doe 5.1class notes

AudienceAudience

611 Whitby Lane Brentwood, CA 945131-925-285-1847drlittle@dr-tom.comwww.dr-tom.com

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

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

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

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)

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

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

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

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

Product Responses

Process or Process or ProductProduct

Factor 1

Factor 2

Factor 3

Factor 4

Factor 5

Response 1

Response 2

Response 3

Product Responses

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

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.

Bigger is Better Smaller is Better

One-sided upper specification limit only

One-sided - lower specification limit only

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?

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)

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

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)

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

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

Best Guess and Tweak

One Factor at a Time

All Combinations of all Factors

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

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:

Customer Requirements

Performance Requirements

System Design (Trade Studies)

Parameter Design (DOE)

Tolerance Design (DOE)

Design & Process Qualified?

(DPPM & Cpk)Yes

Control Product & Process (SPC)

Process Capability Data

Characterize, Optimize, & Control

Deliver to Customer

Systematic Product Development and ImprovementSystematic Product Development and Improvement

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

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

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.

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

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.

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

Non-Robust RobustProcess Process

Even when changes in the average occur the product is still within customer specifications

3. Minimize Variation3. Minimize Variation

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

Factors in the environment that effect the product characteristics of interest

4. Characterize and Minimize Noise Effects4. Characterize and Minimize Noise Effects

Process or Product

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

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

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

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

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

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

0123456789

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?

Interaction Profiles

115111.25107.5103.75100

3026.2522.518.7515

Temperature

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?

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?

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

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

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?

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

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

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

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.

doe 5.1class notes

bc abc ab

std dev yield

blade anglesolder

selecting

fractional

target low

factor response

cat alyst

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