QUALITY BY EXPERIMENTAL DESIGN Fourth Edition This page intentionally left blank QUALITY BY EXPERIMENTAL DESIGN Fourth Edition THOMAS B BARKER Professor Emeritus Rochester Institute of Technology, New York ANDREW MILIVOJEVICH Knowledge Management Group Mississauga, Ontario, Canada CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20151120 International Standard Book Number-13: 978-1-4822-4967-5 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To Mason E Wescott, a teacher of teachers “ the engine was a better engineer than the engineers It told us what kind of piston rings it liked! We just ran errands for it, bringing it a variety to choose from.” —Charles F Kettering (on the development of the diesel engine by empirical methods) Contents Foreword xvii Preface to the Fourth Edition xix Preface to the Third Edition xxiii Preface to the Second Edition xxv Preface to the First Edition xxix How to Use This Book xxxi Section I  The Philosophy of Experimentation Why Design Experiments? Uses of Experimental Design Efficiency First, Experiment .4 Second, Required Information Third, Resources .6 A General Example A Note on the Simulation Going-In Assumptions for Simulation Reasons for Designed Experiments .9 Structured Plan of Attack Meshes with Statistical Analysis Tools 10 Forces Experimenter to Organize 10 Efficiency 10 Appendix: Key Concepts from This Chapter 12 Some Uses of Experimental Design 12 Four Reasons for Experimental Design 12 Efficiency 12 Test 12 Experiment 12 Required Information 12 Resources 12 Organizing the Experiment 13 The Elements of a Good Experiment 13 Prior Knowledge 14 The Qualities of a Response 15 Goals and Objectives 16 Gathering Information 17 Organizational Psychology 18 The Brainstorming Process 19 Experimental Phases 21 Appendix: Key Concepts from This Chapter 23 vii viii Contents Example of Goals and Objectives 23 Guidelines for Brainstorming 25 Sample Report 27 The Neglected Response Variable 29 Quantitative 29 Precise 37 Meaningful 38 Appendix: Key Concepts from This Chapter 41 Section II  Statistical Experimental Design The Factorial Two-Level Design and General Factorial Designs 53 Orthogonality 55 Design Units 56 Yates Order 58 Using Minitab 59 Plotting Interactions .65 Cost 66 General Factorial Designs 67 Using Minitab 68 Appendix 74 Definitions 74 Formulas 74 Fractional Factorials at Two Levels 75 About Interactions 75 A Simple Example 77 Fractionalization Element 81 More Factors—Smaller Fractions 81 The Logical Approach (Information Analysis) 84 Information Analysis 84 Other Designs 87 Putting It All to Use 89 Using Minitab 93 Resolution 99 Final Thoughts 99 Appendix 103 Definitions 103 2k−p Defining Contrast Algorithm and Modulus Algebra Rules 103 Four and Eight Treatment Combination 105 Design Matrix Template 105 Sixteen Treatment Combination 110 Design Matrix Templates 110 Multilevel Designs 121 The Central Composite Design (CCD) 124 A Note on Choosing Levels 128 Contents ix Strategies of Using a CCD 129 Using Minitab to Build a CCD 132 Comments on the Minitab CCD 137 Building a Custom CCD in Minitab 138 Final Thoughts 143 Appendix 145 Some Functional Relationships and Their Polynomial Forms 145 CCD: Center Composite Design 145 Three-Level Designs 147 3k−p Designs 149 Generating a 3k−p Design 150 Information and Resources 152 3k−p Design Rules 153 Larger 3k−p Designs 154 A Comment on Three-Level Fractions 156 Appendix 158 3k−p Design Rules 158 Using Minitab 159 3k−p in Minitab 161 Blocking in Factorial Designs 163 Basis of Blocking 166 Choice of Primary Blocks 167 Appendix 172 Definitions 172 Blocking with Minitab 172 Blocked Fractional Factorials 175 Comments on Blocked Fractional Factorials 175 Randomized Block and Latin Square 179 Complete Randomized Block 179 Generalization of Results 180 Misconceptions in Using Blocked Designs 181 Latin Squares 182 The Misuse of the Latin Square 186 Appendix 189 Definitions 189 10 Nested Designs 191 A Nested Design 192 Coals to Kilowatts 193 Summary 194 Appendix 196 Definitions 196 11 Evolutionary Operation 197 The Prime Directive of Manufacturing 197 Evolutionary Operation 197 693 Statistical Tables and Graphs TABLE 27.7 Coefficients of Orthogonal Polynomials n Polynomial X=1 Linear −1 Linear Quadratic −1 −2 1 Linear Quadratic Cubic −3 −1 −1 −1 −1 −3 1 Linear Quadratic Cubic Quartic −2 −1 −1 −1 −4 −2 −1 −2 −4 2 1 Linear Quadratic Cubic Quartic −5 −5 −3 −1 −3 −1 −4 −4 −4 −1 −7 −3 5 Linear Quadratic Cubic Quartic −3 −1 −2 −7 −1 −3 1 −4 −3 −1 −1 −7 Linear Quadratic Cubic Quartic Quintic −7 −7 −7 −5 −13 23 −3 −3 −3 −17 −1 −5 −15 −5 −3 15 −3 −7 −3 17 −5 −13 −23 7 7 Linear Quadratic Cubic Quartic Quintic −4 28 −14 14 −4 −3 7 −21 11 −2 −8 13 −11 −4 −1 −17 9 −9 −20 18 −17 −9 9 −8 −13 −11 −7 −21 −11 28 14 14 10 Linear Quadratic Cubic Quartic Quintic −9 −42 18 −6 −7 14 −22 14 −5 −1 35 −17 −1 −3 −3 31 −11 −1 −4 12 18 −6 −4 −12 18 −3 −31 11 −1 −35 −17 −14 −22 −14 10 42 18 ΣZ2 λ 2 20 20 10/3 10 14 10 70 1 5/6 35/12 70 84 180 28 3/2 5/3 7/12 28 84 154 1 1/6 7/12 168 168 264 616 2184 2/3 7/12 7/10 60 2772 990 2002 468 5/6 7/12 3/20 330 132 8580 2860 780 1/2 5/3 5/12 1/10 694 Quality by Experimental Design TABLE 27.8 Percentile Points for Q-Test, for Equal Degrees of Freedom ν, and for p Samples ν=1 ν=2 ν=3 ν=4 p 0.99 0.999 0.99 0.999 0.99 0.999 0.99 0.999 10 12 14 15 16 18 20 22 24 26 28 30 32 36 40 45 50 60 64 * 0.920 0.828 0.744 0.671 0.609 0.576 0.528 0.448 0.391 0.365 0.343 0.304 0.273 0.246 0.224 0.206 0.190 0.176 0.163 0.143 0.127 0.111 0.098 0.080 0.074 * * * 0.949 0.865 0.793 0.750 0.694 0.598 0.522 0.490 0.460 0.409 0.367 0.332 0.302 0.276 0.254 0.234 0.218 0.189 0.167 0.145 0.127 0.102 0.094 0.863 0.720 0.608 0.539 0.469 0.412 0.371 0.333 0.276 0.234 0.217 0.202 0.178 0.158 0.142 0.129 0.118 0.108 0.100 0.093 0.082 0.072 0.063 0.056 0.045 0.042 * 0.898 0.773 0.690 0.606 0.537 0.481 0.433 0.358 0.303 0.280 0.261 0.228 0.202 0.180 0.162 0.148 0.135 0.124 0.115 0.100 0.088 0.076 0.067 0.053 0.049 0.757 0.605 0.512 0.430 0.372 0.325 0.287 0.257 0.211 0.178 0.165 0.154 0.135 0.120 0.108 0.098 0.090 0.082 0.075 0.070 0.062 0.055 0.048 0.043 0.035 0.033 0.919 0.754 0.644 0.546 0.471 0.411 0.363 0.324 0.265 0.222 0.205 0.190 0.165 0.146 0.130 0.117 0.107 0.098 0.090 0.083 0.072 0.064 0.055 0.049 0.039 0.037 0.684 0.549 0.443 0.369 0.318 0.276 0.244 0.218 0.179 0.151 0.140 0.130 0.114 0.101 0.090 0.082 0.075 0.069 0.064 0.060 0.052 0.047 0.041 0.037 0.030 0.028 0.828 0.675 0.552 0.461 0.394 0.342 0.300 0.267 0.217 0.181 0.167 0.155 0.135 0.119 0.106 0.096 0.087 0.080 0.074 0.068 0.060 0.053 0.046 0.041 0.033 0.031 ν=5 ν=6 ν=8 ν = 10 p 0.99 0.999 0.99 0.999 0.99 0.999 0.99 10 15 20 30 40 50 60 0.631 0.498 0.399 0.334 0.284 0.246 0.217 0.194 0.123 0.090 0.058 0.042 0.033 0.027 0.760 0.608 0.490 0.407 0.345 0.298 0.261 0.232 0.145 0.104 0.065 0.047 0.036 0.029 0.593 0.461 0.368 0.307 0.261 0.226 0.199 0.178 0.113 0.083 0.053 0.039 0.031 0.025 0.708 0.558 0.446 0.368 0.311 0.268 0.235 0.208 0.131 0.094 0.059 0.043 0.033 0.027 0.539 0.413 0.328 0.271 0.230 0.199 0.176 0.157 0.101 0.074 0.048 0.035 0.028 0.023 0.633 0.490 0.388 0.318 0.268 0.231 0.202 0.179 0.113 0.082 0.052 0.038 0.030 0.024 0.512 0.383 0.303 0.250 0.212 0.184 0.162 0.145 0.094 0.069 0.045 0.033 0.026 0.022 0.999 0.596 0.446 0.351 0.288 0.242 0.209 0.183 0.163 0.103 0.075 0.048 0.035 0.028 0.023 (Continued) 695 Statistical Tables and Graphs TABLE 27.8 (CONTINUED) Percentile Points for Q-Test, for Equal Degrees of Freedom ν, and for p Samples ν = 12 ν = 14 ν = 16 ν = 20 p 0.99 0.999 0.99 0.999 0.99 0.999 0.99 0.999 10 15 20 30 40 50 60 0.486 0.362 0.287 0.236 0.201 0.174 0.154 0.137 0.089 0.066 0.043 0.032 0.025 0.021 0.558 0.415 0.326 0.267 0.225 0.194 0.170 0.152 0.097 0.070 0.045 0.033 0.026 0.022 0.466 0.347 0.275 0.227 0.192 0.167 0.148 0.132 0.086 0.063 0.042 0.031 0.024 0.020 0.530 0.393 0.308 0.253 0.213 0.184 0.162 0.144 0.092 0.067 0.043 0.032 0.025 0.021 0.451 0.335 0.265 0.219 0.186 0.162 0.143 0.128 0.083 0.062 0.040 0.030 0.024 0.020 0.508 0.375 0.295 0.242 0.204 0.176 0.155 0.138 0.089 0.065 0.042 0.031 0.025 0.020 0.429 0.319 0.252 0.209 0.178 0.154 0.136 0.122 0.080 0.059 0.039 0.029 0.023 0.019 0.476 0.351 0.276 0.226 0.191 0.166 0.146 0.130 0.084 0.062 0.040 0.030 0.024 0.020 Source: Anderson and McLean, Design of Experiments: A Realistic Approach, Marcel Dekker, Inc., New York, 1974, Used with permission Note: For ν > 60, calculate pν(pq − 1) and compare with χ2 with (p − 1) degrees of freedom in Appendix *These entries exceeded one using the approximate distribution; because Q ≥ 1, they are omitted 696 Quality by Experimental Design TABLE 27.9 Coefficients {an–i+1} for the W Test for Normality for n = 2(1)50 n 10 0.7071 0.7071 0.0000 0.6872 0.1677 0.6646 0.2413 0.0000 0.6431 0.2806 0.0875 0.6233 0.3031 0.1401 0.0000 0.6052 0.3164 0.1743 0.0561 0.5888 0.3244 0.1976 0.0947 0.0000 0.5739 0.3291 0.2141 0.1224 0.0399 11 12 13 14 15 16 17 18 19 20 0.5601 0.3315 0.2260 0.5475 0.3325 0.2347 0.5359 0.3325 0.2412 0.5251 0.3318 0.2460 0.5150 0.3306 0.2495 0.5056 0.3290 0.2521 0.4968 0.3273 0.2540 0.4886 0.3253 0.2553 0.4808 0.3232 0.2561 0.4734 0.3211 0.2565 0.1429 0.0695 0.1586 0.0922 0.1707 0.1099 0.1802 0.1240 0.1878 0.1353 0.1939 0.1447 0.1988 0.1524 0.2027 0.1587 0.2059 0.1641 0.2085 0.1686 10 0.0000 0.0303 0.0539 0.0000 0.0727 0.0240 0.0880 0.0433 0.0000 0.1005 0.0593 0.0196 0.1109 0.0725 0.0359 0.0000 0.1197 0.0837 0.0496 0.0163 0.1271 0.0932 0.0612 0.0303 0.0000 0.1334 0.1013 0.0711 0.0422 0.0410 21 22 23 24 25 26 27 28 29 30 i n i n i 10 11 12 13 14 15 0.4643 0.4590 0.4542 0.4493 0.4450 0.4407 0.4366 0.4328 0.4291 0.4254 0.3185 0.3156 0.3126 0.3098 0.3069 0.3043 0.3018 0.2992 0.2968 0.2944 0.2578 0.2571 0.2563 0.2554 0.2543 0.2533 0.2522 0.2510 0.2499 0.2487 0.2119 0.2131 0.2139 0.2145 0.2148 0.2151 0.2152 0.2151 0.2150 0.2148 0.1736 0.1764 0.1787 0.1807 0.1822 0.1836 0.1848 0.1857 0.1864 0.1870 0.1399 0.1443 0.1480 0.1512 0.1539 0.1563 0.1584 0.1601 0.1616 0.1630 0.1092 0.1150 0.1201 0.1245 0.1283 0.1316 0.1346 0.1372 0.1395 0.1415 0.0804 0.0878 0.0941 0.0997 0.1046 0.1089 0.1128 0.1162 0.1192 0.1219 0.0530 0.0618 0.0696 0.0764 0.0823 0.0876 0.0923 0.0965 0.1002 0.1036 0.0263 0.0369 0.0459 0.0539 0.0610 0.0672 0.0728 0.7780 0.0822 0.0862 0.0000 0.0122 0.0228 0.0000 0.0321 0.0107 0.0403 0.0200 0.0000 0.0476 0.0287 0.0094 0.0540 0.0358 0.0178 0.0000 0.0598 0.0424 0.0253 0.0084 0.0650 0.0483 0.0320 0.0159 0.0000 0.0697 0.0537 0.0381 0.0227 0.0076 (Continued) 697 Statistical Tables and Graphs TABLE 27.9 (CONTINUED) Coefficients {an–i+1} for the W Test for Normality for n = 2(1)50 i n 10 11 12 13 14 15 16 17 18 19 20 i n 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 31 32 33 34 35 36 37 38 39 40 0.4220 0.2921 0.2475 0.2145 0.1874 0.1641 0.1433 0.1243 0.1066 0.0899 0.0739 0.0585 0.0435 0.0289 0.0144 0.0000 0.4188 0.2898 0.2463 0.2141 0.1878 0.1651 0.1449 0.1265 0.1093 0.0931 0.0777 0.0629 0.0485 0.0034 0.0206 0.0068 0.4156 0.2876 0.2451 0.2137 0.1880 0.1660 0.1463 0.1284 0.1118 0.0961 0.0812 0.0669 0.0530 0.0395 0.0262 0.0131 0.0000 0.4127 0.2854 0.2439 0.2132 0.1882 0.1667 0.1475 0.1301 0.1140 0.9880 0.0844 0.0706 0.0572 0.0441 0.0314 0.0187 0.0062 0.4096 0.2834 0.2427 0.2127 0.1883 0.1673 0.1487 0.1317 0.1160 0.1013 0.0873 0.0739 0.0610 0.0484 0.0361 0.0239 0.0119 0.0000 0.4068 0.2813 0.2415 0.2121 0.1883 0.1678 0.1496 0.1331 0.1179 0.1036 0.0900 0.0770 0.0645 0.0523 0.0404 0.0287 0.0172 0.0057 0.4040 0.2794 0.2403 0.2116 0.1883 0.1683 0.1505 0.1344 0.1196 0.1056 0.0924 0.0798 0.0677 0.0559 0.0444 0.0331 0.0220 0.0110 0.0000 0.4015 0.2774 0.2391 0.2110 0.1881 0.1686 0.1513 0.1356 0.1211 0.1075 0.0947 0.0824 0.0706 0.0592 0.0481 0.0372 0.0264 0.0158 0.0053 0.3989 0.2755 0.2380 0.2104 0.1880 0.1689 0.1520 0.1366 0.1225 0.1092 0.0967 0.0848 0.0733 0.0622 0.0515 0.0409 0.0305 0.0203 0.0101 0.0000 0.3964 0.2737 0.2368 0.2098 0.1878 0.1691 0.1526 0.1376 0.1237 0.1108 0.0986 0.0870 0.0759 0.0651 0.0546 0.0444 0.0343 0.0244 0.0146 0.0049 41 42 43 44 45 46 47 48 49 50 0.3940 0.2719 0.2357 0.2091 0.1876 0.1693 0.1531 0.1384 0.1249 0.1123 0.1004 0.0891 0.0782 0.0677 0.0575 0.0476 0.0379 0.0283 0.0188 0.0094 0.0000 0.3917 0.2701 0.2345 0.2085 0.1874 0.1694 0.1535 0.1392 0.1259 0.1136 0.1020 0.0909 0.0804 0.0701 0.0602 0.0506 0.0411 0.0318 0.0227 0.0136 0.0045 0.3894 0.2684 0.2334 0.2078 0.1871 0.1695 0.1539 0.1398 0.1269 0.1149 0.1035 0.0927 0.0824 0.0724 0.0628 0.0534 0.0442 0.0352 0.0263 0.0175 0.0087 0.0000 0.3872 0.2667 0.2323 0.2072 0.1868 0.1695 0.1542 0.1405 0.1278 0.1160 0.1049 0.0943 0.0842 0.0745 0.0651 0.0560 0.0471 0.0383 0.0296 0.0211 0.0126 0.0042 0.3850 0.2651 0.2313 0.2065 0.1865 0.1695 0.1545 0.1410 0.1286 0.1170 0.1062 0.0959 0.0860 0.0765 0.0673 0.0584 0.0497 0.0412 0.0328 0.0245 0.0163 0.0081 0.0000 0.3830 0.2635 0.2302 0.2058 0.1862 0.1695 0.1548 0.1415 0.1293 0.1180 0.1073 0.0972 0.0876 0.0783 0.0694 0.0607 0.0522 0.0439 0.0357 0.0277 0.0197 0.0118 0.0039 0.3808 0.2620 0.2291 0.2052 0.1859 0.1695 0.1550 0.1420 0.1300 0.1189 0.1085 0.0986 0.0892 0.0801 0.0713 0.0628 0.0546 0.0465 0.0385 0.0307 0.0229 0.0153 0.0076 0.0000 0.3789 0.2604 0.2281 0.2045 0.1855 0.1693 0.1551 0.1423 0.1306 0.1197 0.1095 0.0998 0.0906 0.0817 0.0731 0.0648 0.0568 0.0489 0.0411 0.0335 0.0259 0.0185 0.0111 0.0037 0.3770 0.2589 0.2271 0.2038 0.1851 0.1692 0.1553 0.1427 0.1312 0.1205 0.1105 0.1010 0.0919 0.0832 0.0748 0.0667 0.0588 0.0511 0.0436 0.0361 0.0288 0.0215 0.0143 0.0071 0.0000 0.3751 0.2574 0.2260 0.2032 0.1847 0.1691 0.1554 0.1430 0.1317 0.1212 0.1113 0.1020 0.0932 0.0846 0.0764 0.0685 0.0608 0.0532 0.0459 0.0386 0.0314 0.0244 0.0174 0.0104 0.0035 Source: Anderson and McLean, Design of Experiments: A Realistic Approach, Marcel Dekker, Inc., New York, 1974 Used with permission 698 Quality by Experimental Design TABLE 27.10 Percentage Points of the W Test for n = 3(1)50 Level n 0.01 0.02 0.05 0.10 0.50 0.90 0.95 0.98 0.99 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0.753 0.687 0.686 0.713 0.730 0.749 0.764 0.781 0.792 0.805 0.814 0.825 0.835 0.844 0.851 0.858 0.863 0.868 0.873 0.878 0.881 0.884 0.888 0.891 0.894 0.896 0.898 0.900 0.902 0.904 0.906 0.908 0.810 0.912 0.914 0.916 0.917 0.919 0.920 0.922 0.923 0.924 0.926 0.927 0.928 0.929 0.929 0.930 0.756 0.707 0.715 0.743 0.760 0.778 0.791 0.806 0.817 0.828 0.837 0.846 0.855 0.863 0.869 0.874 0.879 0.884 0.888 0.892 0.895 0.898 0.901 0.904 0.906 0.908 0.910 0.912 0.914 0.915 0.917 0.919 0.920 0.922 0.924 0.925 0.927 0.928 0.929 0.930 0.932 0.933 0.934 0.935 0.936 0.937 0.937 0.938 0.767 0.748 0.762 0.788 0.803 0.818 0.829 0.842 0.850 0.859 0.866 0.874 0.881 0.887 0.892 0.897 0.901 0.905 0.908 0.911 0.914 0.916 0.918 0.920 0.923 0.924 0.926 0.927 0.929 0.930 0.931 0.933 0.934 0.935 0.936 0.938 0.939 0.940 0.941 0.942 0.943 0.944 0.945 0.945 0.946 0.947 0.947 0.947 0.789 0.792 0.806 0.826 0.838 0.851 0.859 0.869 0.876 0.883 0.889 0.895 0.901 0.906 0.910 0.914 0.917 0.920 0.923 0.926 0.928 0.930 0.931 0.933 0.935 0.936 0.937 0.939 0.940 0.941 0.942 0.943 0.944 0.945 0.946 0.947 0.948 0.949 0.950 0.951 0.951 0.952 0.953 0.953 0.954 0.954 0.955 0.955 0.959 0.935 0.927 0.927 0.928 0.932 0.935 0.938 0.940 0.943 0.945 0.947 0.950 0.952 0.954 0.956 0.957 0.959 0.960 0.961 0.962 0.963 0.964 0.965 0.965 0.966 0.966 0.967 0.967 0.968 0.968 0.969 0.969 0.970 0.970 0.971 0.971 0.972 0.972 0.972 0.973 0.973 0.973 0.974 0.974 0.974 0.974 0.974 0.998 0.987 0.979 0.974 0.972 0.972 0.972 0.972 0.973 0.973 0.974 0.975 0.975 0.976 0.977 0.978 0.978 0.979 0.980 0.980 0.981 0.981 0.981 0.982 0.982 0.982 0.982 0.983 0.983 0.983 0.983 0.983 0.984 0.984 0.984 0.984 0.984 0.985 0.985 0.985 0.985 0.985 0.985 0.985 0.985 0.985 0.985 0.985 0.999 0.992 0.986 0.981 0.979 0.978 0.978 0.978 0.979 0.979 0.979 0.980 0.980 0.981 0.981 0.982 0.982 0.983 0.983 0.984 0.984 0.984 0.985 0.985 0.985 0.985 0.985 0.985 0.986 0.986 0.986 0.986 0.986 0.986 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.988 0.988 0.988 0.988 0.988 0.988 1.000 0.996 0.991 0.986 0.985 0.984 0.984 0.983 0.984 0.984 0.984 0.984 0.984 0.985 0.985 0.986 0.986 0.986 0.987 0.987 0.987 0.987 0.988 0.988 0.988 0.988 0.988 0.988 0.988 0.988 0.989 0.989 0.989 0.989 0.989 0.989 0.989 0.989 0.989 0.989 0.990 0.990 0.990 0.990 0.990 0.990 0.990 0.990 1.000 0.997 0.993 0.989 0.988 0.987 0.986 0.986 0.986 0.986 0.986 0.986 0.987 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.989 0.989 0.989 0.989 0.990 0.990 0.990 0.990 0.990 0.990 0.990 0.990 0.990 0.990 0.990 0.990 0.991 0.991 0.991 0.991 0.991 0.991 0.991 0.991 0.991 0.991 0.991 0.991 Source: Anderson and McLean, Design of Experiments: A Realistic Approach, Marcel Dekker, Inc., New York, 1974 Used with permission 699 Statistical Tables and Graphs TABLE 27.11 Generators for Two-Level Fractional Factorial Designs Number of Factors k Generator Components Fractionalization Elements p Number of Runs Single Effect Interaction C AB(12) D ABC(123) 5 16 E D E ABCD(1234) AB(12) AC(13) 6 32 16 F E D E F ABCDE(12345) ABC(123) AB(12) AC(13) BC(23) 7 64 32 16 G F G E ABCDEF(123456) ABCD(1234) ABDE(1245) ABC(123) F G D E F G BCD(234) ACD(134) AB(12) AC(13) BC(23) ABC(123) H G H F G H E F G H ABCDEFG(1234567) ABCD(1234) ABEF(1256) ABC(123) ABD(124) BCDE(2345) BCD(234) ACD(134) ABC(123) ABD(124) H J G H J F G ACDFG(13467) BCEFG(23567) ABCD(1234) ACEF(1356) CDEF(3456) BCDE(2345) ACDE(1345) 8 128 64 32 16 128 64 32 (Continued) 700 Quality by Experimental Design TABLE 27.11 (CONTINUED) Generators for Two-Level Fractional Factorial Designs Number of Factors k Fractionalization Elements p Number of Runs 16 10 128 10 64 10 16 11 64 11 32 Generator Components Single Effect Interaction H J E F G H J ABDE(1245) ABCE(1235) ABC(123) BCD(234) ACD(134) ABD(124) ABCD(1234) H J K G H J K E F G H J K ABCG(1237) BCDE(2345) ACDF(1346) BCDF(2346) ACDF(1346) ABDE(1245) ABCE(1235) ABC(123) BCD(234) ACD(134) ABD(124) ABCD(1234) AB(12) G H J K L F G H J K L CDE(345) ABCD(1234) ABF(126) BDEF(2456) ADEF(1456) ABC(123) BCD(234) CDE(345) ACD(134) ADE(145) BDE(245) Statistical Tables and Graphs GRAPH 27.1 Ternary plot 701 This page intentionally left blank References Chapter Nester, C E and T B Barker (1980) Customer Preference Model (CPM), Xerox Internal Report Rochester, NY Kling, J W and L A Riggs (1971) Experimental Psychology (3rd ed.) Rinehart & Winston, Inc., Holt, p 71 Ross, R T (1934) Optimum orders for the presentation of pairs in the method of paired com­ parisons Journal of Educational Psychology, 25, 375–382 Barker, T B (1993) QED Programs for MSBASIC Rochester Institute of Technology, Rochester, NY Chapter Taffel, A (1981) Physics, Its Methods and Meanings (4th ed.) Allyn & Bacon, New York Davies, O L., ed (1956) Design and Analysis of Industrial Experiments (2nd ed.) Hafner Publish­ ing Co., New York Chapter National Bureau of Standards (1957) Fractional Factorial Experiments Designs for Factors at Two Levels U.S Department of Commerce, Washington, DC Davies, O L (1956) Design and Analysis of Industrial Experiments (2nd ed.) Hafner Publish­ing Co., New York Box, G E P., W G Hunter, and J S Hunter (1978) Statistics for Experimenters Wiley, New York Barker, T B (1993) QED Programs for MSBASIC Rochester Institute of Technology, Rochester, NY Plackett, R L and J P Burman (1946) The design of optimum multifactorial experiments Biometrika, 33, 305–325 Draper, N R and D M Stoneman (1966) Alias relationships for two-level Plackett and Burman designs Technical Report No 96 Department of Statistics, The University of Wisconsin, Madison, WI Box, G E P (1959) Comments on the random balance design Technometrics, 1(2) Box, G E P and J S Hunter (1961) The 2k–p fractional factorial designs Technometrics, 3(311), 449 Chapter Box, G E P and K B Wilson (1951) On the experimental attainment of optimum conditions Journal of the Royal Statistical Society, Series B, 13, 1–45 703 704 References Box, G E P (1954) The exploration and exploitation of response surfaces: Some general con­ siderations and examples Biometrics, 10, 16–60 Box, G E P and J S Hunter (1957) Multi-factor experimental designs for exploring response surfaces The Annals of Mathematical Statistics, 28, 195–241 Chapter Box, G E P and K B Wilson (1951) On the experimental attainment of optimal conditions Journal of the Royal Statistical Society, Series B, 13, Chapter 11 Box, G E P and N R Draper (1969) Evolutionary Operation John Wiley & Sons, New York Chapter 13 Box, G E P (1954) Some theorems on quadratic forms applied in the study of analysis of variance problems: I Effect of inequality of variance in the one way classification Annals of Mathematical Statistics, 25(2), 290–302 Chapter 20 How to make it right the first time (1987, June 8) Business Week, 142–143 Raiffa, H and R Schlaifer (1961) Applied Statistical Decision Theory Harvard Business School Press, Boston Barker, T B (1990) Engineering Quality by Design: Interpreting the Taguchi Approach Marcel Dekker, New York Taguchi, G (1986) Introduction to Quality Engineering Asian Productivity Organization, Tokyo, p 144 Kackar, R N (1985) Off-line quality control, parameter design, and the taguchi method Journal of Quality Technology, 17(4) Fowlkes, W J and C Creveling (1995) Engineering Methods for Robust Product Design Addison Wesley, Reading, MA Shoemaker, A C., K.-L Tsui, and C F J Wu (1991) Economical experimentation methods for robust design Technometrics, 33(4), 415–427 References 705 Chapter 21 Box, G E P and M E Muller (1958) A note on the generation of random normal deviates The Annals of Mathematical Statistics, 29, 610 Barker, T B (1990) Engineering Quality by Design: Interpreting the Taguchi Approach Dekker, New York Taguchi, G (1986) Introduction to Quality Engineering Asian Productivity Organization, Tokyo D’Errico, J R and N A Zaino (1988) Statistical tolerancing using a modification of Taguchi’s methods Proceedings QED 87, Rochester Institute of Technology, Rochester, NY Chapter 22 Barker, T B (1990) Engineering Quality by Design: Interpreting the Taguchi Approach Marcel Dekker, New York Barker, T B (1993) QED Programs for MSBASIC Rochester Institute of Technology, Rochester, NY Chapter 23 Cornell, J A (1990) Experiments with Mixtures—Designs, Models, and the Analysis of Mixture Data John Wiley & Sons Inc, New York Chapter 24 Cornell, J A (1990) Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data John Wiley & Sons Inc, New York Scheffé, H (1958) Experiments with mixtures Journal of Royal Statistical Society Series B, 20, 344–360 Scheffe, H (1963) The simplex-centroid design for experiments with mixtures Journal of the Royal Series B (Methodological) Statistical Society, New York, 25(2), 235–263 Chapter 25 Lewis, A G., D Mathieu, and R Phan-Tan-Luu (1999) Pharmaceutical Experimental Design Marcel Dekker Inc., New York Scheffe, H (1963) The simplex-centroid design for experiments with mixtures Journal of the Royal Series B (Methodological) Statistical Society, 25(2), 235–263 706 References Cornell, J A (1990) Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data John Wiley & Sons Inc., New York Chapter 26 Snee, R D and D W Marquardt (1974) Extreme vertices for linear mixture models Technometrics, 16(3), 399–408 ...QUALITY BY EXPERIMENTAL DESIGN Fourth Edition This page intentionally left blank QUALITY BY EXPERIMENTAL DESIGN Fourth Edition THOMAS B BARKER Professor Emeritus Rochester... Quality by Experimental Design is the perfect companion It is well suited to any Six Sigma program or applied academic course in statistical experimental design It shows practitioners how to design. .. Composite Design 145 Three-Level Designs 147 3k−p Designs 149 Generating a 3k−p Design 150 Information and Resources 152 3k−p Design