ) (

) ( )

( ) (

) (

) (

)

References

“Two Paper Airplane Design Challenges: Customizing for Different Learning Objectives” by

Daniel Z. Meyer and Allison Antink Meyer

Douglas C. Montgomery. Design and Analysis of Experiments, 8th Edition. John Wiley & Sons:

2013.

Slides and notes by Prof. Golgen Bengu

Minitab 15

Videos in YouTube for making the paper airplanes

Documents

IE604_Project_Brier_Golla