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

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1 Complimentary Copy: DOE-I Basic Design of Experiments (The Taguchi Approach) Target Mean Target Quality Engineering Seminar and Software Bloomfield Hills, MI, USA.

2 Page 2 DOE-I Basic Design of Experiments Presented By 3829 Quarton Road Bloomfield Hills, Michigan 48302, USA. Phone and Fax: Web Site: N O T I C E 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:

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 He then worked for General Motors Corp. ( ) 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, 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.

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) Capabilities Qualitek-4 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: 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:

5 Page 5 Table of Contents Section Headings Page# Module-1: Overview and Approach Role of DOE in Product Quality Improvement What is The Taguchi Approach and who is Taguchi? New Philosophy and Attitude Toward Quality New Ways to Work Together for Project Applications New Definition for Quality of Performance New Way for Quantification of Improvement (The Loss Function) New Methods for Experiment Design and Analysis Seminar Objectives and Contents Key Points in the Taguchi Approach Review Questions Module-2: Experiments Using Standard Orthogonal Arrays Module-3: Interaction Studies Basic Concept in Design of Experiments (DOE) Experiment Designs with 2-Level Factors Full Factorial Experiment Design With Seven 2-Level Factors Sample Demonstration of Experiment Design and Analysis Example 1: Plastic Molding Process Study Steps for Experiment Planning (Brainstorming) Results with Multiple Criteria of Evaluation Experiment Designs with Larger Number of Factors Common Terms and their Definitions Accuracy of Orthogonal Array Experiments (An Empirical Verification) Learning Check List and Application Tasks Review Questions Practice Problems Understanding Interaction Effects Among Factors Identification of Columns of Localized Interaction Guidelines for Experiment Designs for Interaction Studies Steps in Interaction Analysis Prediction of Optimum Condition with Interaction Corrections Review Questions Practice Problems Module-4: Experiment Designs with Mixed Level Factors Modification of Standard Orthogonal Arrays Upgrading Three 2-Level Columns to 4-Level Column Downgrading Columns Incompatible Factor Levels Combination Design (Special Technique) Review Questions Practice Problems (Modules 5, 6 & 7 are part of DOE-II Seminar) Module-8: Application Steps Application and Analysis Check List Description of Application Phases 8-1 Considerations for Experiment Planning (Brainstorming) 8-2 Opportunities for the Overall Evaluation Criteria (OEC) 8-4 Attributes of Taguchi Approach and Classical DOE Review Questions & Practice Problems Reference Materials (Appendix): Arrays, TT, References, Application Guidelines, Case Study, Answers, Course Evaluation, etc. 11 A-1-23

6 Module-1 Page 6 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 Things you should learn from discussions in this module: Where DOE fits into quality improvement efforts. How is Taguchi approach relates 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? Before starting to learn the technique, it is important to have an understanding of what the technique is all about and how you can benefit your company products and processes from it. History of Quality Activities Acceptance Sampling s Economic Control of Quality of manufcd. products s Design of experiments (DOE) s Statistical quality control s Management by objectives s Zero Defects s Participative problem solving, SPC, and quality circle s Total quality control (TQM) Design of experiments (DOE) is among the many techniques used in the practice of quality improvement. Historically, individually, or as part of the package, several techniques have been popular in the industry. Today, use of most tools and techniques known are employed under one or many names.

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. 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 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.

8 Page What is The Taguchi Approach and Who is Taguchi? Who is Taguchi? Genichi Taguchi was born in Japan in Worked with Electronic Communication Laboratory (ECL) of Nippon Telephone and Telegraph Co.( ). Major contribution has been to standardize and simplify the use of the DESIGN OF EXPERIMENTS techniques. Published many books and th bj t Design of Experiments (DOE) using the Taguchi Approach is a standardized form of experimental design technique (referred as classical DOE) introduced by R. A. Fisher in England in the early 1920 s. As a researcher in Japanese Electronic Control Laboratory, in the late 1940 s, Dr. Genichi Taguchi devoted much of his quality improvement effort on simplifying and standardizing the application of the DOE technique. What is the Design of Experiment - It all began with R. A. Fisher in England back in 1920 s. - Fisher wanted to find out how much rain, sunshine, fertilizer, and water produce the best crop. Design Of Experiments (DOE): - statistical technique - studies effects of multiple variables simultaneously - determines the factor combination for optimum result Although Dr. Taguchi successfully applied the technique in many companies throughout the world, it was introduced to USA and other western countries only in the early 1980 s. Based on his extensive research, Dr. Taguchi proposed concepts to improve quality in all phases of design and manufacturing. Common areas of application of the technique are: - Optimize Designs using analytical simulation studies - Select better alternative in Development and Testing - Optimize manufacturing Process Designs - Determine the best Assembly Method - Solve manufacturing and production Problems By applying the Taguchi Parameter Design techniques, you could improve the performances of your product and process designs in the following ways: - Improve consistency of performance and save cost - Build insensitivity (Robustness) towards the uncontrollable factors

9 Page 9 Background of Genechi Taguchi - Dr. Taguchi started his work in the early 1940 s - Joined ECL to head the research department - His research focussed primarily on combining engineering and statistical methods to improve cost and quality - He is the Executive Director of American Supplier Institute in Dearborn, Michigan - His method was introduced here in the U.S.A in Most major manufacturing companies use it to improve quality Dr. Taguchi spends most of his time in Japan. He is still quite active and continues to publish considerable amount of literature each year. To make the DOE technique attractive to industrial practitioners and easy to apply, Dr. Taguchi introduced 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! IN: DO IT UP-FRONT: - Return on investment higher in design - The best way is to build quality into the design DO IT IN DESIGN. DESIGN QUALITY - Does not replace quality activities in production - Must not forget to do quality in design What's new in the Taguchi approach? - New Philosophy Timing for quality activity. Building quality into design Estimating the cost of lack of quality General definition of quality 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.

10 Page 10 Product Engineering Roadmap Realistic Expectation Leads to Satisfactory Results: Most applications happens to be in the manufacturing and problem solving Applications in design are slow but yield better returns No matter what the activities, DOE generally is effective 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 investment is much higher when quality issues are addressed further up-front in engineering. 1.4 New Ways to Work Together for Project Applications What s New? Discipline! - BRAINSTORMING: Plan experiments and follow through. - TEAM WORK: Work as a team and not alone. - CONSENSUS DECISIONS: Make decisions democratically as a team. Avoid expert based decisions. - COMPLETE ALL EXPERIMENTS planned before making any conclusions. - RUN CONFIRMATION EXPERIMENTS. Project Team and Planning Work as a team and Plan before experimenting This new ways of working can be understood well by comparing how past method of working has been as shown below. 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:

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 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.

12 Page New Definition for Quality of Performance What s New? Definition of Quality * CONSISTENCY OF PERFORMANCE: Quality may be viewed in terms of consistency of performance. To be consistent is to BE LIKE THE GOOD ONE S ALL THE TIME. * REDUCED VARIATION AROUND THE TARGET: Quality of performance can be measured in terms of variations around the target. Taguchi offered a general definition of quality in terms of consistency of performance: Perform consistently on the target. To be consistent is to be on the target most of the time. Consistency is achieved when variation of performance around the target is reduced. Reduced variation around 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) 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.

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. 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! MEASURING COST OF QUALITY: - Cost of quality extends far beyond rejection at the production - Lack of quality causes a loss to the society. LOSS FUNCTION : A formula to quantify the amount of loss based on deviation from the target performance. L = K ( y - y0 ) 2 Dollar Loss per part, which is the extra cost associated with production, can be computed using the Loss Function. All manufactured product will suffer some loss. Difference in losses, before and after improvement, produce saving.

14 Page New Methods for Experiment Design and Analysis What s New? Simpler and Standardized - APPLICATION STEPS: Steps for applications are clearly defined. - EXPERIMENT DESIGNS: Experiments are designed using special orthogonal arrays. - ANALYSIS OF RESULTS: Analysis and conclusions follow standard guidelines. Upon years of research, Taguchi offered a much simplified and standardized methods for experiment designs and analyses of results. Follow standard steps for experiment planning. Use of orthogonal arrays 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 Dr. Taguchi made considerable effort to simplify the methods of application of the technique and analysis of the results. However, some of the advanced concepts proposed by Dr. Taguchi require careful scrutiny. Things should be as simple as possible, but no simpler. - Albert Einstein Simple designs using standard orthogonal arrays that are applicable in over 60% of the situations are extremely simple. Experiment designs with mixed level require knowledge of the procedures for modification of the standard arrays Robust designs for systems with dynamic characteristics require good knowledge of the system.

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 - PARAMETER DESIGN: Taguchi approach generally refers to the parameter design phase of the three quality engineering activities (SYSTEM - DESIGN, PARAMETER DESIGN and TOLERANCE DESIGN) proposed by Taguchi. - Off-line Quality Control - Quality Loss Function - Signal To Noise Ratio(s/n) For Analysis - Reduced Variability As a Measure The parameter design and other product design improvement activities are also known as off-line quality control effort. Signal-to-noise ratio and Loss Function are also terms very specific to the Taguchi approach. The application follows standard set of steps. The experiment planning, the first step is the most valueadded activity. How Does DOE Technique Work? - An experimental strategy that determines the solution with minimum effort. - Determine the recipe for baking the best POUND CAKE with 5 ingredients, and with the option to take HIGH and LOW values of each. - Full factorial calls for 32 experiments. Taguchi approach requires only 8. The way it works: Hold formal experiment planning session to determine objectives and identify factors. Lay out experiments as per the prescribed technique. Carry out experiments Analyze results Confirm recommendations.

16 Page 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 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 fullfactorial) 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.

17 Page 17 There are a number of reasons why the Taguchi technique is popular with the industrial practitioners. Why Taguchi Approach? - Experimental efficiency - Easy application and data analysis - Higher probability of success - Option to confirm predicted improvement - Quantified improvement in terms of dollars - Improve customer satisfaction and profitability Easy to learn and apply. Generally a smaller number of experiments are required Effects of noise are treated. Improvement can be expressed in terms of dollars. Unique strategy for robust design and analysis of results. 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. Example Case Study (Production For higher effectiveness: 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 time.

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 Stamping / Hobbing Clutch plate made from Deburrin g Clutch plates are tumbled in a Rust Inhibito r Parts are submerge d in a chemical bath Cleaned and 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 Seminar Objectives and Contents Course Content and Learning Objectives DOE-I Course Topics 1. Overview of DOE by Taguchi Approach 2. Basic Concepts in Design of Experiments Simpler Experiment Designs Analysis of Results with Simple Calculations (Main Effect, Optimum Condition & Performance) Standardized Steps in Experiment Planning Experiment Designs with Common Orthogonal Arrays You will Learn How To: Plan Experiments Design Experiments Analyze Results Determine Improvement and/or solve Problems

19 Page 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/Taguchi Approach, Part I & Part DOE-II This session is dedicated for advanced concepts. Building robustness in products and processes with static and dynamic systems are covered here. DOE-I 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 and optimum condition 3. Interactions 4. Mixed level factors 1. Noise Factors, S/N, Analysis 2. Robust Designs, ANOVA 3. Loss Function 4. Problem solving 5. Dynamic Characteristics (DC)

20 Page 20 Seminar Handout Content Major Topics Module 1 Design of Experiment Basics Module 2 Experiment Designs with Standard Orthogonal Arrays Module 3 Interaction Studies Module 4 Mixed-Level Factor Designs Appendix Reference Materials Reference Materials Orthogonal Arrays F-Table Glossary of Terms Mathematical Relations Qualitek4 User Help Project Applications Example Report Review Question Solution Seminar Objectives What Will The Course Cover? How To Design Experiments Using Taguchi Approach. - Use Standard Orthogonal Array (OA) For Simple Design - 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? Learn to Quantify Improvements Expected from Improved 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.

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