Design of Experiments in Solving Real Life Problems

www.LRamanan.com

RAISE - An IIT Alumni Initiative for Learning & Development

Design of Experiments in Solving Real Life Problems Course Code: 6S – DoE – 001 By

Prof. L Ramanan. BE, MS (IITM), MS (BITS) 6 Sigma Quality Champion, Management Consultant & CEO of Member & Title

Lecture Class Material of Delegates … Not for Sale or for Commercial Use…

Request to avoid Copy/Transmission Please

Two Days Work-Shop For Practicing Design, Manufacturing, Quality and Sourcing Professionals of

Acknowledgements • Sri.Mohanram, Sri.Krishnamoorthy, Sri.Srinivas, Sri. Augustin, Sri.Rohith, IMTMA Management, Technology Centre, all of you & your organisations for nominations to this course

• GE, Lucas TVS, Indian Railways, IITM, all past employers, Teachers, Mentors, vendors, suppliers, ASQ, ASME, QCI, IEI, ASM, IUSSTF & IUCEE, BMSI, Minitab, all my professional associations, family, relatives & friends in India & in global poles. Author is grateful to all above and in particular to IITM, Indian Railways, GE & Lucas-TVS for their contributions that made him a SME in CAE & DFSS domains for Predictive and Robust Design Note: • Opinion expressed here are purely that of the author & only for academic purpose of enhancing knowledge. No other interpretations are implied or intended or shall be made. Practical examples picked-up are from the published / presented work of the author and others in public domain. They are referenced and greatly acknowledged, if I missed any in reference I sincerely apologize and is not intentional - Ramanan

2/ LRamanan, March 16, 2012

About The Inspiring & Motivational Faculty

RAISE and RICE… Earn and Educate

3/ LRamanan, March 16, 2012

WE as a Team Will Participate Interactively

Learn New Things Share Thoughts Add Value for Time & Money

Have Lot of Fun Mute Mobile

Arrive On-Time – Every Time

Designed Experiments Part of DFSS 6S-DoE-003

Optimization

Optimise Montecarlo Factor Setting Simulation

Prediction

Taguchi Method

6S-DoE-002

Noise Factor Robust OA Design Control Factor Quality Loss Function S/N Ratio

Robust Design

ANOVA

Orthogonal Array

Factorial and Fractional Factorial DoE

6S-DoE-001

Responses Virtual Model Interactions Factors Resolution CAE - DoE Designs Confounding Randomization Levels Transfer Function Applications Benefits

DoE for Real Life Applications Towards Design For Six Sigma & Robust Product

DoE

What they Said About Professional Attitude? • Engineers: Make it Work • Scientists: Understand Why it Works • Mathematician: Don‟t Care - Prof. William G Hunter at 3rd Taguchi Symposium, American Supplier Institute , 1985 Computer Based Robust Engineering by Taguchi et. Al.

•

• •

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There is a great difference between science and Technology Science is to Study Natural Phenomena and laws of nature can not be changed. Engineering is to design a product that does not exist in nature, but perform the desired function every time & satisfy customer at least cost Engineer‟s Role is to “Make it Work” every time

Aryabhata Mathematician & Astronomer

Engineers Yourself & Myself

An Engineer has Lot of Challenges!!!

Prediction in Engineering & Technology… Equation – Ideal vs Real Apart from Writing

Inventive Usage by Customer

Gap

Design By Engineer for Writing

Closer to Reality… Need to Know A Lot of Info

Real Life Problems Inputs Process

Inputs

Process

Outputs

Outputs

Every Component, Assembly process etc. is a variation

Inputs

Process

Outputs

• Mfg Proces • Measurements • People • Environment

Are Not Single Point Solutions

Elements to Address in Design

Risk Mitigation & Robustness Due to Prediction

Ideal Equation In-Sensitizes All Variations • Customer Use / Abuse • Process & Manufacturing Variations • Environmental Variations • Operator Variations • Variations in Inputs • Product wear • … Design of Experiments… Delivers Robust Design

Why DoE? Is it Necessary? • Practical Applications of Real Life Requires a Pointed Prediction Instead of General Statement • Design of Experiment (DoE) is a Structured scientific approach towards Prediction with Certainty • Researcher work who don‟t use DoE, do not get published (Paul… pp94) Prediction… Closer to Ideal Solution

Statistical Methods For Engg. Quality 1920s Beginnings of Modern Quality Control (Shewhart) 1920s & 1930s Origins of DOE (Fisher, Yates, etc.) 1940s (WW II) Inspection Sampling, Sequential Design, etc. 1950s Work of Deming, Juran, Ishikawa, etc. in Japan 1950s Early developments in Reliability (in Aircraft Industry -- Boeing, etc.) 1970s+80s Japan becomes Quality Leader 1980s Refocus on Q&P in US and Europe 1980s Quality paradigms, Taguchi, etc. in US 1985 Introduction of Six Sigma in Motorola, GE…. 1990+ Continuing emphasis on DFSS and other initiatives )

Do Not Run-Away We Will Have Less of Maths, more of Application examples & Lot of fun

DoE is Essential Part of Controlling Variation

Controlling Variation is Part of DFSS

Fundamental Concept of Six Sigma – Reduce the Variation Target / Centre the Mean

Example of a Safety Critical Medical Product – Stents Imagine Variation in Diameter & Effect

Medical & Aerospace… More than Six Sigma

Why Design of Experiment is Part of DFSS Lean - Methodology

Strength

Design for Six Sigma Methodology

Design Phase

Phases of Product Production Phase

Define Measure Analyse Design Optimise Verify Validate – Design Transfer

Control

Risk Prediction & Mitigation

Product in Infant Phase

Field Issues Due to Non-Prediction Product Towards Maturity Phase

Life of Product

Designed Experiments… Risk Prediction & Mitigation

Four Way Prediction / Learning Process Learning from Some One –

Carries risk …?

Theoretical Derivation –

Life will be … Easier / Done?

Empirical Observation -

Observation from naturally occurring

informative events (Field issues / warranty / customer abuse)

Designed Experiments

–

Deliberate Creation of Informative events Proactively manipulate input, so as to study their behavior in output Invites Informative event to occur Provides powerful information from a well planned experiments 15 / LRamanan, March 16, 2012

Designed Experiment… One Powerful Way to Predict

Some Predictors… • • • • • • •

Gypsies Bookies Tarot Cards Palm Readers Horoscope Fortune Disks Equations??!! Engineered Products… Prediction is Complex

Engineered Products… Prediction is Complex

Design of Experiment (DoE) • Powerful Statistical Technique – Introduced by RA Fisher in 1920s • To study the effect of multiple factors together • Fisher developed it to influence of water, fertilizer, sunshine etc. to produce best crop yield

RA Fisher (1890 – 1962) The Design of Experiment - RA Fisher, (1935) McMillan

A Structured Method for Experimentation

DoE in Industrial Applications Factorial and fractional factorial designs (1930+) Agriculture Sequential designs (1940+) Defense Response surface designs for process optimization (1950+) Chemical Robust parameter design for variation reduction (1970+) Manufacturing & Quality Improvement Virtual (computer) Experiments Simulation Models (1990+) Space, Automotive, Semiconductor, Aircraft, Medical……

DoE in Business Decisions •

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•

•

•

You are In-charge of Manufacturing line Producing Oil for human usage. Produced Oils are canned in capacity of 50 Lts each for large users and are ready for shipping. 1000 cans are ready for shipping to the customer. Before shipping, you got to know one of the can was used to store pesticide temporarily. But, all cans look alike Testing to find the traces of pesticide in the oil with 100% certainty to isolate the can before shipping the can to customer is possible. Each can of Oil costs Rs 5000/- , while the test shall cost Rs 6000/- for confirming the traces of pesticide in oil and shall take 3 Days for results. What to do? Do we need to perform 1000 Experiments for 1000 cans? What is your suggestion?

Designed Experiments Makes Life Simpler…

DoE for Manufacturing •

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Minimizing the number of part counts in an assembly, is one of the key principles in enhancing reliability of the product. World over, rail wheels are assembled to the axle through interference fits, unlike the Automotive, where wheels are assembled by Bolts and Nuts. Force Required in assembly of the wheel to the axle is the critical parameter and is tracked for every assembly towards safety of the joint and the assembly is rejected if the force is below the threshold value. Each assembly line rejection results in loss and delay in delivery of product Recently there are huge rejection in line, as a Manufacturing Engineer you need to Fix the issue.

Where to concentrate? Surface Finish, Hardening, Material, Lubricant, Process of Assembly, etc…

Use DoE… Reduce Rejection & Impact Productivity

DoE in Process Industry •

• • •

Amount and adherence of Chemical deposited at the Tip of the match stick impacts the product quality to lit the fire Match stick thickness Dryness / Moisture content of Stick Adhesion Characteristic of the wood

More of Chemical deposition leads to increase in cost of product or reduction in margin to the organisation Less of Chemical deposition leads to customer dis-satsifaction due to product dis-function Arrive at Optimised Chemical deposit thro DoE Control the Process thro Six Sigma Approach

Use DoE… Reduce Rejection & Impact Productivity

DoE in Defense

Usage of DoE Results in Savings in $$ and Cost

Engineered Products… Complex… But Doable

Prediction

is

Movement of Balls in the return tube of the Ball Screw used in Machine Tools, Special purpose machines Study to maximise the effect on the Fatigue Life of Return Tube due to Impact by Ball Material - Silica, Steel Return Tube – Wall thickness Velocity of Travel Ref:

Animation

MTech Thesis of Lakshmanan, VITU 2008

Industry Guide: L Ramanan

DoE with CAE Simulation… Research and Development

Engineered Products… Complex… But Doable

Prediction

is

Back Pressure Exerted on the Piston governs the effective oil sealing pressure exerted by the Oil Seal due to the compression of O

Ring.

Animation

Variations in geometry of Piston, Oil Grove assembly Variation in Seal Size Variation in Diameter of O Ring Material Charecteristic of O Ring Animation

Ref: L Ramanan (2007) Role of CAE Simulation in Predictive Design, S. Asia CAE Conference

DoE with CAE Simulation… Physics of Behaviour

Engineered Products… Prediction is Complex… But Doable Ref: L Ramanan, IP Publications 1. Method of Testing Patient Handling Table Top – Ref: IPCOM000193362D 2. One-dimensional Linear Motion Systems for Three Dimensional Translatory Motions IPCOM000182841D Ref: L Ramanan

Medical Device comparable to a Complex Special Purpose Machine with Ball Screws, Linear Motion Guides, Composite Table Tops Prediction in Early Stages of Design by Combining DoE with CAE Simulations Mitigates Risks in Product build Stage Virtual Experiments in early stages leads to Robust Design – Close Correlation of Prediction with Actuals, between 90% to 95% at various locations measured. Ref: L Ramanan (2008) CAE Simulation An Inspiring Technology in Medical Device Design

DoE with CAE Simulation… Early Stages of NPI

Prediction

Actual

Engineered Products Are Complex… But Prediction is Doable & Achievable

DoE in Non-Engineering Products & Applications… Possible

Application of DoE is Un-Limited DoE Application is not Restricted Traditional Applications, Like

Engineering Design, IB, NPI Manufacturing

Non-Traditional Applications, Like Vacation Plan

Human Behavior Marketing Sales

Imagine & Apply DoE… Innovate New Ideas

Non Traditional Application of a DoE - Field To achieve Maximum Yield 3 Factors – Fertiliser, Water, Pesticide

Experimental Approach – Experiment 2 Levels

LSL

USL

Fertiliser

10ml

12ml

Water

1lit/day

1.5lit/day

Pesticide

25g

30g

Example – Imagination at DoE

In Brief… DoE A key technology for optimizing product and process design and for quality and reliability – Q & R Improvement Systematically investigate a system's input Systematically input output relationship to: Improve the process (Q&R) Identify the important design parameters Optimize product or process design Achieve robust performance Predict & Mitigate Risk in Early Stages of NPI Reliability Prediction in Virtual Lab in Early Stages •••••

Impacts Business by Building Robustness

One Factor at A Time Experiments One Factor at a Time (OFT):- In this approach, we vary One element / factor / parameter at a time to understand and achieve the desired response / effect. •

Simple and Direct

•

Chances to

an

of

Missing

Interaction

of

response factors,

due which

might be significant is more. Example From Your Coffee Break •

To Serve a Steaming coffee always, do we test the response by changing only, one factor at a time keeping others constant

Boiled Milk, Steaming Brew, Warm Glass

What is Factor, Response …?

32 / LRamanan, March 16, 2012

Designed Experiment Tells the Inside Info Run

One Factor at a Time(OFT):- In this approach, we vary One factor at a time while keeping other factors

Temperature

Pressure

Response

1 Cons

-1

20

2 Cons

1

40

3 Cons

-

4 Cons

-

Constant. Data from an Plating Experiment •

Simple and Direct

•

Chances of Missing response due

Run

to an Interaction of factors, which

Temperature

Pressure

Response

1

-1 Cons

40

2

1 Cons

12

3

-

Cons

4

-

Cons

might be significant is more. Max Yields From OFT Results

•

When T is Constant and P is + ve (40)

•

When P is Constant and T is – ve (40)

•

But Max Yield is 50, when T is –ve P is +ve

Run

Temperature

Pressure

Response

1

-1

-1

20

2

-1

1

40

3

1

1

12

4

1

-1

50

Using a Full Factorial design instead of a one-factor-at-a-time approach allows us to understand much better how the process works.

Key of DoE… Effect of Factor Interactions


Road Blocks in DOE Experimentation Perceived Notion DoE Exercise is Costlier DoE is Time Consuming Previous Designs Does not use DoE Last DoE results were un-clear

Clarity, Ambiguity & Mindset Unclear Problems & Objectives Incomplete Brain Storm for Cause We do not Need DoE & I know!! Lack of Understanding of DoE Lack of Understanding of Tools Lack of Coaching & Training Constraints & Limitations

Lack of Understanding on the Usefulness of DoE 34 / LRamanan, March 16, 2012

When to Use and Not to Use DoE? When the Factor is 1 – Relationship of the Factor to Response is known - ? When the factors are between 1 and 5 Use a Full or Fractional Factorial DoE (Rule of Thumb) LSL

Good Coffee

USL

When Factors are more than 5 use clue generation / Brain storm / Screening DoE Y = fn (X1, X2, X3 ….) to identify Insignificant Factor Glass

To Include the Noise Factors and Insensitize Design use Taguchi Method

Milk

Brew

Temp Sugar Ambience

But be Sure of Objective & Output of DoE is clearly understood and Identified Choose an Appropriate Model…


Why Choose a Model? Based on the Need and Output Expected from Experiment Based on Interaction effect‟s Significance Based on the Number of Experiments that is possible to conduct Based on approach of experiments – Computer Simulations / Actual Experiment

LSL

Y

Glass

Good Coffee

USL

= fn (X1, X2, X3 ….)

Milk

Brew

Temp Sugar Ambience

Based on Time, Money, Resource Based on knowledge on experimentation 36 / LRamanan, March 16, 2012

Experiments Costs Time, Energy Money…

Elements in DOE Experimentation Response Usually Output Variable of a Process & addressed as Response – Y Largely a continuous data in Industry than a discrete (Good Coffee)

Factors

LSL

Good Coffee

USL

Usually Input Variable for the process Addressed by the Term Factors – Xs Y = fn (X1, X2, X3 ….) Xs may be Qualitative or Quantitative Process may have „N‟ Number of Xs Glass Milk Brew Temp Sugar Ambience • Factors Shall be measurable • Factors must be quantifiable

Noise DoE Helps in Building Relation of Factors to Response


Stages in Experimental Design (DoE) Plan the Experiment

Perform the Experiment

Analyze the Results

Replicate, Verify & Validate

Define Goal of Expt Main & Noise Factors Main Factors & Levels Decide Type of Expt Declare Limitations

Perform Experiments Record Results Randomize for Noise

Analysis of Results Transfer Function Significant Factors Performance Settings Confirmation & Final Run

Structured Approach from Test Plan to Result


Goal of the Designed Experiments The most important part of the DoE is

defining the Goal of the experiment, expected outcome, limitations and constraints Ref: www.youtube.com

Planning is a Part of Striking Success


Components of Experiments Output Variables (Response Y) Continuous / Discrete

Input Variables (Factors – Xs) Controllable, Measurable & Quantified

Noise Variable (Factors) – Nuisance / Lurking Variables

Control / Track them

Y – Power of Motor Y = fn (X1, X2, X3 ….)

Y = fn (X1, X2, X3 ….)


Input & Output Variables Output Variables (Response Y) Are Dependent Variable Referred as Yield or response

Input Variables (Factors – Xs) Are Independent Variables Suspected to impact Output significantly Must be controllable & Measurable Arrived thro, a structured process like QFD, FMEA, Solution Tree, Brain Storm… Factors are Quantitative (Continuous Data – Temp, Pr. Etc) or Qualitative (Attribute

– Good / Bad, Machine No etc) or both Y – Power of Motor Y = fn (X1, X2, X3 ….)

Factors Have to Be Controllable


Noise Factor in Design of Experiments To be Accounted if Significant (Taguchi Method) Difficult to know all Noise Factor Generally Considered Insensitive Noise Variable – Continuous & Discrete Remedial Measure, if Insignificant

Randomize Experimental run Fix Variable like Shift, man, M/C If can‟t control – Monitor them Brain Storm & Clue Generation

Noise… Is it Insensitised in the Design? 42 / LRamanan, March 16, 2012

Some Examples of Noise Factors Environmental Temp., Humidity, Vibration, etc

Electrical ESD, Fluctuation, Grounding, etc.

Mechanical Tool Wear, Noise, Fixture..

Raw Material

WWW.WIKI.Com

Composition, Surface, Moisture etc.

Noise… The lurking Variable?


The „Lurking Variable‟ „Lurking‟ Variable An variable that has an important effect and is not considered in the Experiment - its existence is un-known - influence is assumed negligible - historical info / data is unavailable

Approach – Randomize Experiment - Randomization is not standard order - Helps averaging out effect of Noise - Helps in validating statistical conclusion - If Interaction Effects Are Insignificant Switch over to Taguchi Method Ref - “Lurking Variables: Some Examples,” , Joiner, Brian L, The American Statistician, November 1981, Volume 35, No. 4, pp. 227-233.

Lurking Variable … Is it Accounted?


An Example for „Lurking Variable‟ In an example, to study the effect of surface treatment application with bath temperature, Concentration and current as factors, it was not known stirring the bath is a “Lurking Variable” / “Noise”. Two Conditions of stirrer kept On & Off In Condition On – Yield was high

In Condition Off – Yield was low Nullified the effect of On and Off, by averaging out the effect if this is not a factor in the experiment

Randomizing Averages Out the Effect


Experimental Validity Internal Validity Answers the Input variables have really impact the output variable or some Noise factor would have Caused it Randomize the experimental run averages out / Spreads the effect across experiment

External Validity Answers how well the experiments matches the actual process and covers the entire range of variations Can be addressed by allowing Noise to take part in experiment – For example same part / component from different supplier

Effect of NOISE


Levels & Selection 0 -1 If this is the True Effect – Consider 3 Level Example – Concentration of Bath – Low, Medium and High

Number of Experiments = Lk 23 ie 2x2x2 = 8 Experiments 33 ie 3x3x3 = 27 Experiments

1

Example of Factor Levels Level 1 Level 2 Level 3 Qualitative Machine A B Concentra Low High Medium Solder A B Quantitative Pressure(Pa) 30 - 40 90-100 Mass (kg) 75 105

Choose Appropriate Levels


Types of Experimental Design - DoE

Full Factorial Experiments – All combination of Factors are Studied. Using such experimental results, effects of all main factors and their interaction can be estimated Fractional Factorial Experiments – A fraction of Total Number of LSL Good Coffee USL experiments are studied, for the reasons of time, resources & cost Y = fn (X1, X2, X3 ….) Example: Taste of coffee with 4 factors at 2 level, we need to perform 24, 16 experiments. If we decide to reduce number of experiments, then itGlass Milk Brew Temp Sugar Ambience is a fractional Factorial DoE Plackett Burman Box-Behnken Orthogonal Array are examples of fractional factorial 48 / DoE model LRamanan, March 16, 2012

Screening DoE Helps in Identifying Vital Xs

Approach to a DoE Screening DoE

Performed to identify significant factors, When more number of factors are involved and Significant Factor Main Factor is not known

Characterization DoE Performed to understand the effect of main effect of factors and their interactions. Results of experiments are used in Generating Transfer function

Optimization DoE To identify Optimum point for the factors in the process / product

Note: Noise is assumed as Not influencing Response

L, Ramanan (2009) “Role of Six Sigma in Building Robust Products - With Examples from Medical Devices” IV PDMA International Conference on New Product Development, IIT Madras, Chennai - India

Approaches to the Design of Experiments


Type of Experimental Design Response Surface TAGUCHI Method / Robust Engineering Full Factorial with Replication Full Factorial with Repetition Full Factorial without Repetition or Replication

Full Factorial DoE Screening / Fractional Factorial DoE

Higher the Experiment… More is the Info 50 / LRamanan, March 16, 2012

Typical Examples of Objective of a DoE Effect of alternate Material – To Bring down cost Effect of Input variation – Product Reliability (Example Dealt) Impact of Skilled and Un-skilled Operator – Product Quality Impact of highly precised / low cost M/C – Process Quality Process Input Variables – On Product Characteristic

Significance of Input Variable is not Known – Screening DoE Alternate Methods – Best Out puts

Not Exhaustive… But can Generate Spark


Some Examples for Factor Selection FMEA / Cause and Effect

Engineering Knowledge

Hypothesis Testing

Operator Experience

Process Mapping

Scientific Theory

Brainstorming

Customer/Supplier Input

Literature Review

Clue Selection

Solution Tree

Subject Matter Expert Opinion

Past Experience

Scientific Theory

Story Boarding


Affinity

Minimize Factors… Do Not Miss Critical One 52 / LRamanan, March 16, 2012

To Understand Factorial Design Product GEM Clip – Back Ground Gem clip is used to hold the bunch of given number of papers together for a given size. After the clip is removed, user does not know how many paper a given size holds, but keeps on using it. When the clip holds beyond its design intent, gets deformed (opened-up) due to plastic deformation. User pushes it back to shape and starts using it. This cycle continues till clip breaks due to cyclic loading-unloading (Fatigue!!). We shall design an experiment to find which factor is important

Ready for a Simple Exercise?

Seeing is Believing…

Feeling is Experimenting…


Three Factors Full Factorial Designed Experiment Goal of Experiment Fold and Un-Fold the gem Clip till it breaks to understand the Fatigue Life and hence its reliability

How Many Experiments?

Response Record Time / Strokes to break

Gemclip Team Activity Identified Factors 1. Wire Dia A 2. Material B 3. Hardness C

Questions: Is this not Simple and Direct? Do we need to Structure an Experiment? Do n‟t we know the answer off-the hat from experience?

Is there a Need to do a Structured Experiment 54 / LRamanan, March 16, 2012

Standard Order of Designed Experiments Experiment Factor A Factor B 1 -1 -1 2 1 -1 3 -1 1 4 1 1

Experiment Factor A Factor B Factor C 1 -1 -1 -1 2 1 -1 -1 3 -1 1 -1 4 1 1 -1 5 -1 -1 1 6 1 -1 1 7 -1 1 1 8 1 1 1

Two Factors and Two Levels We have Seen this Earlier during OFT

Three Factors and Two Levels We re Seeing it Now

Is there any Observations?

We are Progressing… 2 Factors to 3 Factors




One Observer and One Recorder Operators 3, 3 Samples, 3 Trials

Response Record Time / Strokes to break Identified Factors 1. Wire Dia A 2. Material B 3. Hardness C

Gemclip Team Exercise

(30Mins)

Analysis of Effects Due to Main Factors (A, B, C) Two Way Interaction (A*B, A*C, B*C) Three Way Interaction (A*B*C)

LRamanan, 16, 2012 Structured Experiment… Is it Going to Deliver a News / March Clue?

56 /

DESIGN

of Experiment

Factors (3) k 1. Wire Dia 2. Material 3. Hardness

– Level and Factor

A B C

Levels (2) & (3) LSL, USL Low, Medium, High -1, 1 -1, 0, 1 Number of Experiments = Lk 23 ie 2x2x2 = 8 Experiments 33 ie 3x3x3 = 27 Experiments If all Experiments are performed it is known as „Full Factorial‟ otherwise it is Fractional Factorial. Examples are Orthogonal Array, Plackett Burman etc..

Experiment Factor A Factor B Factor C 1 -1 -1 -1 2 1 -1 -1 3 -1 1 -1 4 -1 -1 1 5 6 7 8 Note :- -1 LSL and +1 is USL

Example of Factor Levels Level 1 Level 2 Level 3 Qualitative Machine A B Concentra Low High Medium Solder A B Quantitative Pressure(Pa) 30 - 40 90-100 Mass (kg) 75 105

DoE – Design Structure




One Observer and One Recorder Operators 3, 3 Samples, 3 Trials

Response Record Time / Strokes to break Identified Factors 1. Wire Dia A 2. Material B 3. Hardness C

Gemclip Team Exercise

(30Mins)

Analysis of Effects Due to Main Factors (A, B, C) Two Way Interaction (A*B, A*C, B*C) Three Way Interaction (A*B*C)

Team Observation… Experiment Results…


DESIGN

of Experiment

– Factor to Factor Interaction Experiment Factor A Factor B Factor C 1 -1 -1 -1 2 1 -1 -1 3 -1 1 -1 4 -1 -1 1 5 1 1 -1 6 1 -1 1 7 -1 1 1 8 1 1 1 Experiment Factor A Factor B Factor C Response 1 -1 -1 -1 37 2 1 -1 -1 36 3 -1 1 -1 19 4 -1 -1 1 17 5 1 1 -1 17 6 1 -1 1 19 7 -1 1 1 39 8 1 1 1 38

Do you have the Answer?


DESIGN

of Experiment

– Factor to Factor Interaction Experiment Factor A Factor B Factor C 1 -1 -1 -1 2 1 -1 -1 3 -1 1 -1 4 -1 -1 1 5 1 1 -1 6 1 -1 1 7 -1 1 1 8 1 1 1 Experiment Factor A Factor B Factor C Response 1 -1 -1 -1 37 2 1 -1 -1 36 3 -1 1 -1 19 4 -1 -1 1 17 5 1 1 -1 17 6 1 -1 1 19 7 -1 1 1 39 8 1 1 1 38

I have one from My Previous Class… We will Use that


DoE Analysis – Main Effect Example of Gem Clip and its Reliability Number of Factors 3 (A, B, C) Number of Levels 2 (High and Low) Let us Study the effect of Main Factor – A Wire Dia Effect = Av. Of High – Av. Of Low

= (36+17+19+38)/4 – = 27.5 – 28 = -0.5 Inference: As the wire dia decreases from Max to Min as in the experiment, the life is reduced by 0.5 points

1. 2. 3.

Wire Dia Material Hardness

Let Us Understand…

A B C


DoE Analysis – Which Main Effect is ??!! Example of Gem Clip and its Reliability Number of Factors 3 (A, B, C) Number of Levels 2 (High and Low) Main Factor – A B C ??!! What are Your Inferences: What is your Recommendation for Manufacturing process Control?

1. 2. 3.


A B C

What is your design suggestion? Is the Interaction of theses Factors Significant?


Can we Conclude Only with Main Effect?

DoE Analysis – Interaction Effects Analysed only Effect of each One of the Factors Independently Important to know in real life Application, the effect of combination of Factors Is there a Particular Combination of factors in which can deliver significant Influence in Output like 1. Get a Max Yield – In Mfg DoE 2. Worst case – For Robust Design 3. Best Scenario – Maximise Profit 4. Customer Delight - Restaurant / Service 5. High Morale – HR example DoE 6. …… Is the Interaction of theses Factors Significant? Precisely – Is there a Interaction, Significant?

Let Us Analyze… Two Factor Interaction 63 / LRamanan, March 16, 2012

DoE Analysis – Interaction Effects Experiment Factor A Factor B Factor C A*B 1 -1 -1 -1 1 2 1 -1 -1 -1 3 -1 1 -1 -1 4 -1 -1 1 -1 5 1 1 -1 1 6 1 -1 1 -1 7 -1 1 1 -1 8 1 1 1 1 (Av of+1) 27.5 28.25 ? 30.667 (Av of -1) 28 27.25 ? 26 Effect -0.5 1 ? 4.7

B*C 1 1 -1 -1 -1 -1 1 1 37.5 18 19.5

C*A 1 -1 1 -1 -1 1 -1 1 28.25 27.25 1

A*B*C Response -1 37 1 36 1 19 1 17 -1 17 -1 19 -1 39 1 38 27.5 28 -0.5

Inference: Interaction effects of B and C Highly Significant Choosing the Material 1 (Factor B) & with Higher Hardness (Factor C) Gives longer life? What will be the effect of if we keep all Factors at +1? Can we develop a Transfer Function? Can we Optimise? Is there a Technique ? What is the risk? Is the Risk can be Quantified? Can it be simulated, useful? Do you have an Observation: Is there any specific observation or mistakes in manual calculation?

More Factors… Complex Manual Analysis


As Factors and Levels Increases, Structuring the experiments & Calculations manually becomes Complex and prone for committing error or mistake

I told you, Now What to Do? Stop DoE…I know it will not work, I told you from my experience, you should listen65 / LRamanan, March 16, 2012

Statistical & Practical Significance Some of the Commercial Software for Experimental Analysis SAS JMP Mixsoft S-Plus Nutek Qualitek-4 Genstat StatSoft Minitab V16 – Is used in RAISE’s Course Adept Scientific DOE_PC IV State-Ease DOE PRO XL Design-Expert Process Builder STRATEGY Echip S-Matrix CARD Statgraphics Qualitron Systems DoES Systat RSD Associates Matrex Umetrics MODDE 6

User Friendly & Makes Life Easier


Comparing with Manual Analysis 1. 2. 3.


A B C Interaction Effects of Material Type and Hardness are Significant in Fatigue Life of Gem Clip

(Gem Clip Life = 27.75 - 0.25*Dia + ….) Transfer Function in Coded Values (-1 to +1 )

There is a mistake? Can you figure out ? – Math – can never go wrong !!!

One Can Also Do Mistake in Entering Data in SW…


Analysis of Experimental Results

Statistical Significance Parallel Lines - Indicative of No Significant Effect due to Interaction of factors Crossing of Lines – Indicative of Strong Effect due to Interaction of Factors

Steeper the Slope – Stronger the Effect of the Variable on the Response / Output

Interaction Effects of Material Type and Hardness are Significant in Fatigue Life of Gem Clip

Interaction of Material and Hardness is Significant


Analysis of Experimental Results Residual Plots for ResponseResidual Plots for Response

Percent

50

10

10 1

1 -0.50

-0.25

0.00 Residual

0.25

0.50

Frequency

Frequency

3 2 1 0.0 Residual

0.00 20 Residual

0.1

0.2

3 2 1 0

-0.1

-0.25

4

4

-0.2

-0.50

Histogram

Histogram

0

50

All points 0.1 Shall0.0lie almost -0.1 on a Straight -0.2 line

0.2

Residual

Percent

90

0.2

0.1

Histogram 0.0 Shall-0.1form shape of Bell -0.2 Curve -0.2 -0.1 0.0

1 2 Residual

These graphs shall not show any trend and non0.25 0.50 25 30 random Fitted Value pattern.

0.2

Residual

90

Versus Fits

0.1 0.0 -0.1 -0.2

35

40

20

Do you have any observations in these Charts 0.1 0.2 3 4 5 6 Observation Order

25 30 Fitted Value

35

40

Versus Order

Versus Order

Residual

99

Normal Probability Plot Versus Fits

99

Residual

Normal Probability Plot

0.2 0.1 0.0 -0.1 -0.2 7

1

8

Graphical Data Analysis

2

3 4 5 6 Observation Order

7


8

Analysis of Experimental Results Is there a Practical Significance? How will We Know? We can Know that from Epsilon Squared

Epsilon Squared is (SSfactor / SStotal) x (100) in percentage

•

Since Wire Dia and its interaction is not Significant, we can drop that in analysing the effect… Though Material and Hardness are not showing significant effect Individually, but their Interactions presents a very high significant effect.

•

Now, instead of having eight different factor combinations with One experiment each, we can have four different factor combinations with Two experiments for each. Since we will have duplicates for each of the factor we can use ANOVA on same results Details of ANOVA covered in course 6S-DoE-002

•

Residual Plots for Response Normal Probability Plot

Versus Fits

99

Residual

Percent

90 50 10 1

0.5 0.0 -0.5 -1.0

-2

-1

0 Residual

1

2

20

Histogram 2.0

1.0

1.5

0.5

1.0 0.5 0.0

25 30 Fitted Value

40

0.0 -0.5 -1.0

-1.0

-0.5

0.0 Residual

0.5

1.0

1

2


0.26% 0.26% 99%

To calculate Epsilon Squared we use the data generated from the balanced ANOVA.

Practical Significance

35

Versus Order

Residual

Frequency

Epsilon Square Quantifies the amount of the variation explained by each factor. In this example Material and Hardness combined interaction effects on the fatigue life of Gem Clip, accounts for 99% of the variation in the data.

1.0


7

8

What is the Lesson Learnt? • It is the Interaction effect of Material and Hardness that contributes significantly towards the life of the Gemclip as found from this exercise • In the absence of the structured experiment DoE, we would not have figured this out • If we would have performed OFT, we would have missed the most important and significant contributor – Interaction Effect • It is not that • It is not what we anticipated when we started this experiment, So DoE is helpful

1. 2. 3.


A B C

Now in the process, we need to put a control on the factors identified and we can do a level setting

Interactions are Important Parameters!!


Some Thoughts on Interaction Effects Interaction IS NOT: 1) Taste of Coffee is not interacting with the glass in which it is served 2) Wearing of Shoes and a Sweater in Winter – To keep Body warm (But no interaction between Shoe & Sweater) But both of them contribute to keep body warm. They are adding to the warm comfort independently Interaction IS: 1) Taste of Coffee is dependent on all the factors and their interactions 2) Hotness of Coffee is interacting with warm / cold Glass in which it is poured, irrespective of Hot Milk and Freshly brewed coffee 3) A perfect example for interaction is fire – Combination of fuel + oxygen + ignition source

Generally, the highest order interaction in experiments are not significant or important.

Interaction is part of an effect that cannot be accounted for as the sum of the involved factors‟ main effects.

More Factors… Complex Manual Analysis


Understanding of Factors & Levels Factors are with Distributions as shown Levels are typically extreme values at both ends of distribution (Red) Levels are representative values LSL USL Good Coffee within which the experiment is Y = fn (X1, X2, X3 ….) valid Choose practically extreme values to avoid experiment laterGlass Milk Brew Temp Sugar Ambience Choose values for Level, Factor accounting Measurement Level System error (Recollect GRR) GRR

DoE Helps in Building Relation of Factors to Response


Risks in 2 Level Designs & Mitigations Risk: Missing the Non-Linear / Curvilinear behaviour of Input variables by including only Two Levels (Min / Max).

Risk Mitigation: Adding Centre Points is an efficient way to test curvilinear behaviour with less number of experiments Look for Three Level Design Example: To enhance yield in the Plating Process, Engineer decides to construct a Two factor DoE, by recognizing Temperature of bath and Reaction Time as Factors. Adds few centre points to understand curvilinear behaviour. Factor

Min

Max

Temperature

1600C

1700C

1800C

Reaction Time

30Mins

35

40Mins

Ref: Minitab Help Manual


Be Aware… As Levels Increase, Number of Experiment Also Increases

Two Factor With Various Designs Normal Plot of the Standardized Effects (response is Yield, Alpha = 0.05)

99.9

Effect Type Not Significant Significant

99 95

Percent

90 80 70 60 50 40 30 20

Time

10 5 1

-4

-2

0

2 4 6 8 Standardized Effect

10

12

14

Normal Plot of the Standardized Effects (response is Yield, Alpha = 0.05)

99.9


99 95

Percent

90 80 70 60 50 40 30 20

Time

10 5 1

-4

-2

0

2 4 6 8 Standardized Effect

10

12

14

Normal Plot of the Standardized Effects (response is Yield1, Alpha = 0.05)

99.9


99 95

Percent

90 80 70 60 50 40 30 20 10 5 1

-2

0

2 4 6 Standardized Effect

8

Two Levels. Center Point. Three Levels

10


Two Factor With Various Designs Residual Plots for Yield 0.10

90

0.05

1

-0.1

0.0 Residual

40.50

0.00

40.25

39.0

1

-

0 10 0.

-

5 07 0.

0 5 0 5 .05 0.02 0.00 0.02 -0 Residual

0

0 .05

0

39.0

39.25 39.00

38.5 30

1

2

3


8

9

160

170

Residual Plots for Yield 0.10

10 0.0 Residual

0.1

39.0

Histogram

40.0

40.5

Versus Order

Residual

Frequency

39.5 Fitted Value

1

-0.10

-0.05

0.00 Residual

0.05

0.00

39.00

-0.05

2

3 4 5 Observation Order

38.5

6

160

7

170

Residual Plots for Yield1

10 -0.2

-0.1

0.0 Residual

0.1

0.00

39.5 Fitted Value

40.0

40.5

0.08 0.04

39.25

0.00

39.00

0.0

-0.08

-0.08

-0.04

0.00 Residual

0.04

0.08

39.5

39.50

1.5

-0.04

Temp1 160 180

40.0

39.75

2.0

Residual

Frequency

39.0

Versus Order

0.5

Data Means

40.5

Time1

40.00

Histogram

1.0

40

Interaction Plot for Yield1

40.25

-0.04 -0.08 38.5

0.2

35 Time

40

Mean

50

35

Temp1

40.50

Mean

Residual

Percent

0.04

30

Data Means

Versus Fits

90

1

180

Main Effects Plot for Yield1

Normal Probability Plot 0.08

39.5

30 1

99

Point Type Corner Center Corner

39.0

39.25

0.05

0.10

Temp 160 170 180

40.0

39.75

-0.10

0

40.5

Point Type Corner Center

39.50

0.10

2

Data Means

Time

40.00

38.5

3

40

Interaction Plot for Yield

40.25

0.00 -0.05

0.2

35 Time

40

0.05

Mean

-0.1

Temp

40.50

-0.10 -0.2

35

Mean

Residual

Percent

50

30

Data Means

Versus Fits

90

1

180

Main Effects Plot for Yield

Normal Probability Plot 99

39.5

0.00

-0.10

5 .07

39.75 39.50

0.05

-0.05

0

40.0

40.5

0.10

Residual

Frequency

39.5 40.0 Fitted Value

Versus Order

2

Temp 160 170 180

40.00

Histogram 3

40.5

Time

-0.05 -0.10 38.5

0.1

Temp

Mean

10

Data Means

Data Means

Mean

50

Interaction Plot for Yield

Main Effects Plot for Yield

Versus Fits

99

Residual

Percent

Normal Probability Plot

39.0

38.5 1

2 3 Observation Order

4

160

180

30

40

30

40 Time1

Two Levels. Center Point. Three Levels


Practical Example – 2 Factors 3 Level We would like to understand in a Chemical surface Treatment process, about the influence of 3 Catalysts and choose the best one in maximising the yield / output. But the organisation decided that it will not change the chemical solution, but OK for varying the temperature of the bath. Management is OK to Conduct the maximum number of experiments to take a right choice / selection of catalyst and looks for a recommendation. Team after brainstorming identifies the bounds of the temperature of the bath considering any noise factors that would influence the bath temperature and decides to go for 2 Factor 3 Level experimentation with 4 Replicates

Can you tell me the total number of experiments for this set-up?

It can be Extended to Electronics, SW …


Example – 2 Factors 3 Level With Replication Maximise response – yield, Temperature 3 Levels Catalyst Type: 1 2 3 Lk Experiments = 32 4 Replications

You can Pre Design the Experiment or You can go through Custom Design

ANOVA… Can it Used for this Set-Up?


Analysis – Thro Custom DoE in Minitab

Thro Custom DoE

Minitab Gives you Lot of Freedom


Analysis of Two Factors 3 Level Experiment

Max. Number of Experiments… Still Curvature? 80 / LRamanan, March 16, 2012

Main Effects – Graphical Info

What is Your Interpretation? What will be the Preferred Settings?

Both Graph & Data Are Important


Interaction Effects – Graphical Info

Now Can we Provide the Recomendations


Practical Example – Automotive IC Engine Specific Fuel Consumption (SFC) in a Diesel Engine is an important Commitment by to the customers. Two factors that fall short-off designing/redesigning engine components are Speed and Timings Subject Matter Experts (SMEs)have identified earlier, speed is a linear relationship, while Timing is non-linear •

2 Factors at 3 Level with 2 replicates will require 18 Experiments 1 Factor at 2 Level and another Factor at • 3 Level with 2 replicates can be completed in 12 Experiments •

Data of experiments as Appended except for SFC (Response)

ANOVA – When we Speed Time 887 have more than one 887 run from same setting. 887 Is this example a fit 887 case for ANOVA? 887 What method you will 887 789 choose? Balanced 789 ANOVA or GLM? 789 In Minitab what path 789 you will choose 789 Clue - Custom DoE? 789

18 18 15 15 12 12 18 18 15 15 12 12

SFC 0.3698 0.3694 0.3701 0.3702 0.3735 0.3707 0.3546 0.3574 0.3591 0.3568 0.3598 0.3605

Example of 2 Factors Mixed 2 and 3 Levels 83 / LRamanan, March 16, 2012

Analysis of Experimental Results

Residual Plots for SFC Normal Probability Plot

Versus Fits

99 0.001

Residual

Percent

90 50 10

0.000 -0.001

1

-0.002

-0.001

0.000 Residual

0.001

0.002

0.355

0.360

Histogram

0.370

Versus Order

4

0.001

3

Residual

Frequency

0.365 Fitted Value

2 1

0.000 -0.001

0

-0

5 01 .0

0 5 01 00 .0 .0 -0 -0

0 00 0.

0

05 00 0.

10 00 0.

15 00 0.

1

2

3

4 5 6 7 8 9 Observation Order

10 11 12

Residual

Interpretation of Data with Graphical Info


Analysis of Main Effects

Understanding More Closely


Analysis of Interaction Effect

RAISE - DoE Class Exercise with 2 and 3 Levels 0.3725

Speed 789 887

0.3700

Mean

0.3675 0.3650 0.3625 0.3600 0.3575 0.3550 12

15 Time

18

Knowing the Interaction… Clue for Optimisation 86 / LRamanan, March 16, 2012

Structured Experiment… More Factors Experiment Factor A Factor B Experiment Factor A Factor B Factor C Experiment Factor A Factor B Factor C Factor D 1 -1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 2 1 -1 2 1 -1 -1 -1 2 1 -1 -1 3 -1 1 3 -1 1 -1 -1 3 -1 1 -1 4 1 1 4 1 1 -1 -1 4 1 1 -1

Two Factors and Two Levels

5 6 7 8

-1 1 -1 1

-1 -1 1 1

1 1 1 1

Three Factors and Two Levels

Is there any Observations ?

5 6 7 8 9 10 11 12 13 14 15 16

-1 1 -1 1 -1 1 -1 1 -1 1 -1 1

-1 -1 1 1 -1 -1 1 1 -1 -1 1 1

1 1 1 1 -1 -1 -1 -1 1 1 1 1

Four Factors and Two Levels 87 / LRamanan, March 16, 2012

As Factors Increases… Factorial Design Shall be Expensive

-1 -1 -1 -1 1 1 1 1 1 1 1 1

Example of Full Factorial DoE with 4 Factor Tough Problems remains un-solved for a longer time because: • •

Root cause is not readily known No time for full experiment/Analysis.

1. Effect of Primary Factors A, B, C & D 2. Two Way Interactions AB, AC, AD, BC, BD, CD BA, CA, DA, CB, DB, DC

Let us consider one such field issue

3. Three Way Interactions

• Team zeroed on 4 Factors as significant

ABC, ABD, ACD, BCD

• Conventionally perform 4 Experiments OAT.

4. Four Way Interactions

• Effect of Primary Factors - A, B, C & D Understood

ABCD

• Effects of Interaction Effect of Factors Missed

16 results including Interaction of all Factors

• Full Factorial DoE shall provide info on Interaction


Primary & Interaction Effects

DESIGN

of Experiment

+1

2 Levels 2 Factors Experiments 22 = 4 -1 Factor1 +1

Factor 2

Factor 2

+1

– 2 Levels & 3 Factors In Space

2 Levels 2Factors Experiments 23 = 8 -1 Factor1 +1

Each of the Vertices represents an experimental Condition Two Factors Can be Considered as Square

Three Factors Can be visualized as a Cube (Level

Factor)is

number of Experiments in a Full Factorial Design

Visualization… A feel for Complexities


DESIGN

of Experiment

– 2 Levels & More Factors

-1

+1 +1

Two Levels 4 Factors is ….. Runs?

Can be visualised as 2 Cubes Two Levels 5 Factors is …. Runs

+1

-1

Can be Visualised as 4 Cubes and these are known as Hyper-Cubes

-1

Visualization on More Factors… Becomes Complex 90 / LRamanan, March 16, 2012

DESIGN

of Experiment

– 2 Levels & 5 Factors

At each Level and Factor there are runs with all min and max One can observe the pattern in designing the

experiments for runs known as standard order For 2 levels 1 factor – 1 Trial – Refer Column A & Color Code

For 2 levels 2 Factor – 4 Trails – Refer Column A & B For a 2 Level 7 Factor - …. Trials? Can you construct an Experiment Design? One at a Time Strategy beyond 3 Dimensional Space (3Factors) is not good as it makes approximations

Experiment Factor A Factor B Factor C Factor D Factor E 1 -1 -1 -1 -1 -1 2 1 -1 -1 -1 -1 3 -1 1 -1 -1 -1 4 1 1 -1 -1 -1 5 -1 -1 1 -1 -1 6 1 -1 1 -1 -1 7 -1 1 1 -1 -1 8 1 1 1 -1 -1 9 -1 -1 -1 1 -1 10 1 -1 -1 1 -1 11 -1 1 -1 1 -1 12 1 1 -1 1 -1 13 -1 -1 1 1 -1 14 1 -1 1 1 -1 15 -1 1 1 1 -1 16 1 1 1 1 -1 17 -1 -1 -1 -1 1 18 1 -1 -1 -1 1 19 -1 1 -1 -1 1 20 1 1 -1 -1 1 21 -1 -1 1 -1 1 22 1 -1 1 -1 1 23 -1 1 1 -1 1 24 1 1 1 -1 1 25 -1 -1 -1 1 1 26 1 -1 -1 1 1 27 -1 1 -1 1 1 28 1 1 -1 1 1 29 -1 -1 1 1 1 30 1 -1 1 1 1 31 -1 1 1 1 1 32 1 1 1 1 1

Patterns Help in Designing the Experiments


Real Life Problems are With Multiple Factors •

•

•

•

•

Medical Product, Design and Technology is an Engineering Marvel with involvement of almost all branches of Engineering Science Picture shows most complex and highly safety critical medical device used for Angio procedures used by the Doctors in Cath Lab of Hospitals used for stenting You are an Engineer involved in Design of Motion and responsible for Motor Selection for various motions shown with arrows of different colors in picture. For example, one of the motion indicated in the picture by letter 1, mass & speed are given to you. How would you go about to select the motor selection Are you sure, your design is the robust?

1

L, Ramanan (2009) “Role of Six Sigma in Building Robust Products - With Examples from Medical Devices” IV PDMA International Conference on New Product Development, IIT Madras, Chennai - India

DoE is Not Complex… Designs a Robust Product

Real Life Problems are More Complex – An Example for Multi Axis Motion & Power Prediction

LP Motion Longitudinal (on Rail) Pivot Rotation C-Arm Swivel Detector Lift (Lateral) Tube Lift (Lateral)

1

LC Motion L Arm Rotation C Arm Swivel Pivot Rotation Tube Slide (Vertical) Detector Slide (Vertical)

Ref: L Ramanan (2009) Role of Six Sigma in Building Robust Products – Examples from Medical Devices,, IV International Conference in New Product Development at IITM – Cath Lab Radiology Machine

DoE – Handles High Complexity with Confidence 93 / LRamanan, March 16, 2012

Max Power for One Motion – Thro DoE Factors That Influence - Complex C Arc – Angulations (LAO 00 thro 1100)

Animation

1

Position of X Ray Tube (SID - SOD) Position of Detector Mass of X-Ray Head (Tube Mass & Drive Elements) Mass of Detector Head (Detector 20” & Drive Elements) Mass of – Cables, Water Pipes, C Arc etc. (C Arc Mtl, Xray Arm, etc ) Speed – Acceleration / Deceleration (Time) - 0 to yy mm/sec in x sec Friction…..

Ref: L Ramanan (2009) Role of Six Sigma in Building Robust Products – Examples from Medical Devices,, IV International Conference in New Product Development at IITM

Y – Power Required for Motion Y = fn (X1, X2, X3 ….)

Functional Variation–Design Risk Prediction & Mitigation 94 / LRamanan, March 16, 2012

Benefits of DoE & Robust Design 1

Typical Power & Torque Curve – From Motor Manufacturer

Ref: “Six Sigma - An Ingredient of Innovative Product Design”, L Ramanan , Indo – US Workshop on Product Design–Impact from Research to Education to Practice 2010

DoE with Rigid Body Dynamics. DoE with CAE Simulation in ADAMS

DoE & CAE for Fail Safe Design… High Reliability

Summary of Full Factorial DoE For each Statistically Significant effect test of Practical Significance, is analysed with Epsilon-Squared.

•

Described the overall concepts of 2k Factorials

•

Creation of Standard Order designs

•

Based on Practical and Statistical Significance, Main / Interaction Effects Plots, decide best settings

•

•

Formulate conclusions and recommendations for a Practical Solution & Optimise

Designed and Analyzed − One at a Time Experiment − using Normal Effects Plot − using ANOVA − Main and Interaction Plots − Use of Center Points - 2, 3 and Mixed Levels

•

Final one Run is made as Validation

•

Blocking in Full Factorials

•

Designed and analyzed Full Factorial Experiments − 2 Factors - each with 3 Levels − 2 Factor 2 Levels

•

•

Institutionalize the change.

Will be Useful In Quiz


General Rule of Thumb… General Sample Size and Recommended Runs are as below 2 to 5 Factors – Full Factorial

5 to 15 Factors – Fractional Factorial Designs Above 15 Factors – Orthogonal Designs

Convenience… Not a Rule


DoE Terminology Experiment (runs)

Interaction

Test under defined conditions to

Effect of a factor on the response

understand the Unknown effect / verify

dependent on the level of another

known law…

factor

Experimental Error

Randomization

Difference in results made under

Assigning the experimental condition to

identical test conditions, which can not

perform at random, not standard order

be attributed to input variables

Repetition

Factor (Parameters)

Multiple measurements on single piece

Independent Variable - Input

Replication

Response (Effect)

Multiple execution of experiment in full

Dependent Variable – Output

/ part with same factor settings on

Level

different samples / lots

Settings of the Factor (Min, Max) (-1, 1)


Typical Examples of Objective of a DoE Effect of alternate Material – To Bring down cost Effect of Input variation – Product Reliability (Example Dealt) Impact of Skilled and Un-skilled Operator – Product Quality Impact of highly precised / low cost M/C – Process Quality Process Input Variables – On Product Characteristic

Significance of Input Variable is not Known – Screening DoE Alternate Methods – Best Out puts

Not Exhaustive… But can Generate Spark


Some Examples for Factor Selection FMEA / Cause and Effect

Engineering Knowledge

Hypothesis Testing

Operator Experience

Process Mapping

Scientific Theory

Brainstorming


Literature Review

Clue Selection

Solution Tree

Subject Matter Expert Opinion

Past Experience

Scientific Theory

Story Boarding


Affinity

Minimize Factors… Do Not Miss Critical One


DoE and Technology Together Can Solve some of the Toughest Problems in Real Life Situations I am convinced that DoE can make a difference to the Product Quality and to the Business

Engineered Products…Prediction is Complex… But Doable… Leverage the Power of DoE with Technology… Solve Some of the Toughest Real Life Problems

Back Ground and Need of Fractional Factorial DoE • Real Life Problems are Very Complex with Many Factors and Interactions, hence it might not be practically possible to perform many experiments with Full Factorial DoE and has to be analysed with less number of experiments necessitates fractional factorial DoE • When less amount of resource availability in performing full factorial experiments • When restricted number of experiments to be designed for understanding the effects of Inputs on response • In a new Design, One do not know which are the main factors / could not decide / finalise Factors / Input

Complex Problems are Candies for Engineers

Why, When and What About Fractional Factorial DoE • Why & When to do a Fractional Factorial Experiment? As the number of factors increases, so do the number of runs. − 2x2 Factorial = 4 runs − 2x2x2 Factorial = 8 runs − 2x2x2x2 Factorial = 16 runs − ….. • Major use is in screening: a relatively large number of factors in a relatively small number of runs. • Usually higher order interactions are assumed to be negligible, it is possible to do a fraction of the full factorial with good estimates of lower order interactions. • Screening experiments are usually done in the early stages of a project.

What to Learn in a Fractional Factorial Experiment? • Design Matrix of a Half Fraction Factorial • Resolution of Fractional Factorial Experiments • Notation of Fractional Factorial Experiments • Design and Analyze a Fractional Factorial Experiment - Minitab

Why When What

Factorial Designs – Number of Runs An Example:

A 7 Factor Full Factorial Design will require 128 Experiments. The same can be concluded with 16 Experiments in a Fractional Factorial Design of Resolution IV

What is Resolution?

What Is Resolution? – Trade Off in Reducing Runs “Cost” of Trading-Off between full factorial DoE with Fractional Factorial is that of the Confounding of effects and interactions depending on the “Resolution Chosen” Resolution III designs shall have main effects confounded with 2 Factor and higher order Interactions. But not with other main factors Resolution IV designs shall have main effects confounded with 3 Factor and higher order Interactions. But not with other main factors and 2 factor interactions. The main effects are clear of 2 factor interactions.

Resolution V designs shall have the main effects confounded with 4 factor and higher order Interactions. But not with other main factors, 2 and 3 factor interactions. Two factor Interactions are clear of each other

What Is Confounding?

Confounding And Aliasing Effects that cannot be estimated separately from one another are said to be confounded. Confounding occurs when you use a fractional factorial design, because you do not run all factor level combinations. For example, if factor A is confounded with the 3-way interaction BCD, then the estimated effect for A is the sum of the effect of A and the effect of BCD. These effects are also said to be aliased. The alias structure describes the confounding that occurs in the design. Effects that are aliased, or confounded, cannot be estimated separately from one another. For example, if the two-way interaction, BC, is confounded with the three-way interaction, ADE, you will not be able to tell whether a significant effect is due to the BC interaction or the ADE interaction. The key to the alias structure is the identity statement, for example, I + ABCDE. To determine which effects are confounded, multiply the term of interest by the identity statement and then eliminate the squared terms. For example, to find the term that BC is confounded with: (BC)(I + ABCDE) = BC + AB2C2DE = BC + ADE Therefore, BC and ADE are confounded with one another. Ref: Minitab V 16

Terminology in DoE

Let Us Test What We Understood on Resolution For an experimental Design, you shall be developing the design with Fractional Factorial Design to limit the number of experiments due to the budget constraints, you get to know from the SMEs, that there are several 2 factor interactions that are significant and important. 1. What resolution design should you choose, why? 2. What is the advantage of a resolution V design over resolution IV design? 3. What is the resolution of screening design?

Key to the Class Exercise on Resolution •

What resolution design should you choose, why? Choose resolution IV or resolution V •

What is the advantage of a resolution V design over resolution IV design? A resolution V design has all 2 Factor interactions clear of each other. Hence, it is easier to identify from the analysis which 2 factor interactions are important. In resolution IV design, 2 factor interactions are confounded together, hence it is shall not be clear which two factor interaction is significant • What is the resolution of screening design? Screening Designs are Resolution III

DoE Class Exercise – Professional Management You are into an Ice Cream Business and intending to launch your own “Brand” and establish. From your experience (SME!!) you have found out “Texture of Ice Cream” (Response) is the Key in winning the Customer repeat visits / orders Texture is affected by the factors below and their interactions. You are not sure of which main and interaction effects are most significant. Fat Content, Pasteurization Temperature, homogenization process, speed of mixing, drawing temperature, emulsifier, stabilizer, cooling speed, Cooling Speed, Fillers like Nuts or Fruits. Suggest an approach to optimise the process

Fun in Learning… Maximize Retention

Notation of Fractional Factorial Design The general notation to designate a fractional factorial design is: • k is number of factors to be investigated • p is number of factors assigned to interactions • 2k-p is the number of runs • R is the resolution • Example: The designation below means four factors will be investigated in 23 = 8 runs. This design is a resolution__________.

Minitab will provide the resolution in the Analysis

Fractional Factorial DoE – Injection Moulding As an Engineer in the production of parts by Injection Molding, your Goal is to produce 100% rejection free products. Normally the rejections are due to “Shrinkage” Response: To identify Important Factors effecting parts Shrinkage Factors: Mold Temperature Moisture Content Holding Pressure Cavity Thickness Booster Pressure Cycle Time Gate Size Screw Speed

Manufacturing Example

Fractional Factorial DoE – Manufacturing Example As an Engineer in the production of parts by Injection Molding, your Goal is to produce 100% rejection free products. Normally the rejections are due to “Shrinkage” Response: To identify Important Factors effecting parts Shrinkage. Less Shrinkage is better Factors: A - Mold Temperature B - Moisture Content C - Holding Pressure D - Cavity Thickness E - Booster Pressure F - Cycle Time G - Gate Size H - Screw Speed

Box, G. E. P., Hunter, W. G., and Hunter J.S., “Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building”, Wiley Interscience, p. 413, 1978

The Team decides it can do 16 Experiments with the Constraints available on Time & Resources, with the set-up that could be advised It is our responsibility as Engineers / SME / Scientist to Choose the right Design and also make others aware of the Implications

Example from Practicals… Enhances Skill

Available Designs

Predefined Designs Custom Designs Screening Design

Select # of Factors

Example from Actuals… Leverage Learning

Plackett-Burman Design R3 - Suitable for Screening Options of 12, 24, … Experiments – RIII Design

Resolution III – Plackett-Burman Design

2 Level Factorial Default Generators – Pre-Defined Options of 16 & 32 Experiments – RIV Design

Choose if you want to fold on certain Factors – Recollect Folding Discussion earlier Generators, defining relation, and design matrix displayed Display confounding pattern up to selected / Default order

Example from Actuals… Strengthens Concepts

2 Level Factorial Default Generators – Design

Example from Actuals… Ensures Retention

Generators, Design Matrix & Confounding in Design

Note: Recollect, what we have learnt in Resolution IV Design on confounding

Reinforcing What is Learnt Earlier

Design for Experiment Chosen & Details The first line for each design gives the number of factors, the number of runs, the resolution (R) of the design without blocking, and the design generators. On the following lines, there is one entry for each number of blocks. The number before the parentheses is the number of blocks, in the parentheses are the block generators, and the number after the parentheses is the resolution of the blocked design. Source: Minitab 16 Help

Design Generators

Analysing the Results – Graphical Info

Anlysing Experimental Results

Analysing the Results – Data Analysis

Data Analysis… Do you Recollect DoF

Analysing the Results – Main Effects

Leads to Clues

Analysing the Results – Interaction Effects

Resolution IV Design – Recollect Interactions!!

Regression – From the Analysis Results

Shall we Proceed to Regression?

Regression – From the Analysis Results

Regression

Case Study – Selection of Choice of Cutter In a mass production Industry with operations involved in machining Aluminum Al 7075 using vertical axis Milling machine on a regular basis. The manufacturing Engineer is responsible for productivity of the operations with lower cost, by using the given machine and largely for machining the same material. Manufacturing Engineer has been provided with 3 Brands of 20mm dia End Mills by sourcing for Machining. He has to choose the best one that provides longer tool life, thereby the manufacturing cost is kept low by reducing the frequency of tool change and less wear(larger tool life) by accommodating all the variations like depth of cut, speed etc. as relevant. Manufacturing Engineer decides to try all the three cutters by machining the given Aluminum Block and take a logical decision on choosing the end mill cutter that would give longer tool life. Performs experimental trials as in the following pages to decide. As a DoE expert can you help him in his decision to choose a right cutter. All the experiments were performed in three different shifts

Mass Production Industry - Manufacturing

Case Study – Selection of Choice of Cutter After an Initial Brain Storming Discussions and an Internal discussions with SMEs, the following are the main factors that are identified which need to be used in evaluation Factors: A. Spindle Speed (95, 360, 565, 950, 1500 rpm) B. Feed Rate (22, 98, 132, 200, 360 mm / min) C. Depth of Cut (0.226, 0.400, 0.600, 0.800, 1.000 mm) D. Cutters ( A, B, C – Make / Brand) E. Operators (X, Y, Z) Shifts (1, 2, 3 – For Blocks)

Response: Tool Life as Measured during Process in Min Constants: Machine and Material as explained in previous slide Goal To identify best tool, important factors that can maximise tool life If Full Factorial DoE – 1125 runs with1 Replicate for 5 Factors


Case Study – Selection of Choice of Cutter Everyone Agrees Structured Approach in Designing an Experiment, is a right way to analyse. But can not afford to have 1000+ experimentation due to time, energy and other resource constraints. But Team is willing to spend time. Money and other resources available to expense at the Maximum of 10% of Total experiments. Manufacturing Engineer suggests he can plan maximum of 25 experiments per shift as his limitation Team gets together along with SME and decides the following structure of experiments.

Spindle Speed in 5 Sets- Each one set with 5 experiments at one Speed

Feed Rate variations of 5 in one set. Total of 5 Sets of experiments

One Cutt er type for 25 exp erim ents and repe ated for othe r two with sam e setup of othe r con ditio Left to Mfg Depth of cut variations of 5 in ns Engineer to first set. Total of alocate for 5 Sets with 75 runs cycling of variations


Case Study – Selection of Choice of Cutter


Case Study– Selection of Choice of Cutter


Case Study– Interaction Effects on Tool Life


Analysis Through Custom DoE – Shift as Block


Interpretations From Exercise To Maximize Tool Life • Cutter Brand C performs better in terms of Tool life when compared to the other cutter Bands A & B

• Spindle Speed, Feed rate, depth of cut are significant & important factors • Interestingly shift 1 trends towards providing higher tool life and needs to understand what is specific about shift 1 • No significant effect of operators • Lot of interactions and confounding. • Experiment of Speed at 360 – 565, Feed at 22-132 & Depth at 0.2-0.4 can be performed to study the interaction effects and optimise

More Factors… Efficient Decisions

Hands-On Example – Steel Rolling Industry This case study related to achieving desired Mechanical Properties by Micro Alloying process of Metalurgy. It is well known the synergy between microalloying elements (MAE) and thermo-mechanical controlled rolling processing (TMCP) to achieve the mechanical properties in microalloyed steels (HSLA). Grain refinement and precipitation hardening are mechanisms which require both steel alloy designs using different MAE (Nb, V, Ti, Mo,etc.) and an optimized rolling practice. Therefore, this work was aimed to set a robust design by using an experimental design combined with metallurgical deterministic models to predict microstructural evolution and mechanical properties of high strength steels. Results by using this methodology were validated in industrial production (Bruna et al, 2004)

Factors: A: Niobium, Nb (0.030 ~ 0.060 %wt) B: Manganese, Mn (1.00 ~ 1.30 %wt) C: Thickness reduction at the 4th finisher stand, rF4 (>23%) D: Thickness reduction at the 5th finisher stand, rF5 (>20%) E: Finishing temperature, FT (840 ~ 900 °C) F: Coiling temperature, CT (550 ~ 650°C) Strip thickness: 6.35 mm

Process Industry - Metalurgical

HAS Steel Analysis Results

Process Industry - Metallurgical

Safety Critical Joint – Interference Assembly

Control Factors: A: Shaft OD (171.95, 172.05) B: Bore ID (171.74, 171.84) C: Surface Finish (0.05 – 0.09 µm) Noise Factors X: Material Property Y: Lubricant Z: Variation in Hub Length

Axle OD mm

Interfer Surfac Bore ID mm ence e

Force in tons

172.00

171.80

200

0.05

93

171.97

171.77

200

0.05

97

171.97

171.77

200

0.06

85

172.04

171.84

200

0.05

73

171.98

171.77

210

0.06

90

171.98

171.77

210

0.05

80

171.98

171.77

210

0.05

70

171.97

171.76

210

0.05

85

Micron

“Thermo-Mechanical Finite Element Analysis of Rail Wheel”, L Ramanan

Example for Robust Design

Safety Critical Joint Design – FEA & DoE Combination Ref: IPCOM000169885, Mechanical Joint with Interference Fit for Use in Hand Rail of Patient Table, L Ramanan , 2010

Control Factors: A: Spacer OD B: Rail Bore ID C: Surface Finish D: Interference Depth E: Shapes (1Factor?) Noise Factors X: Material Property - 2 Y: Lubricant – Y / N Z: Friction Co-Efficient

GE’s Cardio-Vascular Medical Device

Response: Pressing Force (vs Pull Force to Detach)

Picture Ref: L Ramanan (2008), CAE Simulation – An Inspiring Technology in Medical Device Design, ANSYS India User’s Conference


Safety Critical Joint Integrity - Design in Rotating Part, Exposed to High Temperature Ref: IPCOM000193550D, SYSTEM AND METHOD OF MAKING SAFETY CRITICAL X-RAY TUBE ANODE, L Ramanan , 2010

Rotating Anodes X Ray Tube Using Interference Fit, US Patent – 4089612 of GE

Joint Integrity Challenges of Anode Assembly: Operating in High Temperature Ranges, Rotating with High Speed

Control Factors A: Insert OD B: Target ID C: Temperature Dependent Material of Insert D: Temperature Dependent Material of Target E: Operating Temperature Range F: Surface Finish of Insert OD

G: Surface Finish of Target Bore H: Insert ID I: Surface Finish of Insert ID J: Stem OD K: Stem OD Surface Finish L: Temperature Dependent Matl of Stem


M: Speed Range

Summary of Fractional Factorial DoE • Fractional Factorial is helpful in running the experiments with reduced number of runs, when we can not conduct full blown experiments • Fractional Factorial is helpful in running screening experiments when we do not know which factor is very important by checking normal effects plot. • Fractional Factorial results in aliasing of effects, and we need to be aware of in what we are expecting out of the analysis

Factorial Design Helps Towards Robust Design

Taguchi – God Father of Robust Design • Electronics Engineer, Researcher & Statistician • Developed Most Popular Technique on DoE Called Taguchi Method • Targets Robust Design by insensitizing variation due to Noise Factors • Worked during 1950‟s to improve Japan‟s post-WWII telephone communication system

Dr. Taguchi (1924 – ) Author of Many Books on Robust Design. Most Respected in Industry

Insentize Noise… Build Robust Product

Insentize Effect of Noise in Output X1

Noise – We can not Control, but we can insensitize its effect in output

X2 X3

Process

Y

X4

X5 Inputs

Noise – An Example: Environment Temperature

Output

Taguchi’s Approach To Robust Design

Understanding with a Practical Example • Chocolate Bar as a product is to be Strong enough to bite, with all other customer expectations • To be displayed close to cash counter & sold • Imagine the product to be used in Delhi, Bangalore, Chennai during Summer and Winter seasons • Environment Temp is Noise

Robust Design – Taguchi Approach

Overview of Taguchi Method • •

• • •

Cost Effective Method for Improved Performance of a Product & Robustness Reducing Variability in Customer Usage Condition Intended to Improve Companies Competitive position TM is not Interested in Measuring the Interactions between Control Factors Works on the Principle to find a Suitable function called Ideal function that governs Energy Transformation in the System from Input Signal to Output Response, by minimizing the Uncontrollable Noise Factors

Ref: L Ramanan

Ref: IEC 60601-1

Ref: L Ramanan (2010) “Design for Six Sigma- An ingredient to Innovative Product Design”, Indo US Workshop on – “Product Design – Impact from Research to Education to Practice” India

Robust Design - Accounts Variability in Customer Usage Condition

Problem from Manufacturing

Taguchi Method vs Factorial DoE • Full Factorial DoE (FFD) leads to development of Transfer Function with higher order Interactions, while Taguchi Method (TM) is to development of Ideal Function, energy transformation is measured based on S/N ratio • FFD is useful in studying main and Interaction effects, while focus of TM is not for studying Interaction effects • As factors increases, FFD is very costly, while TM shall give a well simplified model • Fractional Factorial DoE (FrFD) is carried out for reducing cost, material etc… One can study in FrFD main effects and selected Interactions from experiments. Orthogonal Array in TM is an example of FrFD Robust Product… Key to Business Success

Robust Engineering or Taguchi Method Brief aspects / approaches of Robust Engineering or Taguchi Method 1. Energy Transformation Principle & Signal to Noise Ratios

2. Exploitation of Interaction between Control & noise Factors 3. Use of Orthogonal Arrays 4. Two-Step Optimization 5. Quality Loss Function Ref: Computer Based Robust Engineering, Genichi Taguchi et. Al, ASQ Publications, New Age International Publishers

Robust Product… Key to Business Success

Best Practices To Follow for Good DoE 1.

Define the Practical problem

13. Conduct Experiment – Random

2.

Convert Practical to Statistical

14. Collect the Data

3.

Establish the Objective

15. Analyze the Data

4.

Define Output Variable

16. Check for Statistical Significance

5.

Define Input Variable

17. Check for Practical Significance

6.

Choose Levels

18. Perform Capping Run – Validation

7.

Identify Noise /Lurking Variable

19. Document experiment Results

8.

Select the Experimental Design

20. Develop Practical Solution

9.

Plan Logistics – Resource

21. Implement Solution

10. Define Experimental Procedure

22. Monitor Effectiveness of solution

11. Ensure all involved understand

23. Follow on Study if warranted

Experimental Plan

24. Share best practices & learning

12. Perform Pilot Run

Check List / Sanity Check


Reference Materials • D.C. Montgomery: ”Design and Analysis of Experiments”, John Wiley&Sons, 5th ed. 2001 • Phadke, M.S.,1989. Quality Engineering Using Robust Design, Prentice-Hall International, Englewood Cliffs, NJ • Taguchi, G., 1985. Introduction to Quality Engineering: Designing Quality into Products and Processes. Asian Productivity Organization, UNIPUB, Kraus Intern. Public.White Plains, N-Y • Computer Based Robust Engineering, Taguchi G, New Age International Publishers • Box, G.E.P.& Draper, N.R., 2007. Response Surfaces, Mixtures and Ridge Analysis, WileyInterscience, John Wiley & Sons • Potentiality and Benefits of Robust Engineering and the Technological Experimentation in the Steel Industry, 2008, La Metalurgica Italiana • Bruna, R.G., et al., 2004. Development of HSLA steel (NB-V-Ti) for ERW pipes by Thermo Mechanical controlled proccessing at Siderar. In: Proceedings of 59th ABM Annual Congress, S.P., Brazil, pp. 373-382. • Michael Montero., 2001, Introduction to Design of Experiments, University of California at Berkeley, Mechanical Engineering Department • Box, G. E. P., Hunter, W. G., and Hunter J.S., “Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building”, Wiley Interscience, 1978 • Devor, R. E., Chang, T. and Sutherland, J. W., Statistical Quality Design and Control: • Contemporary Concepts and Methods, Macmillan, 1992. Ross, P. J., Taguchi Techniques for Quality Engineering, McGraw Hill, 2nd Edition, 1996.

Reference Materials • Wu, C. F. J. and Hamada, M., Experiments: Planning, Analysis, and Parameter Design, Optimization, Wiley Series in Probability and Statistics, 2000. • Myers, R. H. and Montgomery, D. C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley Series in Probability and Statistics, 1995 • Jiju Antony, Design of Experiments for Engineers and Scientists • Walpole, R. E., Myers and R. H., Myers, S. L., Probability and Statistics for Engineers and Scientists, Prentice Hall, 6th edition, 1998. • Sen, A. and Srivastava, M., Regression Analysis: Theory, Methods, and Applications, SpringerVerlag, 1990. • Foster, S. Thomas Jr. Ph. D.: “Designing and Initiating A Taguchi Experiment in a Services Setting” OM Review – Refereed: Volume 9, No. 3. • Taguchi, Genichi: Taguchi on Robust Technology Development: Bringing Quality Engineering Upstream; Asme Press, New York, 1993 • Taguchi, Chowdhury, Taguchi: Robust Engineering: Learn how to boost quality while reducing costs and time to market; McGraw-Hill, New York, 2000

Thank You For Your Attendance!! • Share What You Learnt • Learn from Every Opportunity • Build Robust Product L Ramanan

Design of Experiments in Solving Real Life Problems

Design of Experiments in Solving Real Life Problems

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