Taguchi Methods Benefits, Impacts, Mathematics, Statistics, and Applications by Teruo Mori, PhD, PE translated by Shih-Chung Tsai, PhD, CQE © 2011, ASME, 3 Park Avenue, New York, NY 10016, USA (www.asme.org) Library of Congress Cataloging-in-Publication Data Mori, teruo, 1946- taguchi methods : benefits, impacts, mathematics, statistics, and applications/ by teruo Mori ; translated by Shih-Chung tsai. p. cm. 1. taguchi methods (quality control) 2. quality control–Mathematics. 3. logic. I. title. tS156.M64513 2011 658.5’62–dc22 2011015818 Contents Foreword xix Recommendations xxiii Preface xxix 1 Taguchi Methods for Challenges in Manufacturing 1 1.1 Competition Among Manufacturing Industries and business Administration Strategy 3 1.2 Example: Solving a downstream quality Problem Using a traditional Approach 12 1.3 robust design for downstream Noise Conditions 14 1.4 reduction of output response variation 14 1.5 from a traditional Problem-Solving Approach to a robust design Approach 21 1.6 Assessment of Energy transformation Efficiency 23 859658_FM.indd  Manila Typesetting Company 05/17/2011 11:16PM 1.7 traditional and taguchi-Class optimization Methods 34 1.8 Case Studies based on robust design Procedures 41 2 Mathematical Structural of Orthogonal Arrays 47 2.1 traditional Methods to Select optimal design Conditions 49 2.2 New optimization Method based on orthogonal Arrays 50 2.3 Confirmation of the optimal Condition 53 2.4 Introduction to orthogonal Arrays 56 3 Methods to Select and Compound Noise Factors 61 3.1 fire-Extinguishing Problem: Nagano olympics torch 63 3.2 output variation root Causes 64 3.3 Noise factor Selection 67 3.4 Noise factors and orthogonal Arrays (outer Arrays) 68 3.5 Assigning a Signal factor and Noise factors to an outer (orthogonal) Array 69 3.6 Compounding Noise factors for Preliminary Experiments 70 3.7 Noise factors for Accelerated tests (and overload tests) 71 859658_FM.indd i Manila Typesetting Company 05/17/2011 11:16PM 859658_FM.indd ii Manila Typesetting Company 05/17/2011 11:16PM 3.8 Noise factors for reliability tests 71 3.9 Surrogate Noise factors 73 3.10 Noise factors for Computer Simulations 76 3.11 dr. taguchi’s quality Engineering Strategies for Noise factors 78 4 Electric Motor Optimization Using Dynamic S/N (Signal-to-Noise) Ratios 81 4.1 Electric Motor basic function and Its Evaluation Characteristics 83 4.2 E lectric Motor optimization Using an l orthogonal Array 87 18 5 S/N (Signal-to-Noise) Ratios for Static Characteristics and the Robustness Optimization Procedure 127 5.1 Experimental design Checklist of robustness optimization for business Administrators and Management (Step 1) 130 5.2 Set-up targets for the design objective (Step 2) 130 5.3 generate as Many factors as Possible, Classify the factors, and develop a Cause-and-Effect diagram (Step 3) 131 5.4 Categorize the factors (Step 4) 133 5.5 Selection of orthogonal Arrays (Step 5) 135 859658_FM.indd i Manila Typesetting Company 05/17/2011 11:16PM 859658_FM.indd ii Manila Typesetting Company 05/17/2011 11:16PM 5.6 Number of factor levels and range of levels (Step 6) 137 5.7 Experimental factors and levels in an l (2137) orthogonal Array (Step 7) 141 18 5.8 Selection of Noise factors (Step 8) 143 5.9 Sequence of Experimental runs (Step 9) 145 5.10 Conduct Comparative Experiments (Step 10) 146 5.11 data transformation (Static type S/N ratios) for optimization of Experimental output (Step 11) 146 5.12 optimization Procedure for the Control factors (Step 12) 153 5.13 Confirmation of the Estimate from the Main-Effect Plots (Step 13) 158 5.14 Selection of optimal design Candidates (Step 14) 161 5.15 Adjustment of the gold-Plating thickness to 5 Micron (Step 15) 165 5.16 optimal Settings and Confirmation Experiment (Step 16) 166 5.17 Applying the optimal Settings to the Production Process (Step 17) 166 6 Standard Usage and Transformation of Taguchi-Class Orthogonal Arrays 169 6.1 Experimental optimization Methods 171 6.2 factor Effects and output responses 172 859658_FM.indd iii Manila Typesetting Company 05/17/2011 11:16PM 859658_FM.indd ix Manila Typesetting Company 05/17/2011 11:16PM 6.3 orthogonal Arrays for Product/Process development 173 6.4 Assessment of Interaction Effects 174 6.5 orthogonal Arrays and the Number of factor levels 178 6.6 Useful techniques to Assign Experimental factors to orthogonal Arrays 186 6.7 A Case Study based on the Assignment techniques from the Previous Sections Using an l Array (Improvement of resin film 18 tensile Strength Case Study Using five-level factors, dummy treatment, Infeasible runs, and Missing data) 190 7 Taguchi Methods (Robust Design) and Traditional Experimental Optimization Procedures 205 7.1 traditional Experimental optimization Procedures 209 7.2 Input-output relationship based on Input-output Energy transformation Approach 217 7.3 Improving the Effects of Individual factors 228 7.4 reproducibility of traditional Experimental optimization Methods 232 7.5 traditional Experimental optimization Methods versus taguchi Methods from the viewpoint of business Administrators 233 859658_FM.indd iii Manila Typesetting Company 05/17/2011 11:16PM 859658_FM.indd ix Manila Typesetting Company 05/17/2011 11:16PM 7.6 taguchi Methods in the United States 236 7.7 Summary: Comparisons between traditional Experimental optimization Methods and taguchi Methods 238 8 Historical Events and Milestone Case Studies of Taguchi Methods 241 8.1 biography of dr. genichi taguchi (from birth to Present) 243 8.2 Milestone taguchi Methods Case Studies 247 8.3 brief discussion of Commonly referenced taguchi Methods Case Studies 250 9 Taguchi-Class Experimental Design Methods and Applications 303 9.1 Case Studies based on the row-Assembly Method of taguchi-Class Experimental design (Using Idle Column and Columns of three- and four-level factors) 306 9.2 Case Study based on Modified taguchi-Class Experimental layouts 317 9.3 Categorization-and-grouping Analysis and the Associated long-term reliability Analysis 322 9.4 root Cause Identification for Product defects based on an orthogonal layout 333 859658_FM.indd x Manila Typesetting Company 05/17/2011 11:16PM 859658_FM.indd xi Manila Typesetting Company 05/17/2011 11:16PM 9.5 Multiple Sets of Experiments based on the Same orthogonal Array 335 9.6 treatment for Multiple randomly Associated orthogonal Arrays 337 10 Energy Transformation/Tranfer and Generic Function 351 10.1 transformation from first-level Energy Into Second-level Energy 353 10.2 types of Energy transformation Mechanisms 354 10.3 Energy transformation Mechanisms Case Studies 358 10.4 brake System Improvement Case Study 373 10.5 Energy transferring Mechanism 375 10.6 S/N (Signal-to-Noise) ratios for Energy transformation/transferring Mechanisms 380 10.7 q&A 382 11 Two-Step Design Optimization and Tolerance Design 385 11.1 two-Step design optimization 387 11.2 tolerance design Applications 401 11.3 Summary 409 11.4 tolerance Specification differences 410 859658_FM.indd x Manila Typesetting Company 05/17/2011 11:16PM 859658_FM.indd xi Manila Typesetting Company 05/17/2011 11:16PM 12 Logarithm Transformation of the Output Response Data for Optimization 413 12.1 functional Input-output relationship and Control factor levels 415 12.2 Ideal function of Input-output Energy transformation 416 12.3 A Metric of functional robustness for design optimization 420 12.4 functional relationship between Input Energy and output response 425 12.5 functional relationship of a System 428 12.6 Additivity of business Activities 430 13 Output Characteristics, Statistics, and Calculation Examples of Taguchi Methods 433 13.1 dynamic and Static Characteristics 435 13.2 Classification and Assessment of Static Characteristics 452 13.3 Analysis of Percentage data 468 13.4 Analysis of ranking or Categorical data 469 13.5 operating window Method 471 13.6 dynamic operating window Method (Chemical reaction Example) 472 13.7 Analysis of digital data (optimization based on two types of Error) 479 859658_FM.indd xii Manila Typesetting Company 05/17/2011 11:16PM 859658_FM.indd xiii Manila Typesetting Company 05/17/2011 11:16PM