application of six sigma management tools to increase the quality of a catapult
DESCRIPTION
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 PresentationTRANSCRIPT
Application of Six Sigma Management Tools to Increase the Quality of a Catapult
Lei Chen: 2008210475Kai Han: 2009210546Ying Liu: 2009210559Keming Zhu: 2009210563Jiarui Fang: 2009210565
May 30, 2010 2
Agenda
• Introduction• Define• Measure• Analyze• Improve• Control• Summary• Future work
Introduction
http://images.google.com.hk
May 30, 2010 3
DEFINE
May 30, 2010 4
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
MEASURE
May 30, 2010 6
Structure of the catapult
May 30, 20107
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
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)
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
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
ANALYZE
May 30, 2010 12
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
IMPROVE
May 30, 2010 14
Improvement 1: tentative improvements
May 30, 2010 15
• Casting rod and strength
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
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
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
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
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
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
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
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
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
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
CONTROL
May 30, 2010 26
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
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
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
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
SUMMARY
May 30, 2010 31
Summary
May 30, 2010 32
FUTURE WORK
May 30, 2010 33
Future Work
• Measure systems• Material of the casting rod• A more accurate regression model• The trigger: work more automatically
May 30, 2010 34
May 30, 2010 35
Thanks!