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Apply ing Robust
Engineer ing t o Six Sigm a
Elizabeth CudneyCQE, SSBB
December 5, 2005
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Agenda
Six Sigma Overview
Robust Design Overview
Taguchi System of Quality Engineering
Integrated Robust Engineering and Six Sigma
Case Study
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Six Sigm a Overview
Six Sigma is a customer focused continuousimprovement strategy and discipline that minimizesdefects and variation towards an achievement of 3.4defects per million opportunities in product design,production, and administrative processes.
It is focused on customer satisfaction and cost reductionby reducing variation in processes.
Six Sigma is also a methodology using a metric based
on standard deviation.
Six sigma targets aggressive goals.
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What is Six Sigm a?
Strategy to minimize variation towards the goal of 3.4defects per million.
A philosophy to promote excellence in all businessprocesses.
A 5 phase methodology for continuous improvement.
A statistic which describes the amount of variation in aprocess.
A tool to reduce or eliminate variation.
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What is Six Sigm a?
3.4 defects per million
Six Sigma is about. . .
Reducing cost
ROI Improving quality
Satisfying the customer
Designing better products
REDUCING VARIATION
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What is Six Sigm a?
Six Sigma is a customer focused continuous
improvement strategy and discipline thatminimizes defects and variation towards anachievement of 3 defects per million
opportunities in product design, production, andadministrative processes.
Focused on customer satisfaction and $ resultsby reducing variation in processes.
Methodology
Metric based on standard deviation.
Aggressive goals.
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Why Use Six Sigm a?
Increase capacity
Reduce cost
Improve yields
Reduce the impact of a Hidden Factory
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The Hidden Fac t ory
Each defect must be detected, repaired andplaced back in the process. Each defectcosts time and money.
Time, Cost, People
Inputs
Rework
Scrap
First Time YieldOperation Inspect
Hidden Factory
Pass
Fail
Increased Cost - Lost Capacity
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Six Sigm a Goals
Develop a world class culture
Develop leaders
Support long range objectives
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Six Sigm a Benefi t s
Stronger knowledge of products and processes
Reduction in defects
Increased customer satisfaction level that generatesbusiness growth and improves profitability
Increased communication and teamwork
Common set of tools
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Six Sigm a St ra t egy
Define
Measure
Analyze
Improve
Control
Define
Measure
Control
Improve
Analyze
6
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Define
Project selection
Tools: Voice of the Customer
Value Stream Mapping
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Measure
What processes are involved?
Who is the process owner?
Who are the team members?
Which processes are the highest priority toimprove?
What data supports the decision? (Metric)
How is the process performed? How is the process performance measured?
Is your measurement system accurate and
precise?
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Measure (Cont .)
What are the customer driven specifications for theperformance measures?
What are the improvement goals?
What are the sources of variation in the process?
What sources of variability are controlled and how?
Tools: Process Flow
Capability Analysis
Measurement System Analysis
5S
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Analyze
What are the key variables affecting the average and
variation of the performance measures? What are the relationships between the key variables
and the process output?
Is there interaction between any of the keyvariables?
Tools: Hypothesis Test
TAKT Time
Cause and Effect Diagram
Failure Mode and Effects Analysis (FMEA)
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Improve
What are the key variable settings that optimizethe performance measures?
At the optimal setting for the key variables, whatvariability is in the performance measure?
Tools: Multiple Regression
Design of Experiments
Kanban
Visual Management
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Contro l
How much improvement has the processshown?
How much time and/or money was saved?
Long term metric.
Tools: Process monitoring
Standard workSPC
Control charts
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Six Sigm a Levels
Identify the CTQs
Critical to Quality
Characteristics or
customer requirements
for a product or service
Define Defect
Opportunities
Any step in the process
where a defect could
occur in a CTQ
Look for Defects in
Products or Services
Count defects or
failures to meet CTQ
requirements
Arrive at DPMO
Defects Per Million
Opportunities
Convert DPMO to
Sigma Level
Use the sigma
table
Sigma
Level
Defects per
Million of
Opportunity
Z PPM
2 308,537
3 66,807
4 6,210
5 233
6 3.4
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Robust Design
A product is said to be robust when it isinsensitive to the effects of sources ofvariability, even though the sourcesthemselves have not been eliminated.
Source (Fowlkes and Creveling, 1995)
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Robust Design
Robust Design: Not just strong.Flexible! Idiot Proof! Simple! Efficient!A product/process that produces
consistent, high level performancedespite being subjected to a wide rangeof changing client and manufacturing
conditions.- Genichi Taguchi
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Taguc h i Sys t em of
Qual i t y Engineer ing
Dr. Taguchi, the father of QualityEngineering, introduced to the US in the1980s his approach for achievingrobustness in product design.
There are four steps to ensure robustproduct performance including
1) product parameter design,2) tolerance design,
3) process parameter design, and
4) on-line quality control.
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Taguc h i Sys t em of
Qual i t y Engineer ing
Product
Parameter
DesignTolerance
Design
Process
Parameter
Design
On-line
Quality
ControlNoises
Robust
System
Performance
Degradation
Quality
Loss
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Taguc h i Sys t em of
Qual i t y Engineer ing
The first and most important step in the TaguchiSystem of Quality Engineering (TSQE) is productparameter design which is the most important
action to design a robust system.
The concept of product parameter design is that
the final product is robust or insensitive to theincoming variations or noises.
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Taguc h i Sys t em of
Qual i t y Engineer ing
Robust design is achieved through athree step process:
1) Define the objective,
2) Define the feasible option, and3) Select the best option to meet the objective.
Robust design is measured using theSignal-to-Noise (SN) ratio.
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Pro jec t Desc r ip t ion
The project is to design a disk brakesystem as a variation attenuator.
The goal of the project is to design thesystem so that it provides on target
performance in the presence of all types ofvariation.
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Selec t Vehic le
Ford Explorer 2002
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Approach
Spend about 80% of your time inengineering analysis and planning and
about 20% actually running experimentsand evaluating the results.
- Dr. Genichi Taguchi
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Approach
Ideal Function
P-Diagram
FAST Diagram
Static Experiment
Dynamic Experiment
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Idea l Func t ion
Defines the desired input/outputrelationship.
Displays the ideal relationship between thesignal and the quality characteristic.
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Idea l Func t ion
EnergyTransformation
Input Energy
Pedal Force
Intended Function
Slow Downthe Vehicle
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Brak ing Sim ulat or
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P-Diagram
P-Diagram is used to display variousfactors that affect performance.
It graphically displays the anatomy of a
product
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P-Diagram
AutomotiveBraking System
Input Signal
Pedal Force(lbs)
Quality
Characteristic
SmoothDeceleration
Stopping DistanceStopping Time
Control Factors
Noise Factors
Variation in Vehicle Weight (GVWR)Brake TemperatureVariation in Brake Line Pressure
Variation in Initial VelocityVariation in Coefficient of Friction between Tire & Road
Number of Pistons per Brake (front)Caliper Piston DiameterBrake Booster RatioTire Diameter
Rotor DiameterPad Inner DiameterSubtended Angle
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Func t iona l Analys is Syst em
Tec hnique (FAST) Diag ram
Displays the functional relationshipbetween all elements of a product.
Distributes or flows the system (high
level) functions to lower levels.
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FAST Diagram
Slowlydecelerate
vehicle
Provide tires withgood
Stop rotation ofthe wheels
Emergencybrake
Force frombrake pedal
transferred to
the individualwheels
Provide inputsignal
Provide frictionbetween the
pads and rotor
Pressureexerted on themaster cylinder
pistons
Provide Vacuumassist from Engine
Providevacuumbooster
Apply Force toBrake Pedal
Provide fluidpressure inbrake lines
Provide Brake Pedal
Provide control valve
and
and/or
How?
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St a t ic Ex per im ent
Inner Array - 7 Control Factors
L18 (37)
Outer Array 5 Noise Factors
L8 (25
)
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Input Signal
Signal provided by the vehicle user
Pedal force (lbs)
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Cont ro l Fac t ors
Control factors are parameters selectedto control the performance of a product.
Should have a large effect on mean
performance and a small effect onvariation of mean performance.
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Cont ro l Fac t ors
7 Control Factors, L18 (37
)
Number of Wheel Pistons (front)
Caliper Piston Diameter Brake Booster Ratio Tire Diameter Rotor Diameter Annular Pad Inner Radius Subtended Angle
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Cont ro l Fac t ors
135120110Subtended AngleCF7
3.83.53.2Annular Pad Inner RadiusCF614.013.012.0Rotor Diameter
CF5
30.530.029.5Tire DiameterCF4
6.05.54.5Brake Booster RatioCF3
1.991.811.63Caliper Piston DiameterCF2
21Number of Wheel Pistons (front)CF1
HighMediumLowControl Factor
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Noise Fac t ors
Noise factors represent incomingvariation.
These are parameters that have a
strong effect on performance that wecan not or choose not to control.
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Noise Fac t ors
5 Noise Factors, L8 (25)
Variation in Vehicle Weight (GVWR)
Brake Temperature
Variation in Brake Line Pressure
Variation in Initial Velocity
Coefficient of Friction between Tire and Ground
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Noise Fac t ors
0.850.4Coefficient of Friction betweenTire and GroundE
5% (63 mph)-3% (58 mph)Variation in Initial VelocityD
-5%-2%Variation in Brake Line PressureC500 F40 FBrake TemperatureB
2% (4176 lb)-2% (4012 lb)Variation in Vehicle WeightA
Level 2Level 1Noise Factor
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Qual i ty
Charac ter is t ic
Quality characteristic measures the useful
output of the system.
Smooth deceleration
Stopping distance (GVWR)
Federal Motor Vehicle Safety Standard(FMVSS) 135
Nominal-the-Best (NTB) Signal-to-Noise Ratio
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St a t ic Ex perim ent
Cross-Array Form at
Inner ArrayL18
Outer ArrayL8
PerformanceArray
PerformanceStatistics
NoiseStatistics
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Fac t or Ef fec t s Plo t S/N
Factor Leve l Effect Plot- Factor S/N vs. Level
19.0
19.1
19.2
19.3
19.4
19.5
19.6
19.7
19.8
19.9
20.0
Control factor Level (1, 2 and 3)
S/N
(dB
)
CF1
CF2
CF3
CF4
CF5
CF6
CF7
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Fac t or Ef fec t s Plo t Mean
Factor Level Effect Plot - Mean vs. Level
0.0
50.0
100.0
150.0
200.0
250.0
300.0
350.0
400.0
Control factor Level (1, 2 and 3)
Mean,
ft
CF1
CF2
CF3
CF4
CF5
CF6
CF7
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ANOVA Cont ro l Fac t or
Cont r ibu t ion t o S/N
ANOVA-Control Factor Contribution to S/N
Annular Pad Inner
Diameter
0.46%
Subtended Angle 0.00%
Tire Diameter
0.01%
Number of Pistons per
Brake (front)
82.18%
Caliper Piston Diameter
17.36%
Brake Booster Ratio 0.00%
Rotor diameter
0.00%
1
2
3
4
5
6
7
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ANOVA Cont ro l Fac t or
Cont r ibut ion t o Mean
ANOVA-Control Factor Contribution to Mean
Subtended Angle
0.00%Tire Diameter
8.50%
Brake Booster Ratio 0.00%
Caliper Piston Diameter
14.43%Number of Pistons (front)
66.84%
Annular Pad Inner
Diameter
0.37%
Rotor Diameter
9.85%
1
2
3
4
5
6
7
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Dynamic Ex per iment
Cross-Array Form at
Control FactorsInner Array
L18
M1 M2 M3N1N2 N1N2 N1N2
Outer Array
PerformanceArray
PerformanceStatistics
F t Ef f t Pl t
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Fac t or Ef fec t s Plo t
S/N
Control Factor Effect Plot
S/N vs. Level
-32.10
-32.00
-31.90
-31.80
-31.70
-31.60
-31.50
Level (1, 2 & 3)
S/N
,dB
CF1
CF2
CF3
CF4
CF5
CF6
CF7
F t Ef f t Pl t
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Fac t or Ef fec t s Plo t
Mean
Control Factor Effect PlotMean vs. Level
0.00
50.00
100.00
150.00
200.00
250.00300.00
350.00
400.00
Level (1, 2 & 3)
Mean,
ft
CF1
CF2CF3
CF4
CF5
CF6
CF7
F t Ef f t Pl t
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Fac t or Ef fec t s Plo t
Be ta
Dynamic Estimaged Beta Value
R2 = 0.9977
0
50
100
150
200
250
300
350
400
450
0 20 40 60 80 100 120 140 160
Pedal Force (lbs)
StoppingDistance(ft)
N1
N2
Avg
Linear (Avg)
y = 432.1 - 1.026x
ANOVA C t l F t
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ANOVA Cont ro l Fac t or
Cont r ibu t ion t o S/N
ANOVA-Control Factor Contributions to S/NTire diameter
0.01%
Pad Inner Diameter
0.44%
Number of Pistons per Brake
(front)
82.11%
Caliper piston diameter
17.44%
Rotor Diameter
0.00%
Brake Booster Ratio 0.0% Subtended Angle 0.00%
1
2
3
4
5
6
7
ANOVA C t l F t
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ANOVA Cont ro l Fac t or
Cont r ibut ion t o Mean
ANOVA-Control Factor contribution to Mean
Rotor diameter
12.52% Pad Inner Diameter 0.39%
Number of Pistons per Brake
(front)
71.41%
Caliper Piston Diamter 15.40%
Brake Booster Ratio 0.00%
Tire Diameter
0.26% Subtended Angle
0.00%
1
2
3
4
5
67
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Quest ions???
Thank you!