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# Quality Engineering

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Submitted By mujeeb1406
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QUALITY ENGINEERING DESIGN FOR WEB-BASED CATAPULT

BY

Mohammed Mujeeb Ahmed khan

SUBMITTED TO

PROFESSOR K. M. RAGSDELL

FOR CREDIT IN
EMGT-475: QUALITY ENGINEERING

Contents
1. Introduction
1.1.

An overview of Quality Engineering

1.2.

Problem description

P diagram

Quality characteristics

Control factors

Noise factors

Mathematical Model of Crystal Ball

2. Method and Experimental plan

The static experiment

The dynamic experiment

Fast Diagram

Fault tree Diagram

3. Conclusions
4. References
5. Annexure

Static Experiment

Analysis of means

Analysis of Variance

Dynamic experiment

Confirmation Experiment

2

1. Introduction
The Taguchi system of Quality Engineering is a philosophy and a set of tools and techniques to design and deliver high quality, low cost products in a short time. The foundation of this system was laid by Dr. Genichi Taguchi in Japan. In the decades that followed, Dr. Taguchi’s techniques were applied to an increasing number of applications to solve real world problems. The technique was introduced to the western world in the
1980s, and it quickly created a paradigm shift in the perception of quality.
1.1.

An overview of Quality Engineering System:

Product Parameter Design:
Product parameter design is optimizing the product parameters to give the desired performance. A quality characteristic is chosen whose value should be on target. Specific control factors are identified which affect the system/product’s robustness and their optimum values are determined and verified by experimentation under the influence of the identified noise factors. A Parameter diagram (P-Diagram) is used as a tool to summarize all the factors considered.
3

Tolerance Design:
Tolerance design is the second stage in the system. The output performance of the system is not still satisfactory after the product parameter diagram, hence tolerance design is used now to tighten and loosen the tolerances after studying the sensitivity analysis.

1.2. Problem description
The catapult is a simple model that is used to study the effect of design parameters on output variation. It is a very simple model where the control factors are linearly independent and significantly affect the output performance in the presence of noise. The problem is to conduct the static experiment with the target fixed at 80cm and Also conduct dynamic experiment with the target moving in the range of 70-90cm.
-The P-diagram
Below (Figure 1) is the P-diagram, which illustrates the interactions among noises, input and output signals and control factors.
Noise factors
Cup location, spring force, Stop angle, Base height, Pull-back angle, Band wear

Output

Input
Signal

The Catapult

Signal

Cup location, spring force,
Stop angle, Base height
Control factors
Figure 1: P diagram for the Catapult

4

-The Quality Characteristics
In Robust Design, the measured response of a design is called the ‘quality characteristics’. The selection of a quality characteristic depends on the customer desire; it is chosen depending on what is desired to be measured in the design. In the catapult experiment, quality characteristic is chosen as the distance, which how far the ball travels from the base of the catapult.
-Control factors:
Control factors are the design parameters which need to be optimized. Control factors need to chosen as to minimize the variability and maximize the signal to noise ratio. By the help of Functional Analysis Systems Technique (F.A.S.T.), velocity, height, and release angle are determined to influence the distance in this experiment. Then, the physical effects matrix is constructed as seen in Physical Effects Matrix.

Physical Effects Matrix
Physical Effects
Control Factors

Angle

Speed

X

Cup Location

Height

X

Band Tie Point

X

Stretch Point

X

Stop Angle

X

X

Number of Bands
Catapult Height
Pull-back Angle

X
X

X
X

As seen, there are many interactions between control factors, and this needs to be reduced in order to have robust design. This is achieved by decoupling some of the control factors

5

and so creating a compound control factor. In this sense, band tie point, stretch point, and number of bands are compounded as “Spring Force”. Spring force has three levels as seen below. The new physical effects matrix with compounded control factor (spring force) can also be seen..

Spring Force Levels
Levels
Band Tie
Point

1
2
3

Stretch
Point

Number of bands 1
2
3

Spring Force Levels

1
2
3

1
2
3

Low
Medium
High

Table 1 - New Physical Effects Matrix
Physical Effects
Control Factors
Cup Location

Angle

Height
Weak

Spring Force

Speed
Weak
X

Stop Angle

X

Weak

Catapult Height

X

Pull-back Angle

X

Control Factors and Levels
Control Factors

Levels

A

Cup Location (cm)

16

17.5

19

B

Spring Force

low

medium

high

C

Stop Angle (deg)

45

60

75

D

Catapult Height (cm)

0

10

20

6

-Noise Factors
Noise factors are the causes of the variation in products performance and they are also the reasons for customer dissatisfaction. There are three types of noise factors such as
External, Unit-to-unit, and Deterioration Noise Factors.

External Noise Factors: These are the sources of variability that come from outside of the product. (i.e. temperature and/or relative humidity)

Unit-to-unit Noise Factors: These factors are due to the variation in the manufacturing processes. Any two products cannot be produced exactly the same.
(i.e. resistance of electrical resistors)

Deterioration Noise Factors: These are also referred as internal noise factors because an internal change within the product is the main cause. (i.e. total current passes through a battery)

Mathematical Model of Crystal Ball:

7

Sensitivity Analysis Using Crystal Ball: Crystal ball is used to study the effect of variation on performance of different factors. Sensitivity Analysis is used to study the effect of input variation on output variation caused due to every factor. This gives us an

8

idea about the problem makers in the design and should be more carefully looked at.

9

Thus, stop angle and height show a large effect on output performance.

2. The static experiment:
The aim of static experiment is to hit a fixed target in the presence of noise and control factors. Hence, four control factors were chosen at level 3 and five noise factors were chosen at level 2. The control factors are cup location(A), soring force(B), stop angle(C) and height(D). The noise factors are spring force variation(E), height variation(F), pull back angle variation(G), ball mass variation(H) and band wear variation(I).

Analysis Of Means:
An ANOM was performed on the data collected in the static experiment to identify optimum control factor levels, and to identify compound noises for the dynamic experiment. S/N

A
B
C
1 18.70892 15.86028 16.41968
2 18.16521 19.85819 18.40183
3 18.75617 19.91183 20.80878

D
17.85755
18.46589
19.30686

σ

A
B
C
D
1 6.767601 3.424132 8.507868 6.460133
2 7.022023 6.490992 7.760167 7.58598
3 7.986236 11.86074 5.507825 7.729746

Mean

A
B
C
D
1 65.20146 22.2475 67.70833 57.84583
2 63.55938 63.29271 70.52979 69.28729
3 71.93938
115.16 62.46208 73.56708

Thus from the table it can be seen that A3B3C3D3 show the highest signal to noise ratio and are thus selected to be the levels of control factors. Then a confirmation experiment

10

is run to find out the mean performance and then the scaling factors are selected depending on the factor effect plots.

11

12

ANOVA-Static:

13

14

Static Confirmation Experiment
A confirmation experiment was run to verify results predicted by the additive model using the optimal and worst control factor combinations identified. The additive model assumes that performance is the sum of individual factor effects and that the effects can be separated. The following formulas were used to predict the optimal mean and S/N (see Appendix for calculations): ncf ~  y  ~  y  y opt
 yi i 1 n 

cf
~
~
S / N opt  S / N   S / N i  S / N

i 1

The Dynamic Experiment
The purpose of the dynamic experiment is to design a more robust system before knowing the customer’s requirements. Essentially the target varies in a range of values.
The dynamic experiment involves Identifying optimum control factor levels that make the catapult more insensitive to variation reduced S/N. Also, the system sensitivity coefficient beta (β) is identified. The ideal function of the system was assumed to have the following form: y = βM, where y is the impact distance and M is pullback angle.
This ideal relationship can be used to quickly tune the catapult to changing customer requirements. In this case, the pull back angle is changed from 15 degrees, 30 degrees and 45 degrees using two noise levels(up and down).

The analysis of means for dynamic experiment is shown below:

15

Factor
A1
A2
A3

(S/N)1
(S/N)2
-20.0764
-19.089
-21.0631 -22.5487
-20.2796 -21.0385

sigma
24.43116
21.87768
24.52368

beta
S/N1
S/N2
2.345996 -20.6565 -21.5202
1.996766 -20.6565 -21.5202
2.246599 -20.6565 -21.5202

B1
B2
B3

-20.2071
-20.2231
-20.9889

-24.6767 9.231212 0.946778
-20.1346 20.36357 1.985429
-17.865 41.23775 3.657155

-20.6565
-20.6565
-20.6565

-21.5202
-21.5202
-21.5202

C1
C2
C3

-21.3752
-20.5864
-19.4575

-21.6795 27.24309
2.4215
-21.1666 24.34379 2.20877
-19.8302 19.24564 1.959091

-20.6565
-20.6565
-20.6565

-21.5202
-21.5202
-21.5202

D1
D2
D3

-20.4929
-20.9083
-20.0179

-20.4849 23.02123 2.142024
-21.4709 23.8886 2.163329
-20.7204 23.92269 2.284008

-20.6565
-20.6565
-20.6565

-21.5202
-21.5202
-21.5202

16

The optimum level of control factors selected was (3,2,3,3) and the output performance was well within the range of 70-90cm(70.94). here, no scaling was done as the output performance was within the target. It could have been done.

17

Ball Mass
WHY

HOW
Stop Angle

Provide Power for ball travel

Band Tie Point
Pull Back Angle

WHEN

Number of Bands
Power Provided by Band
Band Wear and
Tear

Throw the ball on target
Appropriate Pull Back angle
Throw at appropriate angle for Projectile
Catapult Lever
Cup Location
Pull
back the catapul t Lever

Height Of The catapult From
Ground
Provide Target distance form the base of Catapult

Provide Power for ball travel Stop Angle

Pull Back Angle

Fig 5 : FAST Diagram

18

Improper Ball
Mass selection
WHY

HOW
Stop Angle chosen inappropriately Inadequate Power for ball travel

Pull Back Angle chosen inappropriately WHEN
Too much variation in Power

Band Tie Point distance not proper
Number of Bands not sufficient or surplus
Band Wear and
Tear not properly adjsuted Ball Not
Thrown t on target
Inappropriate Pull Back angle
Angle of Ascent
Improper
Catapult Lever not easy to operate
Improper Cup Location
Height Of The catapult From
Ground, varies
Ball Travel Variation

Inadequate Power for ball travel Stop Angle

Pull Back Angle, varies FIG 6: FAULT TREE DIAGRAM

19

Conclusions:
The catapult was studied under the effects of control factors and noise factors. The static experimet was carried out and the output was 84.41. It was not on target and it can be brought on target by proceeding to tolerance design by tightening the tolerances. The dynamic experiment was studied and the output range was within the target. The optimal levels of control factors in static were (1,3,3,1) and (3,2,3,3) in the case of dynamic.

References:

Clausing, Don P. Taguchi Quality Engineering System for Robust Design. MIT Video
Course, 1990.
Fowlkes, William Y. and Clyde M. Creveling. Engineering Methods for Robust Product
Ragsdell, K. “Quality Engineering EMgt 475,” Class notes
Reports posted on Blackboard.

For annexure please refer to Excel worksheet attached

20

ality

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