Assignment 3_fractional factorial
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Assignment 3: Fractional Factorial
Parth. M. Patel
Harshit Mistry
Parth Bhuva
Kushal Patel
Santosh Prajapati
Milan Patel
Urvil Patel
Amalsha
Process Quality Engineering – Conestoga College
QUAL 8115: Advance Design of Experiments
Iain Hastings
July 14, 2023
Executive Summary
The helicopter experiment identifies the factors affecting the helicopter's flight falling time. On a scale of
1 to 10, the flight quality is evaluated based on two factors: the falling time and the fall quality. We
analyze the experimental design using 1/8 fractional factorial because there are 7 factors with 2-factor
levels. Based on the study, it was evident that factors influencing the flight, the rotor length, tail length,
tail width, paper width, and wing fold, are of high quality in this case.
Experimental recipe:
To examine the factors which affect the flight time and flight quality of paper helicopters.
Objective statement:
Through this experiment, we want to find the best helicopter performance according to falling time and
falling quality.
Response:
Helicopter time
Factors:
7 factors (Overall width, Rotor length, Tail length, Tail width, Paper type, Paper clip, Point tail)
Levels of Factors:
Each factor with two-level
Experimental design:
1/8 fractional factorial design (no replicates).
Data
StdOr
der
RunOr
der
Cente
rPt
Block
s
over
all widt
h
Rotar
lengt
h
Tail Lengt
h
Tail widt
h
Pape
r type
Pape
r clip
Point
tail
Time
Quali
ty
6
1
1
1
90
105
105
32
Light
yes
No
2.32
8
2
2
1
1
90
105
102
32
Heav
y
No
Yes
1.2
5
7
3
1
1
82
107
105
32
Light
No
Yes
2.5
8
16
4
1
1
90
107
105
36
Heav
y
yes
Yes
1.4
5
5
5
1
1
82
105
105
32
Heav
y
yes
Yes
1.05
4
12
6
1
1
90
107
102
36
Light
No
No
1.9
6
13
7
1
1
82
105
105
36
Heav
y
No
No
1.52
5
11
8
1
1
82
107
102
36
Heav
y
No
Yes
1.62
5
15
9
1
1
82
107
105
36
Light
yes
No
2.1
7
3
10
1
1
82
107
102
32
Heav
y
yes
No
1.9
6
9
11
1
1
82
105
102
36
Light
yes
Yes
2.15
7
1
12
1
1
82
105
102
32
Light
No
No
1.88
6
10
13
1
1
90
105
102
36
Heav
y
yes
No
1.4
5
8
14
1
1
90
107
105
32
Heav
y
No
No
1.6
5
14
15
1
1
90
105
105
36
Light
No
Yes
3.18
9
4
16
1
1
90
107
102
32
Light
yes
Yes
2.3
8
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Full model analysis:
As per the analysis of variance and Pareto chart, only one factor (paper type) and one interaction (rotor
length*tail width) significant. The remaining other factors and interactions are not significant.
Reduced model Analysis
This reduced model was obtained by removing the non-significant terms from the full model analysis by
using the 'Stepwise approach.' Here, overall width, rotor length, tail length, and tail width is not
significant, but two interactions (overall width*rotor length, overall width*tail length, and rotor
length*tail width) are significant. So, all non-significant factors are considered.
Examine of the residual plot
As per the normality residual plot, all points are near the red line except last point which means our data
is normal. From the residual versus fitted graph, one can see that the data is unevenly distributed. So, our
model is best fitted (adequate).
As per the model summary, the R-sq value indicates 93.30% of the model variation. Also, the R-
sq(pred) value of 65.01% defines the ability of the model to predict the response.
Main effect plot:
As per the main effect plot, there is one factor (paper type) that is not parallel to the center line, which
means, the paper type is a significant factor while falling the helicopter. There are other factors like
overall width, Rotar length, Tail length, and Tail width parallel to the center line, which means they all are
not significant.
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The flight meantime is high when overall width (90mm), Rotor length (107mm), Tail length (105mm), Tail
width (36mm), and paper type (light).
Examine the interaction plot.
As per the interaction plot, one can see that overall width*rotor length, overall width*tail length, and rotor length* tail width are significant.
Mathematical model %SS:
As per the regression equation, falling time depends on overall width, rotor length, tail width, paper type,
and interaction of overall width*rotor length, overall width*tail length, and rotor length*tail width.
Analysis of Variance
Source
DF
Adj
SS P-Value
overall width
1 0.02102
0.47%
Rotar length
1 0.02402
0.54%
Tail Length
1 0.10890
2.44%
Tail width
1 0.01690
0.38%
Paper type
1 2.75560
61.86%
overall width*Rotar length
1 0.36602
8.22%
overall width*Tail Length
1 0.27040
6.07%
Rotar length*Tail width
1 0.59290
13.3%
Error
7 0.29820 6.70%
Total
15 4.45397
From the analysis of variance, the highest contribution is paper type(61.86%), overall width (0.47%), rotor
length (0.54%), tail length (2.44%), tail width (0.38%), the interaction of width*rotor length (8.22%), overall width*tail length(6.07%) and rotor length*tail width (13.3%).
Some issues while doing the experiment:
Human error is common while measuring falling flight, like different releasing technique and releasing point is different in every run.
Atmosphere conditions also affect this experiment, especially wind speed.
Recommendation:
The experiment can be done by a two replicate, which reduces the variation and increase the accuracy of result.
The experiment can be done by two persons.
Conclusion:
From the design of the experiment, the factors that affect the dropping time of flight are paper type and interaction of overall width*rotor length, overall width*tail length, and rotor length*tail width.
The maximum dropping time one can be obtained by setting of overall width (90mm), rotor length (105mm), tail length (107mm), tail width (36mm), and light paper type with no clip.
References
(n.d.). Topic 8 Fractional Factorial Designs
. Econestoga. https://conestoga.desire2learn.com/d2l/le/content/761431/viewContent/15909800/View
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