Complimentary Copy:


DOE-I Basic Design of Experiments
              (The Taguchi Approach)




                         ...
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                                     DOE-I Basic Design of Experiments



                                      ...
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Course Overview
         Design of Experiment (DOE) is a powerful statistical technique for improving product/pro...
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                                                     SEMINAR SCHEDULE

                                    Design ...
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                                                         Table of Contents
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                                           Module-1
                       DOE Fundamental, Overview and Approach...
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  Where does DOE fit in the bigger
                                                                       Discip...
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1.2 What is The Taguchi Approach and Who is Taguchi?


  Who is Taguchi?
                                        ...
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   Background of Genechi Taguchi

         - Dr. Taguchi started his work in
                                  ...
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    Product Engineering Roadmap
                                                                       Dr. Taguc...
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  Typical Old Approach             (Series Process)                        •    Work alone with a few
         ...
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1.5 New Definition for Quality of Performance

                                                                 ...
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Strategy for improvement:


     Being on Target Most of the Time
                                              ...
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1.7 New Methods for Experiment Design and Analysis

                                                            ...
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There are a number terms that are used to describe the Taguchi modified design of experiment
technique. The ma...
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1.7 Example Application – Pound Cake Baking Process Study

DOE can conveniently study the effects of ingredients...
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There are a number of reasons why the Taguchi technique is popular with the industrial
practitioners.

     Why ...
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Example Case Study (Production Problem Solving)
I. Experiment Planning
Project Title - Clutch Plate Rust Inhibit...
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3. Experiment Designs to Study Interactions
                       • Understanding Interactions and
            ...
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                                                                     Reference Materials
   Seminar Handout Conte...
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                                   1.9 Key Points in the Taguchi Approach

                        •    Do it up...
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Review Questions (See solutions in Appendix)

1-1: What does Taguchi mean by QUALITY?

1-2: In the Taguchi appr...
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1-8. Based on the Taguchi definition of quality, which set of products would you prefer (a or b)


i)       a: ...
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                                       Module - 2
             Experiment Designs Using Standard Orthogonal Arra...
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                 To study influence of a factor, we must run experiments with two or more levels of the
        ...
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      Four Experiments are:             A1B1         A1B2            A2B1         A2B2

      Likewise three f...
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orthogonal array is an L-4 constructed to accommodate three two level factors.

   Full Factorial Experiments Bas...
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   Properties of Orthogonal Arrays
                                                                           ...
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   Orthogonal Arrays for Common Experiment
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Doe Taguchi Basic Manual1
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Doe Taguchi Basic Manual1

  1. 1. Complimentary Copy: DOE-I Basic Design of Experiments (The Taguchi Approach) Target        Mean           Target  Nutek, Inc. Quality Engineering Seminar and Software Bloomfield Hills, MI, USA. www.Nutek-us.com
  2. 2. Page 2 DOE-I Basic Design of Experiments Presented By Nutek, Inc. 3829 Quarton Road Bloomfield Hills, Michigan 48302, USA. Phone and Fax: 248-540-4827 Web Site: http://nutek-us.com , E-mail: Support@Nutek-US.com NOTICE All rights reserved. No part of this seminar handout may be reproduced or transmitted in any form or by any means, electronically or mechanically including photocopying or by any information storage and retrieval system, without permission in writing from NUTEK, INC. For additional copies or distribution agreement, contact: Nutek, Inc. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  3. 3. Page 3 Course Overview Design of Experiment (DOE) is a powerful statistical technique for improving product/process designs and solving production problems. A standardized version of the DOE, as forwarded by Dr. Genichi Taguchi, allows one to easily learn and apply the technique product design optimization and production problem investigation. Since its introduction in the U.S.A. in early 1980’s, the Taguchi approach of DOE has been the popular product and process improvement tool in the hands of the engineering and scientific professionals. This seminar will cover topics such as: Orthogonal arrays, Main effects, Interactions, Mixed levels, Experiment planning, etc. Participants in this seminar learn concepts with practice problems and hands-on exercise. The goal of the seminar discussion will be to prepare the attendees for immediate application of the experimental design principles to solving production problems and optimizing existing product and process designs. The afternoon of the third day of the class will be dedicated to demonstrating how Qualitek-4 software may be used to easily accomplish experiment design and analysis tasks. Outline • Overviews Standard Experiment Designs • Basic principles of DOE and orthogonal arrays experiments • Simple example showing experiment planning, design, and analysis of results • Experiment planning steps Interaction Studies • Understanding interactions • Scopes of interaction studies and its effect on experiment design • Designing experiment to study interaction & Effect of interaction on the conduct of experiment • Analyses for presence and significance of interaction • Corrective actions for significant interactions Mixed Level Factor Design • Upgrading & Downgrading column levels • Scopes of array modifications • Factor level compatibility requirements & Combination designs Design and Analysis Tasks using Software • Experiment designs • Analysis tasks Principal Instructor’s Background Ranjit K. Roy, Ph.D., P.E. (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. While at GM, he consulted on a large number of documented Taguchi case studies of significant cost savings. Dr. Roy established his own consulting company, Nutek, Inc. in 1987 and currently offers consulting, training, and application workshops in the use of design of experiments using the Taguchi approach. He 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 (January 2001) by John Wiley & Sons, New York. He is a fellow of the American Society for Quality and an adjunct professor at Oakland University, Rochester, Michigan. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  4. 4. Page 4 SEMINAR SCHEDULE Design of Experiments Using Taguchi Approach DOE- I Introduction The Taguchi Approach to Quality Engineering Concept of Loss Function Basic Experimental Designs Designs with Interactions Application Examples Basic Analysis Designs with Mixed Levels and Interactions Column Upgrading Column Degrading Combination Design DOE-II Robust Design Principles Noise Factors and Outer Array Designs S/N Ratio Analysis Learning ANOVA through Solved Problems Computation of Cost Benefits Using LOSS FUNCTION Manufacturer and Supplier Tolerances Brainstorming for Taguchi Case Studies Design and Analysis Using Computer Software Group Reviews Computer Software Qualitek-4 (Qualitek-4) Capabilities Dynamic Systems Class Project Applications Project Presentations General Reference Taguchi, Genichi: System of Experimental Design, UNIPUB Kraus Intl. Publications, White Plains, New York, 1987 Roy, Ranjit: Design of Experiments Using the Taguchi Approach: 16 Steps to Product and Process Improvement, John Wiley & Sons; ISBN: 0471361011 INTERNET: For general subject references (Taguchi + Seminar + Software + Consulting + Case Studies + Application Tips), try search engines like Yahoo, Lycos, Google, etc. For Nutek products, services, and application examples, visit: http://www.nutek-us.com http://www.rkry.com/wp-sem.html http://www.nutek-us.com/wp-sps.html http://www.nutek-us.com/wp-s4d.html http://www.nutek-us.com/wp-q4w.html Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  5. 5. Page 5 Table of Contents Page# Section Headings Module-1: Overview and Approach 1.1 1-1 Role of DOE in Product Quality Improvement 1.2 1-3 What is The Taguchi Approach and who is Taguchi? 1.3 New Philosophy and Attitude Toward Quality 1.4 New Ways to Work Together for Project Applications 1.4 1-5 New Definition for Quality of Performance 1.5 1-7 New Way for Quantification of Improvement (The Loss Function) 1.6 1-8 New Methods for Experiment Design and Analysis 1.7 1-9 Seminar Objectives and Contents 1.8 1-13 Key Points in the Taguchi Approach 1.9 1-16 Review Questions 1-17-18 Module-2: Experiments Using Standard Orthogonal Arrays Basic Concept in Design of Experiments (DOE) 2.1 2-1 Experiment Designs with 2-Level Factors 2.2 2-4 Full Factorial Experiment Design With Seven 2-Level Factors 2.3 2-9 Sample Demonstration of Experiment Design and Analysis 2.4 2-10 Example 1: Plastic Molding Process Study 2.5 2-17 Steps for Experiment Planning (Brainstorming) 2.6 2-17 Results with Multiple Criteria of Evaluation 2.7 2-24 Experiment Designs with Larger Number of Factors 2.8 2-29 Common Terms and their Definitions 2.9 2-30 Accuracy of Orthogonal Array Experiments (An Empirical Verification) 2.10 2-32 Learning Check List and Application Tasks 2.11 2-33 Review Questions 2-35 Practice Problems 2-42-50 Module-3: Interaction Studies Understanding Interaction Effects Among Factors 3.1 3-1 Identification of Columns of Localized Interaction 3.2 3-6 Guidelines for Experiment Designs for Interaction Studies 3.3 3-9 Steps in Interaction Analysis 3.4 3-10 Prediction of Optimum Condition with Interaction Corrections 3.5 3-16 Review Questions 3-18 Practice Problems 3-22-28 Module-4: Experiment Designs with Mixed Level Factors Modification of Standard Orthogonal Arrays 4.1 4-1 Upgrading Three 2-Level Columns to 4-Level Column 4.2 4-2 Downgrading Columns 4.3 4-6 Incompatible Factor Levels 4.4 4-10 Combination Design (Special Technique) 4.5 4-11 Review Questions 4-13 Practice Problems 4-19-22 (Modules 5, 6 & 7 are part of DOE-II Seminar) Module-8: Application Steps Description of Application Phases 8.1 8-1 Considerations for Experiment Planning (Brainstorming) 8.2 8-2 Opportunities for the Overall Evaluation Criteria (OEC) 8.3 8-4 Attributes of Taguchi Approach and Classical DOE 8.4 8-6 Application and Analysis Check List 8.5 8-7 Review Questions & Practice Problems 8-8-8- 11 A-1-23 Reference Materials (Appendix): Arrays, TT, References, Application Guidelines, Case Study, Answers, Course Evaluation, etc. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  6. 6. Page 6 Module-1 DOE Fundamental, Overview and Approach There are a number of statistical techniques available for engineering and scientific studies. Taguchi has prescribed a standardized way to utilize the Design of Experiments (DOE) technique to enhance the quality of products and processes. In this regard it is important to understand his definition of quality, the method by which quality can be measured, and the necessary discipline for most application benefits. This module presents an overview of Taguchi’s quality improvement methodologies. Things you should learn from discussions in this module: • What is DOE and why is the name Taguchi associated with it? • What’s new in the Taguchi version of DOE? • Why should you learn it and how you and your company may benefit from it? • What will this course cover? 1.1 Role of DOE in Product Quality Improvement Overview Slide Contents Before starting to learn the Things you should learn from technique, it is important to have an discussions in this module: understanding of what the technique • Where DOE fits into quality is all about and how you can benefit improvement efforts. your company products and • How is Taguchi approach relates processes from it. to DOE • What did Dr. Genechi Taguchi introduce that is new? • How is quality defined by Taguchi and what is the approach to achieve performance improvement? Nutek, Inc. Design of experiments (DOE) is History of Quality Activities among the many techniques used in • Acceptance Sampling - 1910s the practice of quality improvement. • Economic Control of Quality of manufcd. products - Historically, individually, or as part of 1920s • Design of experiments (DOE) - the package, several techniques 1930s have been popular in the industry. • Statistical quality control - 1940s • Management by objectives - Today, use of most tools and 1950s techniques known are employed • Zero Defects - 1960s under one or many names. • Participative problem solving, SPC, and quality circle - 1970s Nutek, Inc. • Total quality control (TQM) Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  7. 7. Page 7 Where does DOE fit in the bigger Disciplines like Six Sigma, TQM, ISO 9000, QS-9000 are common disciplines employed by businesses today. DOE, SPC, FME are special technical skills needed to accomplish the objectives of the any of the disciplines adopted by a company. Often, the quality disciplines employed (the umbrella) change over time, but the supporting techniques do not. Nutek, Inc. Source of Topic Titles The name Taguchi is associated with the DOE technique is because of the Japanese researcher Dr. Genechi Taguchi. In this module you will learn about the DOE technique and what Dr. Taguchi did to make more attractive for applications in the industry. Understand that for most common experiment design technique, the two terms DOE and Taguchi Nutek, Inc. Approach are synonymous. In other words, as you will find out during the course of this seminar, there is not much difference in experiment design and analysis technique for experiments that most commonly done. However, Taguchi has offered a few unique concepts that are utilized in advanced experimental studies. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  8. 8. Page 8 1.2 What is The Taguchi Approach and Who is Taguchi? Who is Taguchi? Design of Experiments (DOE) using • Genichi Taguchi was born in the Taguchi Approach is a Japan in 1924. standardized form of experimental • Worked with Electronic design technique (referred as Communication Laboratory classical DOE) introduced by R. A. (ECL) of Nippon Telephone and Fisher in England in the early Telegraph Co.(1949 - 61). 1920’s. As a researcher in • Major contribution has been Japanese Electronic Control to standardize and simplify Laboratory, in the late 1940’s, Dr. the use of the DESIGN OF Genichi Taguchi devoted much of EXPERIMENTS techniques. his quality improvement effort on • Published many books and simplifying and standardizing the th bj t Nutek, Inc. application of the DOE technique. What is the Design of Experiment Although Dr. Taguchi successfully - It all began with R. A. Fisher in applied the technique in many England back in 1920’s. companies throughout the world, it - Fisher wanted to find out how was introduced to USA and other much rain, sunshine, fertilizer, and western countries only in the early water produce the best crop. 1980’s. Design Of Experiments (DOE): - statistical technique Based on his extensive research, - studies effects of multiple Dr. Taguchi proposed concepts to variables simultaneously improve quality in all phases of - determines the factor design and manufacturing. combination for optimum result Nutek, Inc. By applying the Taguchi Parameter Design techniques, you could Common areas of application of the technique are: improve the performances of your - Optimize Designs using analytical product and process designs in the simulation studies following ways: - Select better alternative in Development - Improve consistency of and Testing performance and save cost - Optimize manufacturing Process - Build insensitivity Designs (Robustness) towards the - Determine the best Assembly Method uncontrollable factors - Solve manufacturing and production Problems Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  9. 9. Page 9 Background of Genechi Taguchi - Dr. Taguchi started his work in Dr. Taguchi spends most of his the early 1940’s - Joined ECL to head the research time in Japan. He is still quite department active and continues to publish - His research focussed primarily considerable amount of on combining engineering and statistical methods to improve cost literature each year. and quality - He is the Executive Director of American Supplier Institute in To make the DOE technique Dearborn, Michigan attractive to industrial - His method was introduced here practitioners and easy to in the U.S.A in 1980 - Most major manufacturing apply, Dr. Taguchi introduced Nutek, companies use it to improve Inc. quality a few new ideas. Some of these philosophies attracted attention from the quality minded manufacturing organization world wide during the later part of the twentieth century. 1.3 New Philosophy and Attitude Toward Quality Traditionally, quality activities took place only at the production end. Dr. Genichi Taguchi proposed that a better way to assure quality is to build it in the product by designing quality into the product. In general, he emphasized that the return on investment is much more when quality was addressed in engineering stages before production. There are a number of techniques available for use improving quality in different phases of engineering activities. What’s New? Philosophy ! What's new in the Taguchi DO IT UP-FRONT: - Return on investment higher approach? in design - New Philosophy - The best way is to build • Timing quality into the design for quality DO IT IN DESIGN. DESIGN QUALITY activity. Building IN: quality into design - Does not replace quality • Estimating the cost of activities in production - Must not forget to do lack of quality quality in design • General definition of quality Nutek, Inc. Not too long ago, before Dr. Taguchi introduced his quality philosophy to the world, quality activities for a manufacturing plant mainly involved activities like inspection and rework on the production floor. There was hardly any awareness or effort in of quality improvement in activities other than production. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  10. 10. Page 10 Product Engineering Roadmap Dr. Taguchi pointed out that • For long term effect of quality, it must be designed into the products. • All activities of a manufacturing organization have roles to play in building quality into the products. • Return on Nutek, Inc. investment is much Realistic Expectation Leads to Satisfactory higher when quality Results: issues are • Most applications happens to be in the addressed further manufacturing and problem solving up-front in • Applications in design are slow but yield engineering. better returns • No matter what the activities, DOE generally is effective 1.4 New Ways to Work Together for Project Applications Project Team and Planning – Work What’s New? Discipline! as a team and Plan before experimenting - BRAINSTORMING: Plan experiments and follow through. This new ways of working can be - TEAM WORK: Work as a team and understood well by comparing how not alone. - CONSENSUS DECISIONS: Make past method of working has been decisions democratically as a team. as shown below. Avoid expert based decisions. - COMPLETE ALL EXPERIMENTS planned before making any conclusions. - RUN CONFIRMATION EXPERIMENTS. Nutek, Inc. The Taguchi method is most effective when experiments are planned as a team and all decisions are made by consensus. The Taguchi approach demands a new way of working together as a group while attempting to apply the technique in the industrial applications. The major difference can be understood by comparing the new method with the old approach. Traditional (old approach) has the following characteristics: Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  11. 11. Page 11 Typical Old Approach (Series Process) • Work alone with a few people • Wait for problems to occur • Follow experienced based and intuitive fixes • Limited investigation and experiments Nutek, Inc. For best results, the recommended practice is to follow the new disciplines of working together and follow the rigid structure (Five steps, 5P’s) to plan experiment and analyze the results. New Discipline o Work as a team and decide things together by consensus o Be proactive and objectively plan experiments Five-Phase Application Process • Experiment planning is the necessary first step (with many people/team and use consensus decisions) • Design smallest experiments with key factors • Run experiments in random order • Predict and verify expected results before implementation. Nutek, Inc. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  12. 12. Page 12 1.5 New Definition for Quality of Performance Taguchi offered a general definition What’s New? Definition of Quality of quality in terms of consistency of performance: * CONSISTENCY OF PERFORMANCE: • Quality may be viewed in terms of Perform consistently on the consistency of performance. To be target. consistent is to BE LIKE THE GOOD ONE’S • To be consistent is to be on ALL THE TIME. the target most of the time. * REDUCED VARIATION AROUND THE TARGET: • Consistency is achieved Quality of performance can be measured when variation of in terms of variations around the performance around the target. target is reduced. • Reduced variation around Nutek, Inc. the target is a measure of how consistent the performance is. Goals of quality, defined as consistency of performance, can be improved by: Looks of Improvement • Reducing the distance of the population mean to the target and/or • Minimizing the variation around the target (Standard deviation is a measure of variation) Nutek, Inc. The method for achieving performance on the target and reduce variation around the target (or mean when target is absent), is to apply the DOE technique. The Taguchi version of the DOE makes it easy to learn the technique and incorporate the effects of causes of variability (noise factors) for building robust products. When products are made robust, the variability in performance is reduced. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  13. 13. Page 13 Strategy for improvement: Being on Target Most of the Time • The strategy for improvement (variation first or mean first) depends on the current status of performance. • No matter the path followed, the ultimate goal is to be on the target with least variation. Nutek, Inc. 1.6 New Way for Quantification of Improvement (The Loss Function) Taguchi also offered a special mathematical relationship between performance and expected harm (Loss) it can potentially cause to the society. While Taguchi’s Loss Function presents a powerful incentive for manufacturers to improve quality of their products, we will primarily use it to quantify the improvement achieved after conducting the experimental study. What’s New? Loss Function! • Dollar Loss per part, which is the extra cost associated MEASURING COST OF QUALITY: - Cost of quality extends far beyond with production, can be rejection at the production computed using the Loss - Lack of quality causes a loss to the Function. society. • All manufactured product LOSS FUNCTION : A formula to quantify will suffer some loss. the amount of loss based on deviation • Difference in losses, before from the target performance. and after improvement, L = K ( y - y0 ) 2 produce saving. Nutek, Inc. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  14. 14. Page 14 1.7 New Methods for Experiment Design and Analysis Upon years of What’s New? Simpler and Standardized research, Taguchi offered a much - APPLICATION STEPS: Steps for simplified and applications are clearly defined. standardized methods for experiment designs - EXPERIMENT DESIGNS: Experiments and analyses of are designed using special orthogonal arrays. results. - ANALYSIS OF RESULTS: Analysis and conclusions follow standard • guidelines. Follow standard steps for experiment planning. • Use of orthogonal arrays Nutek, Inc. created by Taguchi makes experiment designs a routine task. • A few basic steps using simple arithmetic calculations can produce most useful information. Simpler and Standardized DOE • Simple designs using standard orthogonal arrays Dr. Taguchi made considerable effort that are applicable in over to simplify the methods of application 60% of the situations are of the technique and analysis of the results. However, some of the advanced extremely simple. concepts proposed by Dr. Taguchi • Experiment designs with require careful scrutiny. mixed level require knowledge of the “Things should be as simple as procedures for modification possible, but no simpler.” of the standard arrays - Albert Einstein • Robust designs for systems with dynamic Nutek, Inc. characteristics require good knowledge of the system. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  15. 15. Page 15 There are a number terms that are used to describe the Taguchi modified design of experiment technique. The materials covered in this seminar are part of what he called Parameter Design. When you read books and other literature on the Taguchi methods, you will encounter some of the terms that are indicated here. DOE - the Taguchi Approach - Seminar • The parameter design and - PARAMETER DESIGN: Taguchi other product design approach generally refers to the improvement activities are parameter design phase of the also known as off-line three quality engineering quality control effort. activities (SYSTEM • - DESIGN, PARAMETER DESIGN and Signal-to-noise ratio and TOLERANCE DESIGN) proposed by Loss Function are also Taguchi. terms very specific to the - Off-line Quality Control Taguchi approach. - Quality Loss Function - Signal To Noise Ratio(s/n) For Analysis Nutek, - Inc. Reduced Variability As a Measure The application follows standard set of steps. The experiment planning, the first step is the most value- added activity. The way it works: How Does DOE Technique Work? • Hold formal experiment - An experimental strategy that planning session to determine determines the solution with objectives and identify factors. minimum effort. • Lay out experiments as per the - Determine the recipe for prescribed technique. baking the best POUND CAKE • with 5 ingredients, and with Carry out experiments the option to take HIGH and • Analyze results LOW values of each. • Confirm recommendations. - Full factorial calls for 32 experiments. Taguchi approach requires only 8. Nutek, Inc. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  16. 16. Page 16 1.7 Example Application – Pound Cake Baking Process Study DOE can conveniently study the effects of ingredients in a cake baking process and determine the optimum recipe with a smaller number of experiments. You should easily understand how the factors and levels are defined in this example. You should also have an appreciation about how few experiments among a larger number of possible conditions that are needed for the study. Experiment Factors and their Levels • Factors are synonymous to input, ingredient, variable, and parameter. • Levels are the values of the factors used to carry out the experiment (descriptive & alphanumeric) • Five factors at two levels each can produce 2 5 = 32 different cake recipes. • Only 8 experiments are Nutek, Inc. carried out in the Taguchi approach. In the Taguchi approach, only a small fraction of all possible factor-level combinations are tested in the study. Depending on the number of factors, the fraction of all possible experiments that are carried out (may be viewed as experimental efficiencies) will vary. The larger the number of factors, smaller is the number of fractional experiments. The efficiency with which the experiment designed using the Taguchi orthogonal arrays produce results is analogous to the way a Fish Finder (an instrument used by fishermen) helps track a school of fish. Orthogonal Array - a Fish Finder • The lake is like all possible combinations (called full- factorial) • The big fish in the lake is like the most desirable design condition. • The Fish Finder and the fishing net are like the Taguchi DOE technique. Nutek, Inc. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  17. 17. Page 17 There are a number of reasons why the Taguchi technique is popular with the industrial practitioners. Why Taguchi Approach? • Easy to learn and apply. - Experimental efficiency • Generally a smaller number - Easy application and data of experiments are required analysis • Effects of noise are treated. - Higher probability of success • Improvement can be - Option to confirm predicted improvement expressed in terms of - Quantified improvement in dollars. terms of dollars • Unique strategy for robust - Improve customer satisfaction design and analysis of and profitability results. Nutek, Inc. 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 was 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. For higher effectiveness: Example Case Study (Production • Define and understand problem. • Study process and determine sub-activity which may be the source of problem. • Apply DOE to this activity rather than the entire system. • Go for a quantum improvement instead of addressing all issues at one Nutek, Inc. time. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  18. 18. Page 18 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.) Figure 1. Clutch Plate Fabrication Process Rust Deburrin Stamping Inhibito g / r Hobbing Clutch Parts Clutch plates are plate are submerge made tumbled d in a chemical from in a Cleaned and bath dried parts are boxed for shipping. 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 column 1, 2, and 3. 1.8 Seminar Objectives and Contents Course Content and Learning Objectives You will Learn How To: DOE-I Course Topics Plan Experiments 1. Overview of DOE by Taguchi Approach Design Experiments 2. Basic Concepts in Design of Experiments Analyze Results • Simpler Experiment Designs Determine • Analysis of Results with Simple Improvement and/or Calculations (Main Effect, solve Problems Optimum Condition & Performance) • Standardized Steps in Experiment Planning • Experiment Designs with Common Nutek, Inc. Orthogonal Arrays Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  19. 19. Page 19 3. Experiment Designs to Study Interactions • Understanding Interactions and Scopes of Study • Procedures for Experiment Designs to Study Interactions • Analysis of Interactions and Modification of Optimum Condition • Practical Guidelines for Treatment of Interactions 4. Experiment Designs with Mixed-Level Factors • Upgrading Column Levels • Downgrading Column Levels • Combination Designs The quality engineering concepts offered by Dr. Taguchi is quite extensive and may require quite a few days to cover in the adult learning environment. For convenience in learning the application methodologies, the essential materials are covered in two parts. DOE-I DOE/Taguchi Approach, Part I & Part Covers basic concepts in design of experiments. It puts considerable emphasis on experiment planning and covers interaction studies and mixed level factor designs. 1. Experiment using Std. Orthogonal Arrays 2. Main effect studies Nutek, Inc. and optimum DOE-II condition This session is dedicated for advanced concepts. Building robustness 3. Interactions in products and processes with static and dynamic systems are 4. Mixed level factors covered here. 1. Noise Factors, S/N, Analysis 2. Robust Designs, ANOVA 3. Loss Function 4. Problem solving 5. Dynamic Characteristics (DC) Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  20. 20. Page 20 Reference Materials Seminar Handout Content Orthogonal Arrays Major Topics Module 1 Design of Experiment Basics F-Table Module 2 Experiment Designs with Standard Orthogonal Arrays Glossary of Terms Module 3 Interaction Studies Mathematical Relations Module 4 Mixed-Level Factor Designs Appendix Reference Materials Qualitek4 User Help Project Applications Nutek, Inc. Example Report Review Question Solution Seminar Objectives • How To Design Experiments Using Taguchi Approach. - Use Standard Orthogonal Array (OA) For Simple What Will The Design Course Cover? - Handle Interaction - Handle Mixed Levels - Includes Noise Factors/Outer Array (Robust Design) • Steps in Analysis of Main Effects and Determination of Optimum Condition. - Main effect studies - Interaction analysis - Analysis of Variance (ANOVA) - Signal to Noise ratio (S/N) - Dynamic Characteristics What Will You • Learn to Quantify Improvements Expected from Improved Learn? Designs in Terms of Dollars. Apply Taguchi's loss function to compute $ LOSS. • Learn to Brainstorm for Taguchi Experiments. Determine evaluation criteria, factors, levels, interactions, noise factors, etc. by group consensus. What This Seminar Will Not Do This seminar is not intended to teach Statistical Science or attempt to cover general philosophy of quality improvement. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  21. 21. Page 21 1.9 Key Points in the Taguchi Approach • Do it up front. Apply quality improvement tools as far up in the design as possible. • Measure quality in terms of variation around the target. Quantify ill effects of poor quality to the society. • Incorporate the new discipline of working together in project teams and determine all project related matters by the group consensus. • Use Taguchi's Off-line quality engineering concepts in three phases of engineering and production (Off-Line Quality Control) - System Design (basic research) - Parameter Design (common for industrial applications) - Tolerance Design (usually follows parameter design) Parameter Design is a special form of experimental design technique which was introduced by R. A. Fisher in England in the early 1920's. Parameter design as proposed by Dr. Genichi Taguchi is the subject of this seminar. New Paradigms Cost and Quality can be improved without incurring additional expense – Generally quality is achieved at higher cost. How about achieving higher quality or saving cost without additional expenses? DOE can help you prescribe such designs. Problems can be solved economically by simply adjusting the variables involved – Most problems do not have special causes. Problems that are variation related can be solved by finding a suitable combination (optimum) of the influencing factors. When performance is consistent and on target, problems are eliminated. There is monetary loss even when the products perform within the specification limits – Just-producing parts does not avoid warranty and rejects. The goal should be to be as near the target as possible. The loss associated with performance within the specification limits can be objectively estimated in quantitative terms using the loss function. Review Questions Every module ends with a set of 1-1: What does Taguchi mean by QUALITY? questions regarding materials covered in it. Here are a few 1-2: In the Taguchi approach how is samples questions form this QUALITY measured? module. 1-3: Which statistical terms do you affect when you improve quality and In addition to the Module Review how? Check all correct answers. Questions, there are a number of a. ( ) Move population MEAN closer to Practice Problems starting with the TARGET. Module 2 that are part of the b. ( ) Reduce STANDARD DEVIATION c. ( ) Reduce variation around the required group activities you will target complete in this session. Nutek, ( ) All of the above d Inc. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  22. 22. Page 22 Review Questions (See solutions in Appendix) 1-1: What does Taguchi mean by QUALITY? 1-2: In the Taguchi approach how is QUALITY measured? 1-3: Which statistical terms do you affect when you improve quality and how? Check all correct answers. a. ( ) Move population MEAN closer to the TARGET. b. ( ) Reduce STANDARD DEVIATION c. ( ) Reduce variation around the target d. ( ) All of the above 1-4: Looking from a project engineering point of view, compare the Taguchi method to conventional practices. Use `T' for Taguchi and `C' for Conventional in the following descriptions. a. ( ) Do it alone or with a smaller group b. ( ) Do it with a larger group and plan experiments together c. ( ) Decide what to do by judgment d. ( ) Evaluate results after completion of all experiments e. ( ) Evaluate experiments as you run and alter plans as you learn f. ( ) Determine best design by `hunt and pick' g. ( ) Follow a standard technique to analyze results 1-5: From your own experience, what type of business or activities benefit from Taguchi approach? Check all correct answers. Areas: Projects: ( ) Engineering design ( ) To optimize design ( ) Analysis/Simulation ( ) To optimize process parameters ( ) Manufacturing ( ) To solve production problems 1-6: The first step in application of Taguchi method is the planning session which is commonly known as BRAINSTORMING. The brainstorming for Taguchi method is different from the conventional brainstorming in several ways. Please check the desirable characteristics in the Taguchi method of brainstorming from the following lists. [ ] It requires the project leader to be open to group input and be willing to implement the consensus decisions. [ ] It works well when the group members work as a team. [ ] It is more productive when the session is carried out in an open and democratic environment. 1-7: To get the most by applying the Taguchi method, we need to make some major changes in the way we are used to doing things. Check all answers you agree with: [ ] Work with more people and as a team [ ] Complete all experiments as per plan [ ] Hold all judgments until all planned experiments are done [ ] Analyze results to determine the best design and check optimum performance by running confirmation tests. [ ] Make conclusions that are supported by data In your opinion, which among the above disciplines are most difficult to practice in? your work environment? Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  23. 23. Page 23 1-8. Based on the Taguchi definition of quality, which set of products would you prefer (a or b) i) a: 9 7 11 b: 10 9 8 Ans. ________ ii) Ans:______ a b Targe t a b iii) Ans:_____ Target 1-9: What are the two data characteristics for achieving consistency of performance? Ans: ______________________ ______________________________ Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  24. 24. Page 24 Module - 2 Experiment Designs Using Standard Orthogonal Arrays Modern Industrial environments pose experiments of numerous kinds. Some have few factors, some have many, while there are others that demand factors to have mixed levels. A vast majority of the experiments, however, fall in the category where all factors possess the same number of levels. In Taguchi approach a fixed number of orthogonal arrays are utilized to handle many common experimental situations. Factor and Level Characteristics Things you should learn from Topics Covered: discussions in this module: • What are Factors? [ A:Time, • Basic Experiment B:Temperature, etc.] Design Techniques. • What are Levels? [A1= 5 sec., • Experiments with A2= 10 sec. etc.] • How does continuous factors standard orthogonal differ from discrete ones? arrays. • What are the considerations • Standard analysis of for determining the number of experimental results. Levels of a Factor? • How does nonlinearity influence your decision about Nutek, Inc. the number of levels? 2.1 Basic Concept in Design of Experiments (DOE) DOE is an experimental strategy in which effects of multiple factors are studied simultaneously by running tests at various levels of the factors. What levels should we take, how to combine them, and how many experiments should we run, are subjects of discussions in DOE. Factors are variables (also think of as ingredients or parameters) that have direct influence on the performance of the product or process under investigation. Factors are of two types: Discrete - assumes known values or status for the level. Example: Container, Vendor, Type of materials, etc. Continuous - can assume any workable value for the factor levels. Example: Temperature, Pressure, Thickness, etc. Levels are the values or descriptions that define the condition of the factor held while performing the experiments. Examples: Type of Container, Supplier, Material, etc. for discrete factor 200 Deg., 15 Seconds, etc. when the factors are of continuous type. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  25. 25. Page 25 To study influence of a factor, we must run experiments with two or more levels of the factors. Two is minimum number of levels required to make comparison of the performance and thereby determine the influence. Why not test at more levels? When should you consider testing at more than two levels? Results of tests with two levels produce only two data points. Two data points when joined together represent influence that behave in a straight line, whether the actual behavior is linear or not. So what if the actual behavior is non-linear? We can only detect that in the results when there are more data points generated from tests with factor levels at more than two levels. Thus, if non-linear behavior is suspected, we should consider testing at more than two levels of the factor. While studying the influence of a factor, if we decide to test it at two levels, only two tests are required. Where as, if three levels are included, then three tests will have to be performed. EXAMPLE: Baking Processes at two, three, and four Temperature Settings. Nature of Influences of Factors at If a factor is tested at two levels, you are forced to assume that the influence of the factor on the result is linear. When three or four levels of a factor are tested, it can indicate whether the factor has non-linear response or not. Factor behavior, that is whether it is linear or non-linear, plays important role in deciding whether to study Nutek, Inc. three or four levels of the factor when Desirable levels of factors for study (Notes on Slide the factor is of continuous type. above): • Minimum TWO levels The number of levels of a factor is • THREE levels desirable limited to 2, 3, or 4 in our discussion. • FOUR levels in rare cases • Nonlinearity dictates levels for continuous factors only What about influences of other factors? What if we want to study a number of factors together? How many tests do we need to run? Consider two factors, A and B, at two levels each. They can be tested at four combinations. A1 A2 A => A1 A2 B1 * * B => B1 B2 B * * 2 Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  26. 26. Page 26 Four Experiments are: A1B1 A1B2 A2B1 A2B2 Likewise three factors A, B & C tested at 2-levels each Requires 8 experiments Factors: A: A1, A2 B: B1, B2 C: C1, C2 8 Experiments: A1B1C1 A1B1C2 A1B2C1 A1B2C2 A2B1C1 A2B1C2 A2B2C1 A2B2C2 Which can be written in notation form as shown below: (use 1 for level 1, etc.) Notation and table shown here is a Combination Possibilities – Full good way to express the full factorials conditions for a given set of factors included in the study ONE 2-level factor offer TWO test conditions (A1,A2). TWO 2-level factors create FOUR (22 = 4 test conditions: A1B1 A1B2 A2B1 and A2B2 ) . THREE 2-level factors create EIGHT (23 = 8) possibilities. Nutek, Inc. The total number of possible combinations (known as the full factorial) from a given number of factors all at 2-level can be calculated using the following formulas. Of course the full factorial experiments are always too many to do. What is the least number of experiments to get the most information? How do you select which ones to do? With above questions in mind, mainly for the industrial practitioners, Taguchi constructed a set of special orthogonal arrays. Orthogonal arrays are a set of tables of numbers designated as L- 4, L-8, L-9, L-32, etc. The smallest of the table, L-4, is used to design an experiment to study three 2-level factors The word quot;DESIGNquot; implies knowledge about the number of experiments to be performed and the manner in which they should be carried out, i.e., number and the factor level combinations. Taguchi has constructed a number of orthogonal arrays to accomplish the experiment design. Each array can be used to suit a number of experimental situations. The smallest among the Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  27. 27. Page 27 orthogonal array is an L-4 constructed to accommodate three two level factors. Full Factorial Experiments Based on The size of the full factorial 3 Factors at 2 level 23 = experiments becomes prohibitively 8 large as the number of factor 4 Factors at 2 level 24 = 16 increase. 7 Factors at 2 level 27 = 128 For most project studying more than 15 Factors at 2 level 215 = 32,768 four factors at two levels each becomes beyond what project time What are Partial Factorial and money allow. Experiments? What are Orthogonal arrays and how are they used? Nutek, Inc. 2.2 Experiment Designs with 2-Level Factors Consider that there are three factors A, B and C each at two levels. An experiment to study these factors will be accomplished by using an L-4 array as shown below. L-4 is the smallest of many arrays developed by Taguchi to design experiments of various sizes. Orthogonal Arrays– Experiment Design The L-4 orthogonal array is intended to be used to design experiments with two or 2-level factors. There are a number of arrays available to design experiments with factors at 2, 3, and 4-level. The notations of the arrays indicate the size of the table (rows & columns) and the nature of its columns. Nutek, Inc. (Notes in Slide above) How are Orthogonal arrays used to design experiments? What does the word “DESIGN” mean? What are the common properties of Orthogonal Arrays? Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  28. 28. Page 28 Properties of Orthogonal Arrays Array Descriptions: 1. Numbers in array represent the levels of the factors 2. Rows represents trial conditions 3. Columns indicate factors that can be accommodated 4. Columns of an OA are orthogonal 5. Each array can be used for many experimental Nutek, Inc. situations (Notes in Slide above) Taguchi’s Orthogonal array selects 4 out of the 8 Array Descriptions: possible combinations (Full 1. Numbers represent factor levels factorial combinations) 2. Rows represents trial conditions 3. Columns accommodate factors 3. Columns are balanced/orthogonal 4. Each array is used for many experiments To design experiments, Taguchi has offered a number of orthogonal arrays (OA): Key observations: First row has all 1's. There is no row that has all 2's. All columns are OA for 2-Level Factors balanced and maintain an order. The columns of the array are ORTHOGONAL OA for 3-Level Factors and or balanced. This means that there is equal number of levels in a column. The columns are OA for 4-Level Factors also balanced between any two. This means that the level combinations exist in equal numbers. 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) How does One-Factor-at-a-time experiment differ from the one designed using an Orthogonal array? Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617
  29. 29. Page 29 Orthogonal Arrays for Common Experiment Orthogonal arrays are used to design experiments and describe trial conditions. Experiments design using orthogonal arrays yield results that are more reproducible. Nutek, Inc. An experiment designed to study three 2-level factors requires an L-4 array which prescribes 4 trial conditions. The number of experiments for seven 2-level factors which require an L-8 array is eight. Orthogonal Arrays for Common Experiment Key idea in selecting the array for the design is to match the number of columns required in an array to accommodate all the factors. Notice how the complete notation of the array like L-8 (27) can help you decide which array to select for the design. For instance, when you need to study seven 2-level factors (decisions about number of factors Nutek, Inc. and their levels are decide in the planning session), you would look for an array for two level factors that has Y Ln ) (X enough number of columns. As you review the list of arrays (Appendix – Reference Materials), from the No. of notation (27) of L-8, it would be columns in the array. obvious that it will do the job. No. of No. of rows Similarly, when you need to design an levels in in the the array experiment with four 3-level factors, columns your choice will be an L-9, as shown below. Nutek, Inc. All Rights Reserved Basic Design of Experiments (Taguchi Approach) www.Nutek-us.com Version: 080617

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