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Strategies for Robust Product and Process Design(Short workshop sponsored by ICAM-2006, July 18, 8: 00AM - 12:00 noon at

Marriott Norfolk Waterside, Norfolk, Virginia )

Ranjit K. Roy, Ph.D., P.E. PMP, Fellow of ASQ., President, Nutek, Inc.And

Suren N. Dwivedi,,Ph.D., P.E., Professor, Dept. of Mechanical EngineeringUniversity of Louisiana at Lafayette

Conducted by

9/27/2004 R. Roy/Nutek, Inc. Robust Product and Process Designs http:/nutek-us.com 2

Overview

One of the effective ways to improve product and process quality is to reduce variation in performance that potentially results in reduced rework and rejects downstream. To assure minimum performance variation requires building robustness into the design. Robust products and processes are insensitive to the influence of uncontrollable variables which are the major causes of variation in performance. Use of the Design of Experiment (DOE) technique, in particular, the standardized version of DOE and robust design strategies proposed by Dr. Genechi Taguchi, is a proactive way to achieve robust design. In this workshop, Dr. Roy of Nutek, Inc. presents a brief overview of the basic principles of DOE methodologies and introduces strategies involved in achieving robust products. The use of Qualitek-4 software to accomplish experiment design and analysis of results tasks may be demonstrated.

Nutek Inc. (http://nutek-us.com )3829 Quarton Road, Suite 102,Bloomfield Hills, Michigan 48302. USA.

Tel: 1-248-540-4827 E-mail: [email protected]


Presenters:Ranjit K. Roy, Ph.D., P.E. PMP (Mechanical Engineering, president of NUTEK, INC.), is an

internationally known consultant and trainer specializing in the Taguchi approach of quality improvement. Dr. Roy has achieved recognition for his down-to-earth style of teaching of the Taguchi experimental design technique to industrial practitioners. Based on his experience with a large number of application case studies, Dr. Roy teaches several application-oriented training seminars on quality engineering topics. Dr. Roy began his career with The Burroughs Corporation following the completion of graduate studies in engineering at the University of Missouri-Rolla in 1972. He then worked for General Motors Corp. (1976-1987) assuming various engineering responsibilities, his last position being that of reliability manager.

Dr. Roy is the author of A Primer On The Taguchi Method - published by the Society of Manufacturing Engineers in Dearborn, Michigan and of Design of Experiments Using the Taguchi Approach: 16 Steps to Product and Process Improvement published by John Wiley & Sons, New York. He is a fellow of the American Society for Quality and an adjunct professor at Oakland.

Suren N. Dwivedi, Ph.D.,P.E., is the Regents Eminent Scholar and Professor of Manufacturing in the Mechanical Engineering Department at the University of Louisiana at Lafayette. He has worked in different areas related to IPPD and concurrent engineering for more than 15 years. He was one of the founders of the Concurrent Engineering Research Center at West Virginia University, using the support of the DARPA initiative in concurrent engineering (DICE). This initiative project in Concurrent Engineering has been supported by DARPA for five years.

Dr. Dwivedi was the recipient of the Outstanding Researcher Award for 1990-91 and 1991-92 at West Virginia University. He also received the Outstanding Leadership Award there in 1993. He is currently one of the editors of this journal. He has organized ten international conferences and 12 workshops and training programs for industries in the areas of agile manufacturing and concurrent engineering. He is also the Chief Editor of the journal, entitled the International Journal of Agile Manufacturing. He has guided several projects and has published over 200 research papers in areas related to Integrated Product and Process Development (IPPD), Concurrent Engineering and Agile Manufacturing. His research also includes manufacturing systems and CAD/CAM.


Topics of Discussions

I. Overall Strategy

II. Making Quantum Improvement with Simple DOE

III. Going After Basic Robustness

IV. “Leaving No Stones Unturned” – Building Robustness for Expanded Application Capabilities

V. Qualitek-4 software for design and analysis tasks (time permitting)


Acceptance Sampling - 1910sEconomic Control of Quality of manufcd. products - 1920sDesign of experiments (DOE) - 1930sStatistical quality control - 1940sManagement by objectives - 1950sZero Defects - 1960sParticipative problem solving, SPC, and quality circle - 1970sTotal quality control (TQM) - 1980sSix Sigma - 1990s

Ref: The Evolution of Six Sigma, by Dr. S. Marash, Quality Digest, June 2001Note: For some reason the author did not include ISO/QS 9000 which was popular quality

disciplines implemented by most manufacturing companies.

History of Quality Activities

Ref. Page 1-1


Where does DOE fit in the bigger picture?

Taguchi Approach

FMEA

DOE

SPC

Six Sigma TQM/Lean

Ref. Page 1-2


Design of Experiments (DOE)Using The Taguchi Approach

Source of Topic Titles

What is DOE

Who is Taguchi What is it used for?How do we apply it?

Ref. Page 1-2


Product Engineering Roadmap (Opportunities for Building Quality)

Where do we do quality improvement?

* Design & Analysis

* Design & Development

* Test & Validation

* ProductionReturn on Investment

Ref. Page 1-5


Driving Questions For Quality Improvement(Opportunities for Building Quality)

* Customer Requirements and Design Concepts (APQP)


* Test & Validation

* Production

• Is the performance at its best or at optimum?

• Will it perform the same way all the time, under all application environment?

• Is the design robust?

•Is the manufacturing process robust & adequate?

DESIGN: New questions we may ask.


Leading Questions in Validation Test Planning (Opportunities for cost-effective testing)

* Customer Requirements and Design Concepts (APQP)


* Test & Validation

* Production

• Will the product perform under extremes of application environment?

• How can we cost-effectively test products under all conditions before release?

• What is the worst of all possible application conditions?

•Can we produce the optimized products profitably?

TEST: New questions we may ask.


CONSISTENCY OF PERFORMANCE: Quality may be viewed in terms of consistency of performance. To be consistent is to BE LIKE THE GOOD ONE’S ALL THE TIME. REDUCED VARIATION AROUND THE TARGET: Quality of performance can be measured in terms of variations around the target.

New Definition of Quality

Ref. Page 1-7

This holds true also with performance of any product or process.


Looks of Improvement

Figure 1: Performance Before Experimental Study

Figure 2: Performance After Study

m = (Yavg - Yo )

Yavg. Yo

σσnew

Improve Performance = Reduce σ and/or Reduce m


Poor Quality Not so Bad

Better Most Desirable

Being on Target Most of the Time Ref. Page 1-8


Making Quantum Improvement with Simpler DOE

A minimum first level of effort is to apply simpler experimental design techniques to achieve performance at the desired objective. This would help make the mean population performance move toward the expected level. Simpler DOE using orthogonal arrays generally offer a quantum improvement at a minimum cost.


Easier Ways to do DOE – The Taguchi Approach

Genechi Taguchi was born in Japan in 1924.Worked with Electronic Communication Laboratory (ECL) of Nippon Telephone and Telegraph Co.(1949 - 61). Major Attractions: standardized and simplified techniques.


What is the Design of Experiment (DOE)?

It all began with R. A. Fisher in England back in 1920’s.Fisher wanted to find out how much rain, sunshine, fertilizer, and water produce the best crop.Design Of Experiments (DOE):

statistical technique studies effects of multiple variables simultaneouslydetermines the factor combination for optimum result


DOE Project Application Steps(Plan - Do - Act cycle by Dr. Deming)

PLAN♦Define project

♦Determine performance objectives♦Identify factors to study

TEST & PREDICT

♦Conduct experiments♦Evaluate results

♦Predict improvements

CONFIRM ACHIEVEMENTSTest predicted design and verify that the performance

achieved is acceptable.

Need to follow a structured approach

Need to know the DOE technique

No new knowledge required


PARAMETER DESIGN: Taguchi approach generally refers to the parameter design phase of the three quality engineering activities (SYSTEM DESIGN, PARAMETER DESIGN and TOLERANCE DESIGN) proposed by Taguchi.Off-line Quality Control Quality Loss FunctionSignal To Noise Ratio(s/n) For AnalysisReduced Variability, a Measure Of Quality

DOE - the Taguchi Approach - Seminar Contents

Ref. Page 1-10


EXAMPLE APPLICATIONIt is an experimental technique that determines the solution with minimum effort.In a POUND CAKE baking process with 5 ingredients, and with options to take HIGH and LOW values of each, it can determine the recipe with only 8 experiments. Full factorial calls for 32 experiments. Taguchi approach requires only 8

How Does DOE Technique Work?

Ref. Page 1-10

9/27/2004 R. Roy/Nutek, Inc. Robust Product and Process Designs http:/nutek-us.com 20FIVE factors at TWO levels each make 25 = 32 separate recipes (experimental condition) of the cake.

Ingredients for Baking Pound Cake

Factors Level-1 Level-2

A: Egg

B: Butter

C: Milk

E: Sugar

D: Flour

A2A1

B1 B2

C1 C2

D1D2

E1 E2

Ref. Page 1-11


A1 B1 C1

D1 E1Condition #1

E2

A1 B1 C1

D1Condition #2

Ref. Page N/A

Experimental Conditions


A1 B1 C1

E1Condition #3 D2

E2

A1 B1 C1

Condition #4 D2

Ref. Page N/A



A1 B1

D1 E1Condition #5

E2

A1 B1

D1Condition #6

C2

C2


Ref. Page N/A


A1 B1

E1Condition #7 D2

E2

A1 B1

Condition #8 D2

C2

C2


Ref. Page N/A


Condition # 9 through 30 . . . . .



E1Condition #31 D2

E2Condition #32 D2

C2

C2A2 B2

A2 B2


Ref. Page N/A


Experimental Trial Conditions by L-8 Orthogonal ArrayRef. Page N/A


Experiment Design Using L-8 ArrayRef. Page N/A


3 2-L factors = 8 Vs. 4 Taguchi expts.7 ‘‘ ‘‘ = 128 Vs. 8 Expts.15 ‘‘ = over 32,000 Vs. 16 ‘‘

Fishing Net

Orthogonal Array - a Fish FinderRef. Page 1-11


Standardized application and data analysisHigher probability of successOption to confirm predicted improvementImprovement quantified in terms of dollars

Why Taguchi Approach?Ref. Page 1-12


The Clutch plate is one of the many precision components used in the automotive transmission assembly. The part is about 12 inches in diameter and is made from 1/8-inch thick mild steel.

Objective & Result - Reduce Rusts and Sticky (a) Sticky Parts – During the assembly process, parts were found to be stuck together with one or more parts. (b) Rust Spots – Operators involved in the assembly reported unusually higher rust spots on the clutch during certain period in the year. Factors and Level DescriptionsRust inhibitor process parameters was the area of study.

II. Experiment Design & ResultsOne 4-level factor and four 2-level factors in this experiment were studied using a modified L-8 array. The 4-level factor was assigned to column 1 modified using original columns 1, 2, and 3.

I. Experiment Planning

Project Title - Clutch Plate Rust Inhibition Process Optimization Study (CsEx-05)

Figure 1. Clutch Plate Fabrication Process

Stamping /HobbingClutch plate made from 1/16 inch thick rolled steel

DeburringClutch plates are tumbled in a large container to remove sharp edges

Rust InhibitorParts are submerged in a chemical bath

Cleaned and dried parts are boxed for shipping.

Cleaned and dried parts are boxed for shipping.

Example Case Study (Production Problem Solving)Ref. Page 1-13


Applications in Analytical Simulations

W H

LF

d

D

Elasticity, EI

K

For a cantilever beam, the deflection equation can be expressed as:

D = d + F/K + [4FL3 ]/ [EWH3]

Since Deflection at end is Fl3/(3EI) where I = WH3 /12, d = initial displacement


Tools for Experiment Designs - Orthogonal Arrays

L4 (23) ArrayCols>>Trial# 1 2 3

1 1 1 1 2 1 2 23 2 1 24 2 2 1

Use this array (L-4) to design experiments with three 2-levelfactors

L8(27 ) ArrayCols.>>TRIAL# 1 2 3 4 5 6 7

1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 2 3 1 2 2 1 1 2 2 4 1 2 2 2 2 1 1 5 2 1 2 1 2 1 2 6 2 1 2 2 1 2 1 7 2 2 1 1 2 2 1 8 2 2 1 2 1 1 2

Use this array (L-8) to design experiments with seven 2-level factors

L (XY)n

No. of rows in the array

No. of levels in the columns.

No. of columns in the array.

L9(34)

Trial/Col# 1 2 3 4 1 1 1 1 12 1 2 2 23 1 3 3 34 2 1 2 35 2 2 3 1 6 2 3 1 27 3 1 3 28 3 2 1 39 3 3 2 1

Use this array (L-9) to design experiments with four 3-levelfactors


•Experiment using Std. Orthogonal Arrays•Main effect studies and optimum condition

• Interactions• Mixed level factors

OEC Problem solving

DCLoss

Noise Factors, S/N Analysis, Robust Designs, ANOVA

There are More Steps to Climb

For better returns on investment, more sophisticated experiment design and analysis techniques need to be employed.


III. Going After Basic Robustness

To make design robust is to make its performance insensitive to the uncontrollable (Noise) factors. The strategy here is to select the most desirable combination of the controllable factors based on the performance while exposed to the influence of the noise conditions. The experiment design for such studies require stringent disciplines and care.

Detail can be seen from example applications….


Nature of Influences of Factors at Different LevelsR

esul

t/Res

pons

e/Q

C

A1 A2 A3 A2

Res

ult/R

espo

nse/

QC

A1 A2 A3

Res

ult/R

espo

nse/

QC

• Minimum TWO levels

• THREE levels desirable

• FOUR levels in rare cases

• Nonlinearity dictates levels for continuous factors only

A1 A2 A3 A4

Ref. Page 2-2


Combination Possibilities – Full Factorial Combinations

ONE 2-level factor offer TWO test conditions (A1,A2).TWO 2-level factors create FOUR (22 = 4 ) test conditions A1B1 A1B2 A2B1 A2B2) .

NOTATIONS:A (A1,A2) or A represent 2-level factor

THREE 2-level factors create

EIGHT (23 = 8) possibilities.

A1B1C1 A1B1C2

A1B2C1 A1B2C2

A2B1C1 A2B1C2

A2B2C1 A2B2C2

Simpler notations for all possibilities

or full factorial

Cond.# A B C

1 1 1 1

2 1 1 2

3 1 2 1

4 1 2 2

5 2 1 1

6 2 1 2

7 2 2 1

8 2 2 2

Ref. Page 2-3


3 Factors at 2 level 23 = 84 Factors at 2 level 24 = 167 Factors at 2 level 27 = 12815 Factors at 2 level 215 = 32,768

What are Partial Factorial Experiments?What are Orthogonal arrays and how are they used?

Full Factorial Experiments Based on Factors and Levels

Ref. Page 2-4


How are Orthogonal arrays used to design experiments?What does the word “DESIGN” mean?What are the common properties of Orthogonal Arrays?

Orthogonal Arrays– Experiment Design Tool

2-Level Arrays

L4 (23 )L8 (27)L12 (211)L16 (215) . . . .

3-Level ArraysL9 (34), L18 (21 37) . . .

4-Level ArraysL16 (45) . . . .

L-4 Orthogonal ArrayTrial # 1 2 3

1 1 1 12 1 2 23 2 1 2 4 2 2 1

Ref. Page 2-4


Key observations: First row has all 1's. There is no row that has all 2's. All columns are balanced and maintains an order. Columns of the array are ORTHOGONAL or balanced. This means that there are equal number of levels in a column. The columns are also balanced between any two columns of the array which means that the level combinations exist in equal number. Within column 1, there are two 1's and two 2's. Between column 1 and 2, there is one each of 1 1, 1 2, 2 1 and 2 2 combinations. Factors A, B And C all at 2-level produces 8 possible combinations (full factorial) Taguchi’s Orthogonal array selects 4 out of the 8.

How does One-Factor-at-a-time experiment differ from the one designed using an Orthogonalarray?

L-4 Orthogonal ArrayTrial #A B C1 1 1 12 1 2 23 2 1 2 4 2 2 1

Array Descriptions:1. Numbers represent factor levels2. Rows represents trial conditions3. Columns accommodate factors 3. Columns are balanced/orthogonal 4. Each array is used for many experiments

Properties of Orthogonal ArraysRef. Page 2-5


Orthogonal Arrays for Common Experiment Designs

L (XY)n




Use this array (L-4) to design experiments with three 2-level factors

1

1

2

2

1

2

2

1

1

2

1

2

1

2

4

3

xxxxxx

xxx

xxx

C A BTrial# Results

Ref. Page 2-6



L (XY)n




Use this array (L-8) to design experiments with seven 2-level factors

xx

xx

xx

xx

xx

xx

xx

xx

1

1

1

1

2

2

2

2

1

2

4

3

5

6

8

7

1

2

1

2

2

1

2

1

1

1

2

2

2

2

1

1

1

2

2

1

1

2

2

1

1

2

2

1

2

1

1

2

1

2

1

2

1

2

1

2

1

1

2

2

1

1

2

2

ResultsETrial# A CB FD G

Ref. Page 2-6



L (XY)n




Use this array (L-9) to design experiments with four 3-level factors

Trial# A B C D Results

1 1 1 1 1 xx

2 1 2 2 2 xx

3 1 3 3 3 xx

4 2 1 2 3 xx

5 2 2 3 1 xx

6 2 3 1 2 xx

7 3 1 3 2 xx

8 3 2 1 3 xx

9 3 3 2 1 xx

Ref. Page 2-7


Steps in Experiment Design

Factors Level-1 Levl-2A:Time 2 Sec. 5 Sec.B:Material Grade-1 Grade-2C:Pressure 200 psi 300 psi

L-4 Orthogonal ArrayTrial #A B C1 1 1 12 1 2 23 2 1 2 4 2 2 1

Step 1. Select the smallest orthogonal array

Step 2. Assign the factors to the columns (arbitrarily)

Step 3. Describe the trial conditions (individual experimental recipe)

Trial#1: A1B1C1 = 2 Sec. (Time), Grade-1 (Material), and 200 psi (Pressure)




Ref. Page 2-7


Experiment Designs With Seven 2-Level FactorExperiments with seven 2-level factors are designed using L-8 arrays. An L-8 array has seven 2-level columns. The factors A, B, C, D, ... G can be assigned arbitrarily to the seven column as shown. The orthogonal arrays used in this manner to design experiments are called inner arrays.

Experiment Designs with More Factors?

L8 Orthogonal Array

11

11

22

22

12

43

56

87

12

12

21

21

11

22

22

11

12

21

12

21

12

21

21

12

12

12

12

12

11

22

11

22

ETrial# A CB FD G

Control Factors

Inner Array

Ref. Page 2-8


Full Factorial Arrangement with Seven 2-level FactorsRef. Page 2-9


2-Level ArraysL4 (23)L8 (27)L12 (211)L16 (215)

3-Level ArraysL9 (34)L18 (21 37)

4-Level ArraysL16 (45)

Common Orthogonal Arrays

L (XY)n




Ref. Page 2-10


PLAN

⌧Identify Project and Select Project Team

⌧Define Project objectives Evaluation Criteria

⌧Determine System Parameters (Control Factors, Noise Factors, Ideal Function, etc.)

DESIGN

⌧Select Array and Assign Factors to the columns (inner and outer arrays)

CONDUCT EXPERIMENTS

ANALYZE RESULTS

⌧Factor Effects, Optimum Condition, Predicted Performance, etc.

Planning Before Designing ExperimentsRef. Page 2-10


An ordinary kernel of corn, a little yellow seed, it just sits there. But add some oil, turn up the heat, and, pow. Within a second, an aromatic snack sensation has come into being: a fat, fluffy popcorn.

Note: C. Cretors & Company in the U.S. was the first company to develop popcorn machines, about 100 years ago.

Popcorn Machine Performance Study (Example Experiment)

This example is used to demonstrate “cradle to grave”, mini planning, design, and analyses tasks involved in DOE.

Ref. Page 2-11


Project - Pop Corn Machine performance StudyObjective & Result - Determine best machine settingsQuality Characteristics - Measure unpopped kernels (Smaller is better)

Factors and Level DescriptionsFactor Level I Level IIA: Hot Plate Stainless Steel Copper AlloyB: Type of Oil Coconut Oil Peanut OilC: Heat Setting Setting 1 Setting 2

Experiment Planning & Design

12

43

Trial# C: Ht. Setting A: Hot plate B: Oil Type

C1: Setting 1

C1: Setting 1

C2: Setting 2

C2: Setting 2

A1: Stainless

A2: Copper

A1: Stainless

A2: Copper

B1: Coconut

B2: Peanut

B2: Peanut

B1: Coconut

11

22

C A B12

21

12

12

12

43

Trial# Results

Ref. Page 2-12


Experiment Design & Results

12

43

Trial# C: Ht. Setting A: Hot plate B: Oil Type

C1: Setting 1

C1: Setting 1

C2: Setting 2

C2: Setting 2

A1: Stainless

A2: Copper

A1: Stainless

A2: Copper

B1: Coconut

B2: Peanut

B2: Peanut

B1: Coconut

11

22

C A B12

21

12

12

12

43

Trial# Results

Design Layout (Recipes)

Expt.1: C1 A1 B1 or [Heat Setting 1, Stainless Plate, & Coconut Oil]Expt.2: C1 A2 B2 or [Heat Setting 1, Copper Plate, & Peanut Oil ]Expt.3: C2 A1 B2 or [Heat Setting 2, Stainless Plate, & Peanut Oil ]Expt.4: C2 A2 B1 or [Heat Setting 2, Copper Plate, & Coconut Oil ]

How to run experiments: Run experiments in random order when possible.

Ref. Page 2-12


Experimental Results and Analysis

A1 =__

(5 + 7)/2 = 6.0

11

22

C A B12

21

12

12

12

43

Trial# Results

58

47

__T = (5 + 8 + 7 +4)/4 = 6

11

22

C A B12

21

12

12

12

43

Trial# Results

58

47

A2 =__

(8 + 4)/2 = 6.0

Ref. Page 2-13


Trend of Influence:How do the factor behave?

♦ What influence do they have to the variability of results?

♦ How can we save cost?Optimum Condition:

♦ What condition is most desirable?

Calculations: ( Min. seven, 3 x 2 + 1)

(5 + 8) / 2 = 6.5

(7 + 4) / 2 = 5.5

(5 + 7) / 2 = 6.0

(8 + 4) / 2 = 6.0

(5 + 4) / 2 = 4.5

(8 + 7) / 2 = 7.5

_C2 =

_C1 =

_A2 =

_A1 =

_B1 = _B2 =

Analysis of Experimental Results

A1 Hot plate A2 B1 Oil B2 C1 Heat Setting C2

3

4

6

5

7

8

9UNPOPPED

KERNELS

Main Effects(Average effects of factor influence)

Ref. Page 2-14


QC Plays a key roles in:Understanding factor influence Determination of the most desirable condition.

Quality Characteristics

ExamplesNominal is Best: 5” dia. Shaft,12 volt battery, etc.Smaller is Better: noise, loss, rejects, surface roughness, etc.Bigger is Better: strength, efficiency, S/N ratio, Income, etc.

Role of Quality Characteristics (QC)Ref. Page 2-14


Estimate of Performance at the Optimum Condition

A1 Hot plate A2 B1 Oil B2 C1 Heat Setting C2

3

4

6

5

7

8

9UNPOPPED

KERNELS

Main Effects(Also called: Factorial Effects or Column Effects)

A1 B1C2

Based on QC: Smaller is better

Optimum condition: ( Assuming A1 is less expensive than A2)A1 B1 C2

= 6.0 + ( 6 – 6 ) + (4.5 – 6.0 ) + ( 5.5 – 6.0 )= 4.0 (Assumption: Factor contributions are additive)

__Yopt = T +

__( A1 -

_( C2 -

__T )

__( B1 -

__T ) +

__T ) +

Ref. Page 2-15


Expected Performance:

♦ What is the improved performance?♦ How can we verify it?♦ What is the boundary of expected performance?

(Confidence Interval, C.I.)Notes:

Generally, the optimum condition will not be one that has already been tested. Thus you will need to run additional experiments to confirm the predicted performance.

Confidence Interval (C.I.) on the expected performance can be calculated from ANOVA calculation. These boundary values are used to confirm the performance.

Meaning: When a set of samples are tested at the optimum condition, the mean of the tested samples is expected to be close to the estimated performance.

Interpretation of the Estimated Performance

3.5 Yavg. Yexp. = 4.0 4.5

Confidence level (C.L.), say 90%.

Confidence Interval, C.I. = +/- 0.50

(Calculation not shown)

Ref. Page 2-16


Performance Improvement

Improved performance from DOE = Estimated performance at the optimum condition (Yopt)

Yopt = 4.0 (in this example)

The estimated performance can be expressed in terms of a percent improvement, if the current performance is known.

Assuming that the current performance is the grand average of performance (YCurrent ) = 6.0

Improvement = x 100(Yopt - YCurrent )

YCurrent

= x 100 = - 33%(4 - 6 )

6

Ref. Page 2-16


SolveProblem 2A

Practice and Learn


Practice Problem # 2A: Experiment with L-4

Ref. Page 2-41


Practice Problem # 2A

• Which factor has the most influence to the variability of result?• If you were to remove tolerance of one of the three factors studied, which factor will it be?

Ref. Page 2-41


Practice Problem # 2A

2. Determine the Optimum Condition. Optimum Condition (character notation) = Optimum Condition (level description) =

3. What is the grand average of performance?__T =

4. Calculate the estimated value of the Expected Performance at the optimum condition.Yopt =

5. What is the estimated amount of total contributions from all significant factors?Total contributions from all factors =

6. Assuming that the result of trail # 2 represents the current performance, compute the % Improvement obtainable by adjusting the design to the optimum condition determined.

% Improvement =

[Answers: 1 - (Describe, Factor __ has the most influence, etc. ) 2 - Optimum Cond: 2,2,2, , 3 - Gd. Avg.=28.5, 4 - Yopt = 19, 5 -Contribution = 9.5, 6 - Improvement = 24% ]

Ref. Page 2-42


Group Exercise - Class Project

I. Experiment PlanningProject Title -Objective & Result -(Describe why you initiated the project and what you wish to accomplish)Quality Characteristics: (Describe what you are after and how you would measure the results. Depending on what it is you are after, your quality characteristic will be bigger is better, smaller is better, or nominal is the best)

Factors and Level DescriptionsNotation/Factor Description Level I Level IIA:B:C: etc.

II. Experiment Design & ResultsOur plan is to use _____ array. We/I want to complete design by assigning factors to the columns as.. Etc.


Experiment Designs with Noise Factors

Tr#123

8

1 2 3 4 5 6 7

L8

Control factors

Noise FactorsL 4

Outer Array

Inner Array

R e s u l t s1 2 3 4

123

1 1 2 21 2 1 21 2 2 1

R R R R R R R R

R R R R R R R R

. . . . . . .. . .. . . .. .. . . .. .

73

11

21

Oven type

Temperature

Humidity

*


Why AVERAGE of results is inadequate?Why do we need a new YARDSTICK?

Nominal: MSD = [(Y1 -Yo) 2 +.(Y2 -Yo) 2 + (Y3 -Yo) 2 +. .]/n

Smaller: MSD = [( Y12 + .Y 22 +Y 32 + . .)]/n

Bigger: MSD = [(1 / Y12 + 1 / Y2

2 + 1/Y32 + ...... )]/n

S/N = - 10 LOG10 (MSD)

Why -(Minus) Why base 10

Evaluating Performance Based on Reduced Variation


“Leaving no Stones Unturned” – Building Robustness for Expanded Application Capabilities

While most systems (product and process designs) tend to have a desired performance goal, there are others which need to respond in direct proportion to the strength of the input (called signal factor) condition. For such system, the goal is to achieve performance that maintains a fixed relationship with the magnitude of the input. Such systems are considered to have dynamic response characteristics and require special experiment setup and analysis methods for optimizing designs..


Dealing with Dynamic Systems – Process Diagram

Representing the subject product/process design as a system is a necessary step for understanding its behavior. The system is described in terms of its parameters like factors, signal, response, noise, etc. An absence of variable input/signal to the system renders it as a static system which are dealt with the standard designs discussed earlier.


Example of Dynamic System Response

Example Case: Fuel Gauge ReadingExample Case: Fuel Gauge Reading

Response

(y)

M1 M2 M3Signal (M)

*****

*****

*****

y = β M

β, Slope

y

M

LinearLarge variation

y

M

NonlinearHigh variation

Least Desirable


Comparison of Strategies for Static and Dynamic System

Static System: Tiger Woods putting golf ballsAugust 11, 2004Top spot: Tiger Woods' hold on the world number one ranking is more tenuous now.

“Vijay Singh has been on Tiger's heels for some time now, and if either Singh, or Ernie Ells were to win the PGA Championship, Woods would relinquish his spot atop the rankings.”

Dynamic System: Lance Armstrong biking for Tour de FranceLance Armstrong rides into Paris, collects record sixth consecutive Tour title (Tour de France), Sunday July 25, 2004 5:39PM

PARIS (AP) -- Lance Armstrong raced onto the crowd-lined Champs-Elysees as a yellow blur, bathed in the shimmering light of a 24-carat, gold-leaf bike, a golden helmet and the race leader's yellow jersey.


Dynamic System Examples

Example Case: Voltage Measuring Instrument

Signal Factor (M):Battery voltage

Response (y):Voltage reading

Notes:

Example Case: Voltage Measuring Instrument

Signal Factor (M):Battery voltage

Response (y):Voltage reading

Notes:

Response

(y)

M1 M2 M3Signal (M)

*****

*****

*****y = β M

β, Slope


Dynamic System Examples

Example Case: Weighing Scale Design

Signal Factor (M):Weight of subject

Response (y):Indicated weight

Notes:Weight indicated should be the sameas weight of the subject.

Example Case: Weighing Scale Design

Signal Factor (M):Weight of subject

Response (y):Indicated weight

Notes:Weight indicated should be the sameas weight of the subject.

Response

(y)

M1 M2 M3Signal (M)

*****

*****

*****y = β M

β, Slope


Where to Apply and Why

Apply early in the engineering design stage to optimize process and product designs

WHY?

Very high return on investment (ROI)

(Time for Q&A, Class exercise, Software demonstration)


Application Opportunities & Academic Talents

• Experience with University Education and Training in DOE

• Available Resources (Books & Software)

• Opportunities for Applications in Industrial Settings


References: www.nutek-us.com/wp-txt.html

Training & WorkshopText Books Software (Free DEMO download)

Nutek, Inc.3 829 Quarton Road

Bloomfield Hills, MI 48302.Tel : 1‐248‐540‐4827 Info@Nutek‐us.com

www.Nutek‐us.com

Documents

Strategies for Robust Product and Process Designnutek-us.com/Robust_0607_ICAM.pdf · Strategies for Robust Product and Process Design ... teaches several application-oriented training