[精选]DFSSBB314CentralCompositeDesign--资料

(prediction error is equal in all directions)
OR to ensure that blocks are orthogonal
(block coefficient(s) have no impact on other coefficients in the model)
Alpha = 1, axial pts on the faces
Face centered design
Use only when it is too dangerous to go outside the corner points
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Design for Six Sigma
Central Composite Design
DFSS BB314 Central Composite Design.ppt 314-1
Purpose
Understand the difference between designs that are used to select KPIVs and designs that are used to optimize the settings of already confirmed KPIVs Design and analyze a Central Composite Design (CCD) Apply CCD to an exercise
2-Level factorial designs can be used for the first two models, Central Composite designs are needed for the third model
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If the axial points are on the sides of the square, each factor has 3 settings
Either way, 3 or more points can be used to define a quadratic equation, i.e. – curved line
Copyright © 2001-2004 Six Sigma Academy International LLC All Rights Reserved
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What is Central Composite Design (CCD)?
Advanced regression application Active analysis Used to extend existing data
VERIFY Rally Points 5-8 Set Initial Control Systems/Plans
Verify Product Performance Verify Process Performance
Test Plans & Reports
Failure modes and analyses
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Properties of CC Designs
Alpha = distance (in coded units) from center of design to axial points
Alpha > 1, axial pts outside corner pts
Default alpha set to ensure Rotatability
Identify Customer Needs/Wants Establish Critical to Quality Characteristics (CTQC’s) Establish Technical Features
CONCEPT Rally Points 1-2 Identify CTQC Metrics/Measures Identify Key Measurement Systems Develop Optimal Design Concept Develop Business Case & Schedule
Find critical Y=f(x)
relationships
Optimize Y’s &
critical X’s, RMI, WIP,
FGI & Supply Chain
Set critical X’s, kan-
bans Check Key Y’s
Why Central Composite Design?
Copyright © 2001-2004 Six Sigma Academy International LLC All Rights Reserved
314-10
Steps to Conduct a CCD Experiment (1)
Step 1: State the practical problem and objective of the experiment
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Analyze/Minimize Product & Process Risks
Model & Analyze Tolerances & Sensitivities
Develop/Evaluate Measurement Systems
Initial Robust Product Design
for a straight line
Center points are only used to test for curvature
Copyright © 2001-2004 Six Sigma Academy International LLC All Rights Reserved
If the axial points are outside the square, as here, each factor has 5 settings
314-8
Alpha
-1
0 +1
Possible Central Composite (CC) Designs
These are the CC designs available in MINITAB – from 2 to 6 factors. Note how the number of runs can get large – it is always good to reduce the number of factors as much as possible.
- Quadratic terms - Uses continuous data
Used with Response Surface Methods Keep small (2-6 factors), gets large fast
Copyright © 2001-2004 Six Sigma Academy International LLC All Rights Reserved
DESIGN Rally Points 3-4 Design System, Subsystems &
Components Design Processes Model & Assess Critical Parameters
Copyright © 2001-2004 Six Sigma Academy International LLC All Rights Reserved
Copyright © 2001-2004 Six Sigma Academy International LLC All Rights Resp
Determine Customers
& Y’s:
Quality, Price & Product Demand
314-5
Important Formulas (Review)
First-Order Linear Model
Y = B0 + SBiXi + e Y = B0 + B1X1 + B2X2 +…+ BkXk + e Linear Model With 2-Way Interactions
Y = B0 + SBiXi + SSBijXiXj + e Y = B0 + B1X1 + B2X2 +…+ BkXk + B12X1X2 +…+ e Second-Order Quadratic Model Y = B0 + SBiXi + SBiiXi2 + SSBijXiXj + e Y = B0 + B1X1 + B2X2 +…+ BkXk + B12X1X2 +…+ B11X12 + B22X22 +…+ BkkXk2 + e
Step 2: State the factors and levels of interest
Step 3: Screen initial factors – reduce to as few as possible
Step 4: Establish design strategy
Step 5: Create CC design in MINITAB; randomize the runs
Copyright © 2001-2004 Six Sigma Academy International LLC All Rights Reserved
314-9
Properties of Default MINITAB CC Designs
Notes: 2 factors = 4 cube pts (Full) 3 factors = 8 cube pts (Full) 4 factors = 16 cube pts (Full) 5 factors = 16 cube pts (Res V, half-fraction) or 32 cube pts (Full) 6 factors = 32 cube pts (Res V, half-fraction) or 64 cube pts (Full) Most designs rotatable Orthogonal blocks
Develops Quadratic Models Relatively inexpensive Supports sequential experimentation strategy Optimizes process knowledge Commonly used with Response Surface Methods
Initial Product Platform key X’s, product velocities
Measure the X’s and Y’s
DEFINE Rally Points 0-1 Establish Business Needs & Priority
Develop Project Charter & Plan Identify Target Markets & Segments
OPTIMIZE Rally Points 4-6 Minimize Product Complexity
Maximize Product Velocity Optimize Critical Inputs - Final
Robust Design Optimize, Simulate Processes Final Robust Product Design
314-6
Two-Level Factorial
What is a Central Composite Design?
Cube Points Center Points Axial points
Central Composite
Each factor run at two settings (Lo and Hi) –Two points define the equation