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Applied Design of Experiments and Taguchi Methods APPLIED DESIGN OF EXPERIMENTS AND TAGUCHI METHODS 10 8 y 6 1 4 0 B -1 -1 0 A 1 K. Krishnaiah P. Shahabudeen Applied Design of Experiments and Taguchi Methods Applied Design of Experiments and Taguchi Methods K. KRISHNAIAH Former Professor and Head Department of Industrial Engineering Anna University, Chennai P. SHAHABUDEEN Professor and Head Department of Industrial Engineering Anna University, Chennai New Delhi-110001 2012 ` 395.00 APPLIED DESIGN OF EXPERIMENTS AND TAGUCHI METHODS K. Krishnaiah and P. Shahabudeen © 2012 by PHI Learning Private Limited, New Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN-978-81-203-4527-0 The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus, New Delhi-110001 and Printed by Baba Barkha Nath Printers, Bahadurgarh, Haryana-124507. To My wife Kasthuri Bai and Students — K. Krishnaiah To My Teachers and Students — P. Shahabudeen Contents Preface ............................................................................................................................................... xiii PART I: DESIGN OF EXPERIMENTS 1. REVIEW OF STATISTICS ........................................................................................... 3–21 1.1 Introduction ..................................................................................................................... 3 1.2 Normal Distribution........................................................................................................ 3 1.2.1 Standard Normal Distribution .......................................................................... 4 1.3. Distribution of Sample Means ........................................................................................ 6 1.4 The t-Distribution ........................................................................................................... 7 1.5 The F-Distribution .......................................................................................................... 7 1.6 Confidence Intervals....................................................................................................... 7 1.6.1 Confidence Interval on a Single Mean (m) .................................................... 8 1.6.2 Confidence Interval for Difference in Two Means....................................... 8 1.7 Hypotheses Testing......................................................................................................... 9 1.7.1 Tests on a Single Mean ................................................................................. 11 1.7.2 Tests on Two Means ...................................................................................... 14 1.7.3 Dependent or Correlated Samples ................................................................. 18 Problems ................................................................................................................................. 20 2. FUNDAMENTALS OF EXPERIMENTAL DESIGN ............................................. 22–48 2.1 Introduction ................................................................................................................... 22 2.2 Experimentation ............................................................................................................ 22 2.2.1 Conventional Test Strategies ......................................................................... 22 2.2.2 Better Test Strategies...................................................................................... 24 2.2.3 Efficient Test Strategies ................................................................................. 24 2.3 Need for Statistically Designed Experiments ............................................................ 24 2.4 Analysis of Variance .................................................................................................... 25 2.5 Basic Principles of Design .......................................................................................... 26 2.5.1 Replication ....................................................................................................... 26 2.5.2 Randomization ................................................................................................. 26 2.5.3 Blocking ........................................................................................................... 27 vii viii Contents 2.6 Terminology Used in Design of Experiments .......................................................... 27 2.7 Steps in Experimentation............................................................................................. 28 2.7.1 Problem Statement .......................................................................................... 28 2.7.2 Selection of Factors, Levels and Ranges ..................................................... 28 2.7.3 Selection of Response Variable..................................................................... 29 2.7.4 Choice of Experimental Design .................................................................... 29 2.7.5 Conducting the Experiment ........................................................................... 30 2.7.6 Analysis of Data.............................................................................................. 30 2.7.7 Conclusions and Recommendations .............................................................. 30 2.8 Choice of Sample Size ................................................................................................ 31 2.8.1 Variable Data.................................................................................................... 31 2.8.2 Attribute Data ................................................................................................... 31 2.9 Normal Probability Plot............................................................................................... 31 2.9.1 Normal Probability Plotting ........................................................................... 31 2.9.2 Normal Probability Plot on an Ordinary Graph Paper ............................... 32 2.9.3 Half-normal Probability Plotting ................................................................... 33 2.10 Brainstorming................................................................................................................ 36 2.11 Cause and Effect Analysis .......................................................................................... 36 2.12 Linear Regression ......................................................................................................... 37 2.12.1 Simple Linear Regression Model .................................................................. 37 2.12.2 Multiple Linear Regression Model ............................................................... 41 Problems ................................................................................................................................. 47 3. SINGLE-FACTOR EXPERIMENTS ......................................................................... 49–84 3.1 Introduction ................................................................................................................... 49 3.2 Completely Randomized Design ................................................................................ 49 3.2.1 The Statistical Model...................................................................................... 49 3.2.2 Typical Data for Single-factor Experiment .................................................. 50 3.2.3 Analysis of Variance ...................................................................................... 51 3.2.4 Computation of Sum of Squares ................................................................... 52 3.2.5 Effect of Coding the Observations ............................................................... 54 3.2.6 Estimation of Model Parameters ................................................................... 55 3.2.7 Model Validation............................................................................................. 56 3.2.8 Analysis of Treatment Means ........................................................................ 60 3.2.9 Multiple Comparisons of Means Using Contrasts ...................................... 67 3.3 Randomized Complete Block Design ........................................................................ 70 3.3.1 Statistical Analysis of the Model .................................................................. 71 3.3.2 Estimating Missing Values in Randomized Block Design......................... 73 3.4 Balanced Incomplete Block Design (BIBD) ............................................................. 74 3.4.1 Statistical Analysis of the Model .................................................................. 75 3.5 Latin Square Design .................................................................................................... 77 3.5.1 The Statistical Model...................................................................................... 78 3.6 Graeco-Latin Square Design ....................................................................................... 80 3.6.1 The Statistical Model...................................................................................... 80 Problems ................................................................................................................................
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