Download Using 6-Sigma Experimental Design Tools in Product

Using 6-Sigma
Experimental Design Tools
in Product Improvement Testing
MAESC
May 11, 2005
Paul Babin, P.E.,
William Parker
Using 6-Sigma Experimental Design
Tools in Product Improvement Testing
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What is 6-Sigma?
Experimental Design
Rubber Plug Example
Planning the Test
Results – ANOVA
Engineering Model
Regression Analysis
Synthesis of Models and Experiments
What is 6-Sigma? 3.4 ppm
3.4 PPM
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0
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6-Sigma Process Improvement Methodology
Define the key
processes that affect
customers.
Define
Analyze the data, converting
it to insightful information.
Measure
Analyze
Control the process to
assure that important
improvements are
sustained.
Improve
EXECUTION
Measure the
performance of key
characteristics.
Improve the process to
achieve the results desired.
Control
Comparing Six Sigma, Lean, TOC
ref Dave Nave, Quality Progress, March 2002
Program
Six Sigma
Lean Thinking
Theory of Constraints
Theory
Reduce variation
Remove waste
Manage constraints
Application
Guidelines
1.
2.
3.
4.
5.
Define
Measure
Analyze
Improve
Control
1.
2.
3.
4.
5.
Focus
Problem focused
Identify
value
Identify
value
stream
Flow
Pull
Perfect
Flow Focused
1.
2.
3.
4.
5.
Identify constraint
Exploit constraint
Subordinate
constraint
Elevate constraint
Repeat cycle
System constraints
6-SigmaTools by DMAIC Phase
ref Implementing 6-Sigma, Breyfogle 2003
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Define
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Project Selection Matrix
Cost of Quality
Project Charter
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Key process output variables
Financial Metrics
Voice of the Customer
Analyze
Box Plots, Pareto Charts, Control
Charts
Scatter plots, Comparison Tests
Regression Analysis
ANOVA (Analysis of Variance)
Improve
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Measure
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Key process input variables
DOE (Design of Experiments)
Full Factorial DOEs
2k Fractional Factorial DOEs
Robust Designs
Response Surface Methodology
Improvement Recommendations
Control
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Process Maps, SOPS,
Failure Mode and Effects Analysis,
Mistake Proofing
Control Plan
Change Management
Experimental Design
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Statistical Methods that provide an
investigator with a way to overcome the
difficulties typically encountered including:
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Experimental Error (noise)
Confusion of correlation with causation
Complexity of the effects to be studies
Adapted from Box, Hunter, and Hunter 1978
Design of Experiments
Factors
Process
Experimental Error
(Noise)
Response
Using DOE in a 6-Sigma Project
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Select an appropriate Response Variable
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Continuous Variable (ratio level)
Measurable
Identify possible factors and interactions
Select factors and factor levels
Plan the experiment (treatment combinations)
Conduct the experiment
Analyze the Results
Recommend Improvements (or further testing)
Example : Plug DOE
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Response Variable:
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Factors (and levels):
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Holding Pressure
Tube Size (5 sizes)
Tube Wall (thick and thin)
Plug Material (old & new)
Temp (high & low)
Full factorial design
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40 treatment combinations
(5x2x2x2)
Running The Test
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Insert Plug and
condition for 24 hours
Slowly increase air
pressure
Note the pressure at
which the plug just
starts to move
Running the Test
ANOVA
Source DF
SS
MS
F
p
Model
7
2660.45
380.06
13.01
<.0001
Error
32
934.65
29.21
Total
39
3595.10
R2 = 0.74
Source
Nparm
DF
SS
F
P
Size
4
4
1366.35
11.69
<.0001
Wall
1
1
313.60
10.74
0.0025
Matl
1
1
980.10
35.56
<.0001
Temp
1
1
0.40
0.014
0.9076
ANOVA
Source DF
SS
MS
F
p value
Model
7
2660.45
380.06
13.01
<.0001
Error
32
934.65
29.21
Total
39
3595.10
R2 = 0.74
Source
Nparm
DF
SS
F
P value
Size
4
4
1366.35
11.69
<.0001
Wall
1
1
313.60
10.74
0.0025
Matl
1
1
980.10
35.56
<.0001
Temp
1
1
0.40
0.014
0.9076
What does that mean?
Validated Test Method.
 Reduced (but not eliminated) noise
 Discriminate between important
differences
 Factors explained 74% of the variation
 Temperature not important
 No Interactions
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Engineering Model
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Predictive Model
Press Fit Concentric Model
Response: Holding Pressure
Variables:
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Coefficient of Friction
Elastic Modulus & Poisson’s Ratio
Amount of Compression
Cross Sectional Area
Regression Analysis of Engineering Model :
Average Test Pressure Observed vs. Predicted
Engr Model vs. Average Test Pressure
y = 0.833x + 3.9208
R2 = 0.809
50
Observed
40
30
20
10
0
0
10
20
30
Predicted
40
50
Future Analysis – FEA models
Comparing the Models
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Factorial Experiment
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Holding Pressure =
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Engineering Model
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b1 * Material +
b2 * Size +
b3 * Wall +
error
no temperature effect
no interactions between
factors
R2 = 74%
Holding Pressure = Nonlinear function of
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Amount of Compression
Plug Wall thickness
Coefficient of friction
Young’s modulus
Poisson’s ratio
Plug length
R2 = 80% (using averages)
But where do we get all the parameters to plug in? Experimentation!
Synthesis
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Engineering Models
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Describe behavior
based on physical
properties
Provides a precise
predicted average value
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Factorial Experiment
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Describe experimental
variation
Determine important
factors
Validate Engr Model
6-Sigma Product Improvement
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Understand and Reduce Variation
$$$
References:
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Breyfogle, Forrest W. III, “Implementing Six Sigma – Smarter
Solutions Using Statistical Methods, 2nd Edition”, Wiley, 2003.
Box, George E.P., William G. Hunter, J. Stuart Hunter,
“Statistics for Experimenters – An Introduction to Design,
Data Analysis, and Model Building”, Wiley, 1978.
Nave, Dave, How to Compare Six Sigma, Lean and the
Theory of Constraints. Quality Progress, March 2002.
ASTM D 2990 – Standard Test Methods for Tensile,
Compressive, and Flexural Creep and Creep-Rupture of
Plastics.
Brewer, Peter C., Jan E. Eighme, Using Six Sigma to
Improve the Finance Function, Strategic Finance, May 2005.
Questions?
Extra Slides
Test Methods
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ASTM D 2990 – Standard Test Methods for
Tensile, Compressive, and Flexural Creep
and Creep-Rupture of Plastics.
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Viscoelastic Creep
Note 8 – Precision and Bias
Attempts to develop a precision and bias
statement for these test methods have not been
successful…
3 sigma = 99.73%
2700 ppm defective
99.73% within +/- 3sigma
2700 ppm defective
Low er
Specification
Limit
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Upper
Specification
Limit
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6 sigma = 99.999660%
3.4 ppm defective even with shift in mean
Low er
Specification
Limit
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Upper
Specification
Limit
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Another 6-SigmaTool list
ref Using Six Sigma to Improve the Finance Function, Brewer 2005
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Define
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Surveys, CTQ Ranking
Pareto Chart, Five Whys Technique
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Company-Wide definition Guidelines
Data Collection Plan & Sheets
Sigma Calculation
Prioritization Matrix
Analyze
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Process Mapping, Value Added
Analysis
Bottleneck Analysis, Fishbone
Diagram
Outside Suggestions
Deductive Reasoning and FMEA
Pareto Chart, Histogram, Dot Plots,
Regression Analysis
Discussion, Voting
Improve
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Measure
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Brainstorming
Outside Suggestions
Voting
Cost/Benefit Analysis
Solution Prioritization Matrix
Piloting Plan
Control
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Standard Operating Procedures
Project Library
Control Chart
Pareto Chart
Balanced Scorecard
Mistake Proofing