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Course project of DOE, 2010 spring. By Group 11. :. 沈坤，孙维，袁怡潇，于漠南，朱雯. 1. Photo art courtesy: smart_katalog_fortwo_2007.pdf, Daimler AG. 2. Introduction. Factor Analysis. ID: 182634

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Slide1

Experiment on Farthest Throw of Catapult

Course project of DOE, 2010 springBy Group 11:沈坤，孙维，袁怡潇，于漠南，朱雯

1

Photo art courtesy: smart_katalog_fortwo_2007.pdf, Daimler AG

Slide22

IntroductionFactor AnalysisExperiment and AnalyzingSummary

Agenda

Slide3Background

Catapult in history

Application of the principal of leverage

A tool for attack

How to make it have a launch on the largest distance?

Catapult in experimentComposed of a band, a ball, some bolts and the basic wooden structure

Slide4Objectives

A

statistical model of significant factors in response to the cast distance of the

catapult

The optimal combination of the significant factors to maximize the cast

distance

An estimation of this “optimal distance”

Slide5Related Chapters in Textbook

23 full factorial designResponse surface analysis --- The steepest ascent methodFitting regression modelGeneral linear model

5

Slide6Related Papers

《利用响应曲面法确定竹叶中黄酮最佳提取条件》，冯涛、曹东旭、高辉、季光，2003年6月，《天津轻工业学院学报》。《试验设计与优化》，李波、徐泽民、李方、张新申，2003年1月，《中国皮革》。《Experiment of washing process》，于航等。 （五字班DOE课程小组大作业报告）《An investigation on data entry effectiveness & efficiency 》，张重阳等。 （五字班DOE课程小组大作业报告）

6

Slide77

Introduction

Factor Analysis

Experiment and Analyzing

Summary

Slide8Response variable

Cast distance of the catapultRange 0.5 through 3.5 metersMeasurementband tape + number of floor tires

Slide9Effect factor

Catapult

The

open angel of the cast arm

The

position of the apron

Tiredness

Concentration

Put the cast arm to the precise angel

Humidity

Air resistance

The right position of the ball

Temperature

Wind velocity

Put the cast arm to the precise angel

The height of the catapult

The radius of the ball

The precision of the band tape

The front fixture of the band

The

back

fixture of the band

Operator

Measurement

Catapult

Environment

Cast distance of the catapul

t

Slide10Constant Variables & Noise Variables

Slide11Control the interference factor

Slide12Control Variables

Real factorRangeCategoryInfluenceLevelFront fixture of the band1,2,3,4DiscreteTension of the band1,3 (a)Position of the apron1,2,3,4,5,6DiscreteAngel of the ball4,6 (b)Open angel of the cast arm0~180 degreeContinuousCast speed of the ball160 and180 degree (c)

(a)

(b)

(c)

Slide13Real factorVariable nameRangeCategoryCoded value—+Front fixture of the bandA1,2,3,4Discrete13Position of the apronB1,2,3,4,5,6Discrete46Open angel of the cast armC0~180 degreeContinuous160180

The 23 factorial design

Replications: 5

Slide1414

Introduction

Factor Analysis

Experiment and Analyzing

Summary

Slide15Our experimenting and analyzing process

Slide16The qualitative analysis of factors’ effects

Slide17The further analysis of response surface

We will show the process in Minitab.Regression model:When A=1, B=6, C=180 :

Slide18A GLM between distance and the significant factors and interactionsResources: A, B, C, AC, BCThe functionThe theoretical optimal solution:Setting A at “1”, B at “6”, C at “180”

General Linear Model

18

Slide1919

Special verification of “B”

Whether or not factor B is significant to DistanceFull factorial design: B is proved to have no significant effectGeneral linear model: B’s effect seems to be significantAdvanced analysis: Based on more data10 replications

Slide20Data in detail:ConclusionB has a slight positive effect to the response variable DistanceOptimal style: A=1, B=6, C=180

Box-plot:

Special verification of “B”, cont

Slide21Under A=1, B=6, C=18020 replications95% confidence interval Our estimation of the “Largest distance”: (544.98, 551.02)

Estimating the Optimal Value

Slide2222

Introduction

Factor Analysis

Experiment and Analyzing

Summary

Slide2323

Our methodology

Slide2424

Our final result

Optimal style: A=1, B=6, C=180Optimal value: (544.98, 551.02)

Slide25The End !Thank you!

Q & A

25

Photo art courtesy: smart_katalog_fortwo_2007.pdf, Daimler AG

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