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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. Introduction.

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Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

Optimization - The Finishing Touch in Product DesignSeventh Annual International Users ConferenceHosted by Ricardo Software, Southfield, Michigan, USA.March 8, 2002

by

Ranjit K. Roy

Nutek, Inc.

www.rkroy.com


Introduction

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. The statistical 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. This brief presentation offers an overview of how the Taguchi standardized form of DOE ca be applied to analytical performance models for identifying the best among the available design options.

- RKR 3/8/02

Taguchi Approach - Overview


Presentation contents

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

  • Taguchi Approach - Overview


    Our values rationale for optimization

    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 all possible 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.

    Taguchi Approach - Overview


    Product engineering roadmap opportunities for building quality

    Where do we do quality improvement?

    * Production

    * Test & Validation

    * Design & Development

    * Design & Analysis

    Product Engineering Roadmap (Opportunities for Building Quality)

    There are opportunities for improvement in all phases of product development.

    Taguchi Approach - Overview


    Maximizing return on investments

    Maximizing Return on Investments

    Where should we put our effort to optimize designs?

    Return on investment (ROI) is greater when efforts are made to optimize in design and analysis stages.

    ROI: 1 : 1 in production

    ROI: 1 : 10 in process design

    ROI: 1 : 100 in development

    ROI: 1 : 1000 in analyses

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    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.

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    What is the Design of Experiment (DOE) Technique?

    • 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):

      • Is a statistical technique used to study effects of multiple variables simultaneously.

      • It helps you determines the factor combination for optimum result.

    Taguchi Approach - Overview


    Looks measure of improvement

    Figure 1: Performance Before Experimental Study

    Figure 2: Performance After Study

    Improve Performance = Reduce and / or Reduce m

    m = (Yavg - Yo )

    Yavg. Yo

    new

    Looks & Measure of Improvement

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    Poor Quality

    Not so Bad

    Most Desirable

    Better

    Being on Target Most of the Time

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    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.

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    Factors Level-I Level-II

    A: Egg

    B: Butter

    C: Milk

    D: Flour

    E: Sugar

    Experiment Factors and their Levels

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

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    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

    Taguchi Approach - Overview


    Example case study production problem solving

    Example Case Study (Production Problem Solving)

    I. Experiment Planning

    Project Title - Adhesive Bonding of Car Window Bracket

    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.

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    Example Case Study# S2: (Casting Process Optimization)

    I. Experiment Planning

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

    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 & ResultReduce Scraps

    Quality Characteristics- Smaller is better (S)

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

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

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

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

    4Non-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.

    II. Experiment Design & Results

    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.

    Taguchi Approach - Overview


    Example case study production problem solving1

    Figure 1. Clutch Plate Fabrication Process

    Rust Inhibitor

    Parts are submerged in a chemical bath

    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

    Cleaned and dried parts are boxed for shipping.

    Example Case Study (Production Problem Solving)

    I. Experiment Planning

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

    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 Descriptions

    Rust inhibitor process parameters was the area of study.

    II. Experiment Design & Results

    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.

    Taguchi Approach - Overview


    Example case study s9 sporting event optimization

    Example Case Study # S9:( Sporting Event Optimization)

    I. Experiment Planning

    Project Title - Bow & Arrow Tuning Study

    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, & AxC

    II. Experiment Design & Results

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

    Taguchi Approach - Overview


    Example case study s10 race car optimization

    Example Case Study # S10:( Race Car Optimization)

    I. Experiment Planning

    Project Title - Race Car Suspension Parameter 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 beevaluated 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)

    II. Experiment Design & Results

    Up to 11 factors as shown above can be studied by designing an experiment using an L-12 array.

    Taguchi Approach - Overview


    Example doe popcorn machine example application not included in seminar handout

    [Example DOE]Popcorn Machine(Example application. Not included in seminar handout.)

    • 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.

    Taguchi Approach - Overview


    I experiment planning

    I. Experiment Planning

    • Title of Project - Pop Corn Machine performance Study

    • Objective & Result - Determine best machine settings

    • Quality Characteristics - Measure unpopped kernels (Smaller is better)

      Factors and Level Descriptions

      Notation Factor DescriptionLevel ILevel II

      A:Hot PlateStainless SteelCopper Alloy

      B:Type of OilCoconutPeanut

      C:Heat SettingSetting 1Setting 2

    Taguchi Approach - Overview


    Orthogonal arrays for common experiment designs

    Orthogonal Arrays for Common Experiment Designs

    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

    L4 (23) Array

    Cols>>

    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 4

    1 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 with four 3-level factors

    Taguchi Approach - Overview


    Ii experiment design results

    II. Experiment Design & Results

    # C A B Results (oz)*

    11115

    21228

    32127

    42214

    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

    Taguchi Approach - Overview


    Iii analysis of results

    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 =

    _

    C1 =

    _

    C2 =

    _

    A1 =

    _

    A2 =

    _

    B1 =

    _

    B1 =

    9

    Main Effects

    (Average effects of factor influence)

    8

    7

    6

    UNPOPPED KERNELS

    5

    4

    3

    A1 Hot plate A2 B1 OilB2 C1 Heat SettingC2

    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?

  • Taguchi Approach - Overview


    Iii analysis of results contd

    Yopt= + + +

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

    = 4.0

    _

    T

    __

    A1 +

    _

    ( A1 +

    _

    ( C2 +

    _

    ( B1 +

    _

    T )

    _

    T )

    _

    T )

    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.)

    • 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.

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    Analytical Simulations With Seven FactorsA 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*GHyperbolic: 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 Results

    1 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

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    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 2 391.190

    43 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 2 415.890

    73 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

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    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 <= Highest value

    89 2 1 2 2 1 1 1 383.220 90 2 1 2 2 1 1 2 394.650

    91 2 1 2 2 1 2 1 402.660* 92 2 1 2 2 1 2 2 414.090

    93 2 1 2 2 2 1 1 385.020 94 2 1 2 2 2 1 2 396.450

    95 2 1 2 2 2 2 1 404.460 96 2 1 2 2 2 2 2 415.890

    97 2 2 1 1 1 1 1 382.840 98 2 2 1 1 1 1 2 394.270

    99 2 2 1 1 1 2 1 402.280 100 2 2 1 1 1 2 2 413.710

    101 2 2 1 1 2 1 1 384.640 102 2 2 1 1 2 1 2 396.070

    103 2 2 1 1 2 2 1 404.080* 104 2 2 1 1 2 2 2 415.510

    105 2 2 1 2 1 1 1 382.760 106 2 2 1 2 1 1 2 394.190*

    107 2 2 1 2 1 2 1 402.200 108 2 2 1 2 1 2 2 413.630

    109 2 2 1 2 2 1 1 384.560 110 2 2 1 2 2 1 2 395.990

    111 2 2 1 2 2 2 1 404.000 112 2 2 1 2 2 2 2 415.430

    113 2 2 2 1 1 1 1 382.920 114 2 2 2 1 1 1 2 394.350

    115 2 2 2 1 1 2 1 402.360 116 2 2 2 1 1 2 2 413.790

    117 2 2 2 1 2 1 1 384.720 118 2 2 2 1 2 1 2 396.150

    119 2 2 2 1 2 2 1 404.160 120 2 2 2 1 2 2 2 415.590

    121 2 2 2 2 1 1 1 382.840 122 2 2 2 2 1 1 2 394.270

    123 2 2 2 2 1 2 1 402.280 124 2 2 2 2 1 2 2 413.710

    125 2 2 2 2 2 1 1 384.640 126 2 2 2 2 2 1 2 396.070

    127 2 2 2 2 2 2 1 404.080 128 2 2 2 2 2 2 2 415.510

    The Maximum Y is 415.97 at condition # 88 (88 2 1 2 1 2 2 2 415.970 ).

    Taguchi Approach - Overview


    Calculated results based on conditions defined by an l 8 array design

    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 2396.530 # 86

    6 2 1 2 2 1 2 1402.660 # 91

    7 2 2 1 1 2 2 1404.080 # 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

    <= 100% accurate

    Taguchi Approach - Overview


    Analytical simulation with nonlinear complex equation

    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 0.347  Highest value

    Taguchi Approach - Overview


    Calculated results based on conditions defined by an l 8 array design1

    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 20.256 # 86

    6 2 1 2 2 1 2 10.263 # 91

    7 2 2 1 1 2 2 10.259 # 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. <= Highly accurate.

    Taguchi Approach - Overview


    Conclusions and comments

    Conclusions and Comments

    • Most optimization studies tend to involves 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 application principles.

    • Automation in analysis is not a substitute for knowledge of science and physics.

    Thank you for attending- Ranjit K. Roy

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    Thoughts for the day . .

    One morning, having moved into a new neighborhood, the family noticed that the school bus didn't show up for their little boy. The dad volunteered saying, “I will drive 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, dad asked, “Why did you make me drive so long to get to the school this close to home”. The boy replied, “But dad, that’s 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”

    Taguchi Approach - Overview


    Optimization the finishing touch in product design seventh annual international users conference hosted by ricardo s

    QT4

    Nutek, Inc.3829 Quarton RoadBloomfield Hills, MI 48302, USA.Tel: 1-248-5404827, E-mail: [email protected]://www.rkroy.com

    Training & Workshop, Assistance with application, Books and Software for

    Design of Experiments Using

    The Taguchi Approach


    Nature of nutek training services

    Nature of Nutek Training Services

    • Seminar with hands-on application workshop (Taguchi Approach)

      [Our seminar, books, & software use consistent notations 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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