doe 5.1class notes
TRANSCRIPT
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AudienceAudience
611 Whitby Lane Brentwood, CA [email protected]
This course is designed for those individuals directly working on product and process development to characterize, optimize and control product and process performance.
Presentation of course materials is designed for 16 hours of instruction.
Prerequisites:
Engineering Statistics and Data Analysis is recommended
Software:
JMP 5.1
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Topic Page Number
Section I Introduction to DOE and robust design principles 6Section II Experimental preparation 49Section III Full factorial designs 71Section IV Screening designs 124Section V Taguchi designs (optional) 149 Section VI Custom designs
167Section VII Optimization designs 204Section VIII Mixture designs (optional) 219
DOE Table of ContentsDOE Table of Contents
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Upon completion of the course the participants will be able to:
1. Apply the principles of robust design
2. Design experiments appropriate for the information of interest
3. Use and apply the structures of orthogonal arrays for industrial problem solving
4. Assure the experimental design is efficient
5. Use regression techniques in order to analyze the results and make process/product improvements
6. Use JMP software to design and analyze experiments
Course ContentCourse Content
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Section ISection I
Introduction to DOE and robust design principles Experimental preparation Full factorial designs Screening designs Taguchi designs (optional) Custom designs Optimization designs Mixture designs (optional)
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To improve process and design centering and design margins
Performance optimization
Improve product and process robustness
Establish valid design targets, transfer functions and sensitivity budgets
For new equipment characterization and qualification
Developing new process recipes
Problem solving
Variation reduction and performance enhancement
Yield improvement and defect reduction
When processes and systems are complex
DOE is typically the best approach to achieve breakthroughs in parameter design for new products and processes
General Use of DOEGeneral Use of DOE
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Ad-Hoc Data Analysis Versus DOEAd-Hoc Data Analysis Versus DOE
Ad-Hoc
Results data from the product and process
Goal was to make all the products the same
Problem is some of the parts are not yielding
Poor range of the Xs
Some correlation of the Xs
Results are often muddy and the signal is weak
Structured Experiments
Results data from the product and process
Goal was to make the product differently to learn what are the effects
Experiment is typically off-line
The range of the Xs is purposefully manipulated
Zero or near zero correlation of the Xs
Results are often clear and the signal is strong
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Experimental ProcessExperimental Process
1. Define the problem and goals
2. Brainstorm factors, experimental levels and responses
3. Design the experiment using JMP
a) Experimental matrix
b) Sampling plan
c) Error control plan
4. Run experiment, collect data
5. Analyze data, fit model and optimize the response
6. Validate the solution and implement the improvement
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Factor (X, Input)
A feature in the design or process which influences a resulting quality characteristic. Cost and time of the experiment is largely a function of the number of factors in the study. An X can be nominal or continuous.
Response (Y, Output)
A measurable quality characteristic of the product. A Y can be either nominal or continuous.
Level (Settings for each X)
Parameter settings for the experiment. Typical designs have 2-3 levels during characterization, 4-5 during optimization. The number of categorical levels are as many as are considered useful.
Language of DOELanguage of DOE
Process or Process or ProductProduct
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Response 1
Response 2
Response 3
Xs
Ys
Product Responses
Process or Process or ProductProduct
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Response 1
Response 2
Response 3
Xs
Ys
Product Responses
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ConstantFactors
Are held fixed during the experiment
ExperimentalFactors
Are changed during the experiment
CovariateFactors
Factors that cannot be controlled; however may influence the response
All constant factor effects during the experiment are considered to be zero. Single machine, single operator, one material lot etc. (error control).
The goal of the experiment is to characterize all experimental factors. Experimental factors are continuous, categorical or mixture.
Covariate factors must be measurable to be useful. The two types of covariates are insitu and fixed covariates. JMP only refers to fixed covariates during design.
More on FactorsMore on Factors
Effects of blocking factors are removed from the results as not to mix in with the estimation of other factors. (error control)
BlockingFactors
Factors included to control for potential sources of error
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Custom Design JMP Factor DefinitionCustom Design JMP Factor Definition
Select DOE, Custom Design, Factors, Add Factor to see the factor types in designing an experiment.
Once factors are defined they can be saved by selecting Custom Design, Save Factors.
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Bigger is Better Smaller is Better
One-sided upper specification limit only
USL
One-sided - lower specification limit only
LSL
Two-sided specifications
LSL USL
Target is Best
Three Types Of ResponsesThree Types Of Responses
Unacceptable Good
Good Unacceptable Unacceptable Good Unacceptable
What are some Company examples of each of these?
0
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Defining Responses in JMPDefining Responses in JMP
Select Add Response when adding responses to an experiment.
Once responses are defined they can be saved by selecting Custom Design, Save Responses.
Goals are defined:
Maximize (Lower Limit only)
Match Target (Upper and Lower)
Minimize (Upper Limit only)
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Linear Effects
Only 2 levels are required. Linear effects are about 70% + of all effects.
Interaction Effects
Two or more factors are required. Interactions are found in most systems. Interactions are about 10-20% of all effects.
Quadratic Effects
Three or more levels are required. Non linear effects are common. Curvature effects are about 5-15% of all effects.
Linear, Interaction & Quadratic EffectsLinear, Interaction & Quadratic Effects
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Factor & Response ExamplesFactor & Response Examples
In Class Exercise: 5 Min
Pre-Experimental DesignExperiment Name:
Date:Experimental Problem, Objectives and Goals: Experimenter(s):
Do the following:
1. Open the file Factor Response Matrix.xls
2. Select a product, process or test condition for characterization or improvement
3. Define the problem for the experiment
4. Determine the objectives of the experiment
5. Determine the goals of the experiment (maximize, minimize or hit some target)
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Responses:Responses:
Output: 1000 ft/hr or >
Dia.: 2.54” .03”
Cracks: < 10 per hour
Factors:Factors:
Speed: 200-100 rpmSpeed: 200-100 rpm
Temperature: 300-250Temperature: 300-250
Time: 10-5 minutesTime: 10-5 minutes
Pressure: 30-15 psiPressure: 30-15 psi
Manufacture of Extruded Plastic Rod
DOE simulationDOE simulation
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20 Trials to Solve the Problem20 Trials to Solve the Problem
Run Speed Temperature Time Pressure Output Diameter Cracks123456789
1011121314151617181920
In Class Exercise: 45 Min
Factors Responses
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Best Guess and Tweak
One Factor at a Time
All Combinations of all Factors
DOE
a structured development strategy for product/process engineering in order to characterize, optimize and control the product with minimal waste. This is accomplished by experimenting with many factors at the same time.
Commonly Used Development MethodsCommonly Used Development Methods
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System Design: is the selection of the general technology and or approach for the design or process
Parameter Design: is the selection of the targets for the design or process. For the design they are product design targets, for the process they are process parameter targets.
Tolerance Design: is the allowable deviation or limits from the target parameter. Bigger is better, smaller is better or target is best.
System, Parameter & Tolerance DesignSystem, Parameter & Tolerance Design
Dr. Genichi Taguchi: All development/design can be broken down into the following:
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Customer Requirements
Performance Requirements
System Design (Trade Studies)
Parameter Design (DOE)
Tolerance Design (DOE)
Design & Process Qualified?
(DPPM & Cpk)Yes
No
Control Product & Process (SPC)
Process Capability Data
Characterize, Optimize, & Control
Deliver to Customer
Systematic Product Development and ImprovementSystematic Product Development and Improvement
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PLAN Activity Time Importance
Statement of Objectives 10 % 70%
Organization of Support Team
Background Research
Selection of the Factors and Levels
DO Design and Run the Experiments 65% 10%
CHECK Modeling, Analysis, and Validation 20% 15%
ACT Optimization 5% 5%
Begin With the End in MindBegin With the End in Mind
Identification of the right factors and right levels are critical for achieving optimal results out of the experimentation process
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GOAL::
Ensure every design point and process operation is Robust with respect to its intended function.
ROBUST::
Insensitive to product or process variation. A robust product/process continues to provide high quality results even when variation is present.
Robust DesignRobust Design
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Taguchi Quadratic Loss FunctionTaguchi Quadratic Loss Function
Loss = k(2 + (-T)2)
$ Loss
LSL USL
Taguchi quadratic loss function is a good conceptual model for improving robustness. We need the right targets and right tolerances in order to minimize all losses in cost and performance. Quality is not a step function.
Dollar loss (K) includes:
Yield loss Quality incidents Customer loss Consumer loss Reliability loss Product recalls Customer sat. Market share loss
Example is a target is best loss function. There are also smaller is better and bigger is better functions as well.
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1. Design in Margin
2. Achieve Target
3. Minimize Variability
4. Characterize and Minimize Noise Effects
5. Design to the Flats
6. Use Parameter Combinations
7. Optimize Designs and Processes
8. Use Interactions to Tune Out Sensitivities
8 Robust Design Principles8 Robust Design Principles
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Typical design margins are 15% greater than worst case
100100 100 100
100 lb. rated
No Margin
100 Base 100 WC+ 30 Margin 230 lb.
1. Design in Margin1. Design in Margin
System design is the primary focus for margin improvement; material selection, product design, capital equipment, etc.
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GOAL: = Target
±1.5 Shifts inthe mean are commonduring productionRuns.
Keeping the product on target (not just within specification) is often the quickest and most simple way to make improvements in production yields and minimizes loss. This is particularly true for multi-step operations.
LSL USL
TARGET
LSL USL
TARGET
2. Achieve Target2. Achieve Target
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Non-Robust RobustProcess Process
Even when changes in the average occur the product is still within customer specifications
3. Minimize Variation3. Minimize Variation
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Variation Reduction MethodsVariation Reduction Methods
DFM Simplify product designs and follow design rules for a highly manufacturable product
Design of Experiments Improved targets, run conditions & controls
SPC Minimize over and under control errors
Correct Capital Equipment Determine if process is capable, reengineer, retool or capitalize if incapable
Buy better components Reduced assembly defects and improved products
POV/COV/REML studies Locate source of variation and make improvements
Supplier Qualification Allow only qualified parts into the assembly
MSA Eliminate or reduce gauge/tester error from the production system
Standardized work Clean, organized, ESD free, methods of work
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Noise
Factors in the environment that effect the product characteristics of interest
4. Characterize and Minimize Noise Effects4. Characterize and Minimize Noise Effects
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Process or Product
Raw
Mat
eria
l
Mac
hine
Ope
rato
r
Hum
idity
ES
D
Tem
perature
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Response 1
Response 2
Response 3
Internal Noise (Factors or Covariates)
External Noise (Factors or Covariates)
Particles
4. Characterize and Minimize Noise Effects4. Characterize and Minimize Noise Effects
Xs
Xs
Xs
Ys
Consider using the internal and external noise Xs as factors during your experiments. Then determine how to minimize their influence based on sensitivities.
Design parameters, Materials and Machine Settings
Product Responses
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Factor ATemperature
Volume
5. Design to the Flats5. Design to the Flats
Must include the quadratic term in the experiment and model in order to estimate curvature
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Use parameter combinations to reduce variation and place response on-target
Low Setting of A High Setting of A
Off-TargetLow Variation
On-TargetHigh Variation
6. Use Parameter Combinations6. Use Parameter Combinations
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High Setting of Factor A
Off-TargetLow Variation
On-TargetLow Variation
shift due to Factor B
Design or process characterization must be complete before an engineer can use this method
6. Use Parameter Combinations6. Use Parameter Combinations
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05
101520253035404550
5 10 15 20 25 30 35 40
Tons Shoveled per Manper Day
21.5 lb. optimum shovel load for any material
Old Way New WayNo. of laborers 500 140Tons per man per day 16 59Earnings per man per day $1.15 $1.88Cost per Ton .07 .03
600 workers & 15 different shovel geometries were used
Shovel Load
7. Optimize7. Optimize
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0123456789
10
1.0 1.2 1.4 1.6 1.8 2.0 2.2
BondStrength (lbs)
Cure Time (sec.)
Customer Requirement
7. Optimize7. Optimize
How does optimizing improve product robustness?
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Interaction Profiles
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49
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Speed
115111.25107.5103.75100
3026.2522.518.7515
Temperature
Th
ickn
ess
Th
ickn
ess
8. Use Interactions to Tune Out Sensitivities8. Use Interactions to Tune Out Sensitivities
Interactions can be used to tune the design or process to the flattest most robust condition.
What speed setting will cause the change in temperature to have little to no affect on thickness?
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Class III Class IVAffects only the Does not affectaverage the response
Class I Class IIAffects both the Affects the standard average and standard deviation only deviation
Types of Factor InfluenceTypes of Factor Influence
How would these look if displayed as scatter diagrams?
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Replicates are multiple runs and or measurements at identical test conditions. Experimental replicates are an excellent way to gather information concerning process and product variation.
3 to 5 replicates of the test condition are typically sufficient to characterize the mean and standard deviation.
In order to determine factor class, replicates must be used in the experiment and the Y response is summarized into mean and standard deviation from the replicated experimental raw data for each treatment combination.
Between unit (independent) replicates are much more expensive and highly desirable. Between unit replicates require additional units run at the same settings. (between replicates will add 3-5X the cost)
Within unit (dependent) replicates are inexpensive and very valuable. Within unit replicates are multiple measurements taken on the same unit. Within unit replicates are sometimes referred to as pseudo replicates.
ReplicatesReplicates
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1. Experimental Design
2. Statistical Tests and Analysis
No amount of statistical manipulation will correct for poorly planned and conducted experimentation
Good designs will result in good interpretation of the results
Experimental Design and Statistical TestsExperimental Design and Statistical Tests
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Test Validity
Test appropriate for the measure
Tests the condition of interest
Valid test results are considered to be true
Test Repeatability
Same results time-after-time
Can a test be repeatable and not valid?
Test ValidityTest Validity
Patterned silicon substrates are expensive, un-patterned glass substrates are cheap. Which substrate should you select for the experiment?
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Internal Validity
Results are valid within the test
The effects we see are real
Results are not confounded
DOE is excellent for internal validity
External Validity
Results can be generalized and repeatable
Given similar conditions (materials, machines, etc.) we will see similar results
Threats to ValidityThreats to Validity
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1. Unknown Events
2. Systematic Change
3. Measurement Error
4. Lost Tests
5. Identification
6. Test Reaction
7. Selection
8. Regression
9. Outliers & Data Entry Errors
Threats to Internal ValidityThreats to Internal Validity
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1. Unknown Events
An event occurs during the experiment that has an effect. The effect of the event is confused with another factor.
2. Systematic Change
Some systematic change occurs in the system during the experiment. The systematic change is confused with another factor.
3. Measurement Error
Problems with accuracy, linearity, repeatability, reproducibility, and stability of measurement. The measurement errors are mistaken for factor effects.
Threats to Internal ValidityThreats to Internal Validity
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4. Lost Tests Missing data does not allow for proper analysis of the data and false conclusions are drawn.
5. Identification
Test results are misidentified or not identified at all. The link between results and the test conditions are corrupted. This is the #1 error in large experiments.
6. Test Reaction The parts and or materials change as a direct result of measurement.
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