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Optimization -The Finishing Touch in Product Design

Seventh Annual International Users Conference

Hosted by Ricardo Software, Southfield, Michigan, USA.

March 8, 2002

by

Ranjit K. Roy

Nutek, Inc.

www.rkroy.com
http://www.rkroy.com/http://www.rkroy.com/wp-nut.htmlhttp://www.rkroy.com/

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10/25/2001 Taguchi Approach - Overview 2

Introduction

All engineering activities have roles to play in

improving the product quality. Toward this

goal, optimization of designs in the analytical

stage presents an attractive opportunity. Thestatistical technique known as design of

experiments (DOE), which is commonly used

to experiment with prototype parts, can often

be effectively utilized to optimize product

designs using analytical simulations. Thisbrief presentation offers an overview of how

the Taguchi standardized form of DOE can

be applied to analytical performance models

for identifying the best among the available

design options.

- RKR 3/8/02

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Presentation Contents

Drive & Rational for Optimization

Ultimate Goal - Robust Design

Tool for Optimization

Understanding DOE/Taguchi Approach

Industrial Applications

DOE Example - Popcorn machine optimization

Efficiencies in analytical applications

Linear model Nonlinear model

Conclusions, Comments, and Q&A

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Our Values & Rationale for

Optimization

We wish to improve our products and do that we shall

Leave no stone unturned

Seek out and settle with the best among allpossible alternative design possibilities

Look for ways to optimize designs quickly

and economically (Go after most benefits with

least cost)

Why optimize product and

process designs?

Reduce rework, rejects, and warranty costs.

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Product Engineering Roadmap(Opportunities for Building Quality)

Where do we do

quality improvement?

* Design &

Analysis

* Design &

Development

* Test &

Validation

* Production

There are opportunities forimprovement in all phases of product

development.

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Maximizing Return on

Investments

Where should we put our effort to

optimize designs?

Return on investment (ROI) is greater whenefforts are made to optimize in design and

analysis stages.

ROI: 1 : 1 in production

ROI: 1 : 10 in process design

ROI: 1 : 100 in developmentROI: 1 : 1000 in analyses

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Do It Right The First Time!

Do It Up-front In Design!

Build Quality In Design!

Who is Taguchi?

Genechi Taguchi was born in Japan in

1924.

Worked with Electronic Communication

Laboratory (ECL) of Nippon Telephone

and Telegraph Co.(1949 - 61).

Major contribution has been to standardize

and simplify the use of the DESIGN OF

EXPERIMENTS techniques.

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What is the Design of

Experiment (DOE) Technique?

It all began with R. A. Fisher in

England back in 1920s.

Fisher wanted to find out how muchrain, sunshine, fertilizer, and water

produce the best crop.

Design Of Experiments (DOE):

Is a statistical technique used to

study effects of multiple variablessimultaneously.

It helps you determines the factor

combination for optimum result.

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Looks & Measure of

Improvement

Figure 1: Performance

Before Experimental Study

Figure 2: Performance After

Study

m = (Yavg - Yo )

Yavg. Yo

new

Improve Performance = Reduce

and / or Reduce m

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Poor Quality Not so Bad

Better Most Desirable

Being on Target Most of the Time

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How Does DOE/Taguchi Work?

Follows an experimental strategy that

derives most information with

minimum effort. The technique can be applied to

formulate the most desirable recipe for

baking a POUND CAKE with FIVE

ingredients, and with the option to take

HIGH and LOW values of each. Full factorial calls for 32 experiments.

Taguchi approach requires only 8.

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Experiment Factors and

their Levels

FIVE factors at TWO levels each make 25 = 32separate recipes (experimental condition) of the cake.

Factors Level-I Level-II

A: Egg

B: Butter

C: Milk

E: Sugar

D: Flour

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Orthogonal Array Experiments

Work Like a Fish Finder

3 2-L factors = 8 Vs. 4 Taguchi expts.

7 = 128 8 Expts.

15 over 32,000 16

Fishing Net

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Example Case Study (Production Problem Solving)

An assembly plant of certain luxury car vehicle experienced frequent

failure of one of the bonded plastic bracket for power window

mechanism.The cause of the failure was identified to be inadequate

strength of the adhesive used for the bonding.

Objective & Result - Increase Bonding Strength

Bonding tensile (pull) strength were going to be measured in three axial

directions. Minimum force requirements were available from standards

set earlier.

Quality Characteristics - Bigger is better(B)

Factors and Level Descriptions

Bracket design, Type of adhesive, Cleaning method, Priming time,

Curing temperature, etc.

II. Experiment Design & Results

Six different process parameters were quickly studied by experiments

designed using an L-8 array.

I. Experiment Planning

Project Title - Adhesive Bonding of Car Window Bracket

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In a die casting process, metal (generally alloys of Aluminum, Zinc &

Magnesium) parts are formed by flowing molten metals (at 1200 1300

deg F) in the cavities of the dies made of steel.

Objective & Result Reduce Scraps

Quality Characteristics - Smaller is better (S)

# Criteria Descriptions Worst - Best Reading QC Rel. Wt.

1 Crack and Tear (length) 10 mm 20 mm S 20

2 Heat Sinks (diameter) 15 mm 0 mm S 30

3 Lamination (area) 5 sq.cm 0 sq.cm S 25

4 Non-Fill (area of void) 2 sq.cm 0 sq.cm S 25

Commonly Observed Characteristics

There are many types of observed defects that result in scrapped parts.The common defects observed are, Surface abnormalities (Cold flaw,

Cold lap, Chill swirls, Non-fill, etc.), Lamination (layers of metal on

inside or outside surface), Gas Porosity, Blister, Shrinkage Porosity, Heat

sinks, Crack & tears, Drags, Gate porosity, Driving ejector pins, etc.


An L-12 array was used to design the

experiment to study 10 2-level factors.

Factors are assigned to the column in

random order. The results of each criteria

of evaluations were analyzed separately.


Project Title - Die-Casting Process Parameter Study (CsEx-01)

Example Case Study# S2: (Casting Process Optimization)

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Example Case Study (Production Problem Solving)

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.


Rust inhibitor process parameters was the area of study.


One 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.


Project Title - Clutch Plate Rust Inhibition Process Optimization Study

(CsEx-05)

Figure 1. Clutch Plate Fabrication Process

Stamping /

Hobbing

Clutch plate

made from

1/16 inch

thick rolled

steel

Deburring

Clutch plates

are tumbled

in a large

container to

remove sharp

edges

Rust

Inhibitor

Parts are

submerged

in a

chemical

bath

Cleaned and dried parts

are boxed for shipping.

Cleaned and dried parts

are boxed for shipping.

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Example Case Study # S9: ( Sporting Event Optimization)

There are a number of structural and geometrical factors in bow and

arrow that determines how well the arrow fly. A contestant for Olympic

archery competition planned to use DOE to lay out a set of experiments

to determine the best bow and arrow setting for best performance.

Objective & Result: Improve accuracy of hitting the bullseye. The

accuracy can be measured in terms of radial distance of the hit from the

center of the bullseye.

Quality Characteristics:

Radial distance measured in inches. Smaller is better

Factors and Level Descriptions:

A:Arrow Stiffness (Force required to pull the string)

B:Draw Length

C:Draw Weight (Force when not linearly proportional with draw length)

D:Point Weight (Weight of point of arrow, steel, 90 - 110 grams)

E:Plunger Button Tension (Compression force at guide - arrow rest)

F:Center shot (Horizontal location of the guide)

G:String Type (Plastic, Kevlar, etc.)

H:Knocking Location (Location of the arrow nock on string)

Interactions: AxE, ExF, AxB, & AxCII. Experiment Design & Results

This experiment is designed using an L-16 array to study 8 factors and 4

interactions.


Project Title - Bow & Arrow Tuning Study

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Example Case Study # S10: ( Race Car Optimization)

To achieve highest performance, major suspension parameters of

race cars like those for Daytona Superspeedway (2.5 mile oval; 31

degrees banking in 1-4 turns) are fine tuned for the track. Test

vehicle components can be evaluated by laying out simple

experiments to determine the most desirable combination.

Objective & Result: Determine the best combination of suspension

parameters for the race car.

Quality Characteristics: Time to complete the track. Smaller is better.

Factors and Level Descriptions: (Source: USA Today, February 15, 2002)

A:Right Front Tire Pressure (23 - 55 psi) Green = Superspeedway

B:Left Front Tire Pressure (15 - 30 psi)

C:Right Rear Tire Pressure (20 - 50 psi)D:Left Rear Tire Pressure (15 - 30 psi)

E:Right Front Spring Rate (1,900 - 800 lbs/in)

F:Left Front Spring Rate (700 - 800 lbs/in)

G:Right Rear Spring Rate (225 - 350 lbs/in)

H:Left Rear Spring Rate (15 - 30 lbs/in)

I:Rear Spoiler Angle (0 - 55 degrees)


Up to 11 factors as shown above can be studied by designing an

experiment using an L-12 array.


Project Title - Race Car Suspension Parameter Optimization

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An ordinary kernel of

corn, a little yellow

seed, it just sits there.

But add some oil, turnup 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.

[Example DOE]Popcorn Machine

(Example application. Not included in seminar handout.)(Example application. Not included in seminar handout.)

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Title of Project - Pop Corn Machine performance Study

Objective & Result - Determine best machine settings

Quality Characteristics - Measure unpopped kernels (Smaller is

better)


Notation Factor Description Level I Level II

A: Hot Plate Stainless Steel Copper Alloy

B: Type of Oil Coconut Peanut

C: Heat Setting Setting 1 Setting 2

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Orthogonal Arrays for Common

Experiment Designs

L4 (23

) ArrayCols>>

Trial# 1 2 3

1 1 1 1

2 1 2 2

3 2 1 2

4 2 2 1

L8(27 ) Array

Cols.>>

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

L9(34)

Trial/Col# 1 2 3 41 1 1 1 1

2 1 2 2 2

3 1 3 3 3

4 2 1 2 3

5 2 2 3 1

6 2 3 1 2

7 3 1 3 2

8 3 2 1 3

9 3 3 2 1

Use this array (L-9) to

design experiments

withfour 3-level

factors

Use this array (L-4) to

design experiments with

three 2-level factors

Use this array (L-8) to design

experiments with seven 2-level

factors

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# C A B Results (oz)*

1 1 1 1 5

2 1 2 2 8

3 2 1 2 7

4 2 2 1 4

Design Layout (Recipes)

Expt.1: C1 A1 B1 or [Heat Setting 1, Stainless

Steel 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

Steel 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

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III. Analysis of Results

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 + 7 + 4 ) / 4 = 6

(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

_

T =

_

C2 =

_

C1 =

_

A2 =

_

A1 =

_

B1 =

_

B1 =

A1

Hot plate A2

B1

Oil B2

C1

Heat Setting C2

3

4

6

5

7

8

9

UNPOP

PED

KERNELS

Main Effects(Average effects of factor influence)

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III. Analysis of Results (contd.)

Expected Performance:

What is the improved performance?

How can we verify it?

What are the boundaries of expected performance?

(Confidence Interval, C.I.)

__

A1 +

Yopt = + + +

= 6.0 + ( 6 6 ) + (4.5 6.0 ) + ( 5.5 6.0 )

= 4.0

_

T

_

T )

_

( A1 +

_

T )

_

( C2 +_

T )

_

( B1 +

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.

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Analytical Simulations With Seven Factors

A process performance (Y) which is dependent on seven factors (A, B, C, ...) can be

represented by many types of mathematical functions as shown here.

Linear: Y = C1*A + C2*B + C3*C + C4*D + C5*E + C6*F + C7*G

Hyperbolic: Y = 100*(C1+C2+C3+C4+C5+C6+C7)/(A+B+C) + (D+E)/(F+G)

Polynomial: Y = C1*A + C2*B^2 + C3*C^2 + C4/D^3 + C5*E/(F + G)^2

Complex: Y = 0.50 - ((A + B + C) * D^3) / (4000 * E * F * G^3)

Logarithmic:Y = 10 * LOG((C1/A^5 + C2/B^4 + C3*C^3 + C4*D^2 + C5*E^3 + C6*F*C7*G) / 1000)

Linear Equation: (constants assumed)

Y = 0.02*A + 0.001*B + 0.0001*C + 0.04*D + 1.5*E + 21.6*F + 12.7*G

Factors A B C D E F G

Level 1 2500 1900 4000 32.0 29.5 6.90 10.5

Level 2 2650 1520 4800 30.0 30.7 7.80 11.4

Full Factorial Experiments (All possible combinations (* Taguchi L-8 conditions)

)

# Description Results # Description Results1 1 1 1 1 1 1 1 380.220* 2 1 1 1 1 1 1 2 391.650

3 1 1 1 1 1 2 1 399.660 4 1 1 1 1 1 2 2 411.090

5 1 1 1 1 2 1 1 382.020 6 1 1 1 1 2 1 2 393.450

7 1 1 1 1 2 2 1 401.460 8 1 1 1 1 2 2 2 412.890

9 1 1 1 2 1 1 1 380.140 10 1 1 1 2 1 1 2 391.570

11 1 1 1 2 1 2 1 399.580 12 1 1 1 2 1 2 2 411.010

13 1 1 1 2 2 1 1 381.940 14 1 1 1 2 2 1 2 393.370

15 1 1 1 2 2 2 1 401.380 16 1 1 1 2 2 2 2 412.810*

17 1 1 2 1 1 1 1 380.300 18 1 1 2 1 1 1 2 391.730

19 1 1 2 1 1 2 1 399.740 20 1 1 2 1 1 2 2 411.170

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21 1 1 2 1 2 1 1 382.100 22 1 1 2 1 2 1 2 393.530

23 1 1 2 1 2 2 1 401.540 24 1 1 2 1 2 2 2 412.970

25 1 1 2 2 1 1 1 380.220 26 1 1 2 2 1 1 2 391.650

27 1 1 2 2 1 2 1 399.660 28 1 1 2 2 1 2 2 411.090

29 1 1 2 2 2 1 1 382.020 30 1 1 2 2 2 1 2 393.450

31 1 1 2 2 2 2 1 401.460 32 1 1 2 2 2 2 2 412.890

33 1 2 1 1 1 1 1 379.840 34 1 2 1 1 1 1 2 391.270

35 1 2 1 1 1 2 1 399.280 36 1 2 1 1 1 2 2 410.710

37 1 2 1 1 2 1 1 381.640 38 1 2 1 1 2 1 2 393.070

39 1 2 1 1 2 2 1 401.080 40 1 2 1 1 2 2 2 412.510

41 1 2 1 2 1 1 1 379.760 42 1 2 1 2 1 1 2 391.19043 1 2 1 2 1 2 1 399.200 44 1 2 1 2 1 2 2 410.630

45 1 2 1 2 2 1 1 381.560 46 1 2 1 2 2 1 2 392.990

47 1 2 1 2 2 2 1 401.000 48 1 2 1 2 2 2 2 412.430

49 1 2 2 1 1 1 1 379.920 50 1 2 2 1 1 1 2 391.350

51 1 2 2 1 1 2 1 399.360 52 1 2 2 1 1 2 2 410.790*

53 1 2 2 1 2 1 1 381.720 54 1 2 2 1 2 1 2 393.150

55 1 2 2 1 2 2 1 401.160 56 1 2 2 1 2 2 2 412.590

57 1 2 2 2 1 1 1 379.840 58 1 2 2 2 1 1 2 391.270

59 1 2 2 2 1 2 1 399.280 60 1 2 2 2 1 2 2 410.710

61 1 2 2 2 2 1 1 381.640* 62 1 2 2 2 2 1 2 393.070

63 1 2 2 2 2 2 1 401.080 64 1 2 2 2 2 2 2 412.510

65 2 1 1 1 1 1 1 383.220 66 2 1 1 1 1 1 2 394.650

67 2 1 1 1 1 2 1 402.660 68 2 1 1 1 1 2 2 414.090

69 2 1 1 1 2 1 1 385.020 70 2 1 1 1 2 1 2 396.450

71 2 1 1 1 2 2 1 404.460 72 2 1 1 1 2 2 2 415.89073 2 1 1 2 1 1 1 383.140 74 2 1 1 2 1 1 2 394.570

75 2 1 1 2 1 2 1 402.580 76 2 1 1 2 1 2 2 414.010

77 2 1 1 2 2 1 1 384.940 78 2 1 1 2 2 1 2 396.370

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79 2 1 1 2 2 2 1 404.380 80 2 1 1 2 2 2 2 415.810

81 2 1 2 1 1 1 1 383.300 82 2 1 2 1 1 1 2 394.730

83 2 1 2 1 1 2 1 402.740 84 2 1 2 1 1 2 2 414.170

85 2 1 2 1 2 1 1 385.100 86 2 1 2 1 2 1 2 396.530*

87 2 1 2 1 2 2 1 404.540 88 2 1 2 1 2 2 2 415.970

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Calculated Results Based on Conditions

Defined by an L-8 Array Design

TRIAL# A B C D E F G Results Comb.#

1 1 1 1 1 1 1 1 380.220 # 1

2 1 1 1 2 2 2 2 412.810 # 16

3 1 2 2 1 1 2 2 410.790 # 52

4 1 2 2 2 2 1 1 381.640 # 61

5 2 1 2 1 2 1 2 396.530 # 866 2 1 2 2 1 2 1 402.660 # 91

7 2 2 1 1 2 2 1 404.080 # 103

8 2 2 1 2 1 1 2 394.190 # 106

From full factorial (analytical simulation): Highest value from L-8

design: 415.966, which compares with # 88 2 1 2 1 2 2 2 415.970

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Analytical Simulation with

Nonlinear (Complex) Equation

Complex Equation:

Y = 0.50 - ((A + B + C) * D^3) / (4000 * E * F * G^3)

Factors A B C D E F G

Level 1 2500 1900 4000 32.0 29.5 6.90 10.5

Level 2 2650 1520 4800 30.0 30.7 7.80 11.4

Calculations of Y for all possible conditions (128)

produce...

...

46 1 2 1 2 2 1 2 0.328

47 1 2 1 2 2 2 1 0.305

48 1 2 1 2 2 2 2 0.347Highest value

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Calculated Results Based on Conditions

Defined by an L-8 Array Design

TRIAL# A B C D E F G Results Comb. #

1 1 1 1 1 1 1 1 0.208 # 1

2 1 1 1 2 2 2 2 0.340 # 16

3 1 2 2 1 1 2 2 0.288 # 52

4 1 2 2 2 2 1 1 0.257 # 61

5 2 1 2 1 2 1 2 0.256 # 866 2 1 2 2 1 2 1 0.263 # 91

7 2 2 1 1 2 2 1 0.259 # 103

8 2 2 1 2 1 1 2 0.317 # 106

From full factorial (analytical simulation): #48 1 2 1 2 2 2 2 0.347 ,

which compares with O.35.

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Conclusions and Comments

Most optimization studies tend to involve

unnecessary complications that is not cost

effective. Simpler DOE/Taguchi with focus on

robustness produce the most benefit.

Most optimization technique would work

well for most jobs when applied with

proper understanding of the applicationprinciples.

Automation in analysis is not a substitute

for knowledge of science and physics.

Thank you for attending

- Ranjit K. Roy

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Thoughts for the day . .

One morning, having moved into a new

neighborhood, the family noticed that the

school bus didnt show up for their little

boy. The dad volunteered saying, I willdrive you, if you show me the way. On

their way the young student directed dad

to turn right, then a left, and a few more

lefts and rights. Seeing that the school

was within a few blocks from home, dadasked, Why did you make me drive so

long to get to the school this close to

home. The boy replied, But dad, thats

how the school bus goes everyday.

- Mort Crim, WWJ 950 Radio, Detroit, MI, 10/30/01

When you always do what you always did,

you will always get what you always got

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Nutek, Inc.3829 Quarton Road

Bloomfield Hills, MI 48302, USA.Tel: 1-248-5404827, E-mail: [email protected]

http://www.rkroy.com

Training & Workshop, Assistance with

application, Books and Software forDesign of Experiments Using

The Taguchi Approach

QT4
http://www.rkroy.com/http://www.rkroy.com/

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Nature of Nutek

Training Services

Seminar with hands-on application workshop

(Taguchi Approach)

[Our seminar, books, & software use consistentnotations and terminology. Class lecture focuses

on application, with most discussions on method

rather than the math.]

Length of training - This 4-day training

consists of two days of class room

seminar and two days of hands-on

computer workshop, during which the

attendees learn how to apply the

technique in their own projects.

Training objectives - Teach attendees

the application methodologies & prepare

them for immediate applications.

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