application of six sigma management tools to increase the quality of a catapult

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Application of Six Sigma Management Tools to Increase the Quality of a Catapult Lei Chen: 2008210475 Kai Han: 2009210546 Ying Liu: 2009210559 Keming Zhu: 2009210563 Jiarui Fang: 2009210565

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Application of Six Sigma Management Tools to Increase the Quality of a Catapult. Lei Chen:2008210475 Kai Han: 2009210546 Ying Liu: 2009210559 Keming Zhu: 2009210563 Jiarui Fang: 2009210565. Agenda. Introduction Define Measure Analyze Improve Control Summary Future work. - PowerPoint PPT Presentation

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Page 1: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Lei Chen: 2008210475Kai Han: 2009210546Ying Liu: 2009210559Keming Zhu: 2009210563Jiarui Fang: 2009210565

Page 2: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

May 30, 2010 2

Agenda

• Introduction• Define• Measure• Analyze• Improve• Control• Summary• Future work

Page 3: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Introduction

http://images.google.com.hk

May 30, 2010 3

Page 4: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

DEFINE

May 30, 2010 4

Page 5: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Define

• Defect ◦ The inaccurate or imprecise shooting distance of the catapult. ◦ Accuracy

− Shift between the observed hitting point and the target hitting point.◦ Precise

− Variation of shooting distances from the observed average.• Goal

◦ Make the shooting distance of the catapult as accurate and precise as possible.

◦ USL – LSL = 8.4 cm (2 diameters of the golf ball).

May 30, 2010 5

Page 6: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

MEASURE

May 30, 2010 6

Page 7: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Structure of the catapult

May 30, 20107

Page 8: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Establish measure system capability

• 5 landing points and 3 operators • First try

◦ Cast the ball to hit the ground directly.◦ Operators guess the landing point by watching then give the

measurements.◦ Gage R&R: more than 30%

• Improve ◦ Blank papers with carbon papers

May 30, 2010 8

Page 9: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Establish measure system capability

May 30, 2010 9

部件间再现性重复量具 R&R

100

50

0

百分比

% 贡献% 研究变异

0. 50

0. 25

0. 00

样本极差

_R=0. 2467

UCL=0. 6350

LCL=0

CL LY ZKM

199. 9

198. 7

197. 5样本均值 __

X =198. 051UCL=198. 303LCL=197. 799

CL LY ZKM

54321

200

198

196

Uni t

ZKMLYCL

200

198

196

Oper at or

54321

199. 9

198. 7

197. 5

Uni t

平均

CLLYZKM

Operator

量具名称: 研究日期:

报表人: 公差: 其他:

变异分量

R 控制图(按 Operator)

Xbar 控制图(按 Operator)

Di s � Uni t

Di s � Operator

Operator 乘 Uni t 交互作用

Di s 的量具 R&R (方差分析)

Page 10: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Establish baseline process capability

215

210

205

200

195

190

185

Dis_

Firs

tTim

e

Di s_Fi rstTi me 的箱线图

220210200190180

99

9590

80706050403020

105

1

Di s_Fi rstTi me

百分比

均值 201. 3标准差 6. 760N 34AD 0. 282P 值 0. 617

Di s_Fi rstTi me 的概率图正态

May 30, 2010 10

Page 11: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Establish baseline process capability

LSL Mean USL192.91 201.31 209.71

216208200192184

LSL USL

LSL 192. 91目标 *USL 209. 71样本均值 201. 309样本 N 34标准差(组内) 6. 81098标准差(整体) 6. 75959

过程数据

Cp 0. 41CPL 0. 41CPU 0. 41Cpk 0. 41

Pp 0. 41PPL 0. 41PPU 0. 41Ppk 0. 41Cpm *

整体能力

潜在(组内)能力

PPM < LSL 88235. 29PPM > USL 88235. 29PPM 合计 176470. 59

实测性能PPM < LSL 108763. 70PPM > USL 108699. 28PPM 合计 217462. 99

预期组内性能PPM < LSL 107025. 05PPM > USL 106960. 89PPM 合计 213985. 93

预期整体性能

组内整体

Di s_Fi rstTi me 的过程能力

May 30, 2010 11

Cp = 0.41

Page 12: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

ANALYZE

May 30, 2010 12

Page 13: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Cause and effect analysis

Large Variation

Materials Casting Methods

Operator

Machine

Material of barrier rods

Material of casting rod

Material of shot ball

Strength

Environment

Air resistance

Stability of the base

Fatigue strength Of the rubber band

Direction control ofthe casting rod

Measurements

Mark methods

Holding position when releasing

Casting gesture

Joint of parts

StabilityFloorMeasurement methods

May 30, 2010 13

Page 14: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

IMPROVE

May 30, 2010 14

Page 15: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Improvement 1: tentative improvements

May 30, 2010 15

• Casting rod and strength

Page 16: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Process capability analysis

Di s_SecondTi meDi s_Fi rstTi me

220

210

200

190

180

数据

Di s_Fi rstTi me, Di s_SecondTi me 的箱线图

Trial Standard deviation

Decreased by Range Decreased

by

1 6.76 — 27.80 —2 4.07 40% 15.80 43%

May 30, 2010 16

Page 17: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Process capability analysis

220216212208204

LSL USL

LSL 205. 4目标 *USL 222. 2样本均值 213. 8样本 N 33标准差(组内) 4. 10563标准差(整体) 4. 07369

过程数据

Cp 0. 68CPL 0. 68CPU 0. 68Cpk 0. 68

Pp 0. 69PPL 0. 69PPU 0. 69Ppk 0. 69Cpm *

整体能力

潜在(组内)能力

PPM < LSL 0. 00PPM > USL 0. 00PPM 合计 0. 00

实测性能PPM < LSL 20379. 68PPM > USL 20379. 68PPM 合计 40759. 35

预期组内性能PPM < LSL 19603. 21PPM > USL 19603. 21PPM 合计 39206. 42

预期整体性能

组内整体

Di s_SecondTi me 的过程能力

LSL Mean USL205.4 213.8 222.2

Cp = 0.68

May 30, 2010 17

Page 18: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Improvement 2: design of experiment• The objective is to find optimal configuration for least variation• Response

◦ Standard deviation− Shoot 5 times in each run in order to compute the standard deviation

• Factors◦ Operator

− 3 operators

◦ Fixing Style− Hand− Ground− Trigger

Run Order PtType Block Shooter FixingType STD

5 1 1 1 KM Trigger 1.53

1 2 1 1 LY Ground 2.31

2 3 1 1 LY Trigger 1.22

3 4 1 1 LY Hand 5.91

4 5 1 1 KM Ground 1.85

8 6 1 1 JR Trigger 2.20

7 7 1 1 JR Ground 1.89

9 8 1 1 JR Hand 6.07

6 9 1 1 KM Hand 5.49

May 30, 2010 18

Page 19: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Design of experiment

• ResultAnalysis of Variance for STD, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PShooter 2 0.2771 0.2771 0.1385 1.04 0.432FixingType 2 31.9810 31.9810 15.9905 120.43 0.000Error 4 0.5311 0.5311 0.1328Total 8 32.7891

S = 0.364391 R-Sq = 98.38% R-Sq(adj) = 96.76%

May 30, 2010 19

Page 20: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Process capability analysis

Di s_Thi rdTi meDi s_SecondTi meDi s_Fi rstTi me

220

210

200

190

180

数据

Di s_Fi rstTi me, Di s_SecondTi me, Di s_Thi rdTi me 的箱线图

Trial Standard deviation

Decreased by Range Decreased

by

1 6.76 — 27.80 —2 4.07 40% 15.80 43%3 2.12 48% 7.60 52%

May 30, 2010 20

Page 21: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Process capability analysis

216213210207204201

LSL USL

LSL 200. 54目标 *USL 217. 34样本均值 208. 937样本 N 30标准差(组内) 2. 13484标准差(整体) 2. 11652

过程数据

Cp 1. 31CPL 1. 31CPU 1. 31Cpk 1. 31

Pp 1. 32PPL 1. 32PPU 1. 32Ppk 1. 32Cpm *

整体能力

潜在(组内)能力

PPM < LSL 0. 00PPM > USL 0. 00PPM 合计 0. 00

实测性能PPM < LSL 41. 92PPM > USL 41. 38PPM 合计 83. 29

预期组内性能PPM < LSL 36. 36PPM > USL 35. 88PPM 合计 72. 24

预期整体性能

组内整体

Di s_Thi rdTi me 的过程能力

LSL Mean USL200.54 208.94 217.34

Cp = 1.31

May 30, 2010 21

Page 22: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Summary of increasing precise improvements

May 30, 2010 22

Trial Standard deviation

Decreased by Range Decreased

by Improve measures

1 6.76 — 27.80 — —

2 4.07 40% 15.80 43%

Add sticks beside the casting rod;

A piece of rope to pull the casting rod;

Fix a point on the ground;

3 2.12 48% 7.60 52%DOE: trigger-aided shooting with fixed

place

Page 23: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Assess the relationship of key X and Y

5045403530

300

250

200

150

100

X

Y

Y 与 X 的散点图多项式回归分析 :Y 与 X 回归方程为Y = 263.6 - 13.92 X + 0.2947 X**2S = 2.43154 R-Sq = 99.8% R-Sq (调整) = 99.8%

方差分析来源 自由度 SS MS F P回归 2 220904 110452 18681.37 0.000误差 60 355 6合计 62 221259

方差的序贯分析来源 自由度 SS F P线性 1 215061 2116.70 0.000二次 1 5843 988.26 0.000

840-4-8

99. 999

90

50

10

10. 1

残差

百分比

300250200150100

5. 0

2. 5

0. 0

-2. 5

-5. 0

拟合值

残差

420-2-4

16

12

8

4

0

残差

频率

605550454035302520151051

5. 0

2. 5

0. 0

-2. 5

-5. 0

观测值顺序

残差

正态概率图 与拟合值

直方图 与顺序

Y 残差图

May 30, 2010 23

• X: the distance between the trigger and the base of the catapult

• Y: the distance

Page 24: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Summary of increasing accuracy improvements

• Standard deviation has been reduced from 6.76 to 2.12• Do another experiment

◦ Target Y: 200cm◦ By the regression model, X is 42.1cm◦ Fix the trigger and repeat casting 30 times

• Results◦ Mean: 202.34 ◦ Standard deviation: 2.36◦ Range: 9.10

• Hypothesis testing

May 30, 2010 24

0 2, 1202.34 200 5.340 2.048

/ 2.36 29 nxt ts n

Reject H0

Page 25: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Summary of increasing accuracy improvements

LSL Mean USL191.6 200.0 208.4

Cp = 1.16Cpk=0.84

207204201198195192

LSL 目标 USL

LSL 191. 6目标 200USL 208. 4样本均值 202. 338样本 N 29标准差(组内) 2. 40945标准差(整体) 2. 36468

过程数据

Cp 1. 16CPL 1. 49CPU 0. 84Cpk 0. 84

Pp 1. 18PPL 1. 51PPU 0. 85Ppk 0. 85Cpm 0. 83

整体能力

潜在(组内)能力

PPM < LSL 0. 00PPM > USL 0. 00PPM 合计 0. 00

实测性能PPM < LSL 4. 16PPM > USL 5935. 47PPM 合计 5939. 63

预期组内性能PPM < LSL 2. 80PPM > USL 5179. 84PPM 合计 5182. 64

预期整体性能

组内整体

Di s_TargetKnown 的过程能力

May 30, 2010 25

Page 26: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

CONTROL

May 30, 2010 26

Page 27: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Control actions

• Heavy objects should be used to fix the base of the catapult.

• The trigger (a taper holder) should be fixed on the ground.

• Use the same shot ball.

May 30, 2010 27

Page 28: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Statistical process control (SPC)• Design the SPC experiment

◦ Target Y: 200cm◦ By the regression model, X is 42.1cm◦ Fix the trigger and repeat casting 30 times

• Notes◦ The regression model is rough

− Truncation errors◦ Limitation of experiment conditions

− Lack of real-time control policies◦ Focusing on the past product quality

May 30, 2010 28

Page 29: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Statistical process control (SPC)

28252219161310741

210

205

200

195

190

观测值

单独值 _

X =200

UB=208. 4

LB=191. 6

2

2

22

22

2

66

6

5

Landi ng Poi nt 的单值控制图

• Analysis of SPC result

May 30, 2010 29

Page 30: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Statistical process control (SPC)

• Discussion◦ Real-time control policy: adjust X to get a better Y◦ Find a confidence interval of X and adjust the value of

X in the interval

May 30, 2010 30

Page 31: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

SUMMARY

May 30, 2010 31

Page 32: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Summary

May 30, 2010 32

Page 33: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

FUTURE WORK

May 30, 2010 33

Page 34: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

Future Work

• Measure systems• Material of the casting rod• A more accurate regression model• The trigger: work more automatically

May 30, 2010 34

Page 35: Application of Six Sigma Management Tools to Increase the Quality of a Catapult

May 30, 2010 35

Thanks!