Modern engineering statistics by ryan

Modern Engineering Statistics THOMAS P RYAN Acworth, Georgia A JOHN WILEY & SONS, INC., PUBLICATION Modern Engineering Statistics Modern Engineering Statistics THOMAS P RYAN Acworth, Georgia A JOHN WILEY & SONS, INC., PUBLICATION Copyright C 2007 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008 or online at http://www.wiley.com/go/permission Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic formats For more information about Wiley products, visit our web site at www.wiley.com Wiley Bicentennial Logo: Richard J Pacifico Library of Congress Cataloging-in-Publication Data: Ryan, Thomas P., 1945– Modern engineering statistics / Thomas P Ryan p cm Includes bibliographical references and index ISBN 978-0-470-08187-7 Engineering–Statistical methods I Title TA340.R93 2007 620.0072–dc22 20060521558 Printed in the United States of America 10 Contents Preface xvii Methods of Collecting and Presenting Data 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 Observational Data and Data from Designed Experiments, Populations and Samples, Variables, Methods of Displaying Small Data Sets, 1.4.1 Stem-and-Leaf Display, 1.4.2 Time Sequence Plot and Control Chart, 1.4.3 Lag Plot, 11 1.4.4 Scatter Plot, 12 1.4.5 Digidot Plot, 14 1.4.6 Dotplot, 14 Methods of Displaying Large Data Sets, 16 1.5.1 Histogram, 16 1.5.2 Boxplot, 20 Outliers, 22 Other Methods, 22 Extremely Large Data Sets: Data Mining, 23 Graphical Methods: Recommendations, 23 Summary, 24 References, 24 Exercises, 25 Measures of Location and Dispersion 45 2.1 Estimating Location Parameters, 46 2.2 Estimating Dispersion Parameters, 50 2.3 Estimating Parameters from Grouped Data, 55 v vi contents 2.4 Estimates from a Boxplot, 57 2.5 Computing Sample Statistics with MINITAB, 58 2.6 Summary, 58 Reference, 58 Exercises, 58 Probability and Common Probability Distributions 3.1 Probability: From the Ethereal to the Concrete, 68 3.1.1 Manufacturing Applications, 70 3.2 Probability Concepts and Rules, 70 3.2.1 Extension to Multiple Events, 73 3.2.1.1 Law of Total Probability and Bayes’ Theorem, 74 3.3 Common Discrete Distributions, 76 3.3.1 Expected Value and Variance, 78 3.3.2 Binomial Distribution, 80 3.3.2.1 Testing for the Appropriateness of the Binomial Model, 86 3.3.3 Hypergeometric Distribution, 87 3.3.4 Poisson Distribution, 88 3.3.4.1 Testing for the Appropriateness of the Poisson Model, 90 3.3.5 Geometric Distribution, 91 3.4 Common Continuous Distributions, 92 3.4.1 Expected Value and Variance, 92 3.4.2 Determining Probabilities for Continuous Random Variables, 92 3.4.3 Normal Distribution, 93 3.4.3.1 Software-Aided Normal Probability Computations, 97 3.4.3.2 Testing the Normality Assumption, 97 3.4.4 t-Distribution, 97 3.4.5 Gamma Distribution, 100 3.4.5.1 Chi-Square Distribution, 100 3.4.5.2 Exponential Distribution, 101 3.4.6 Weibull Distribution, 102 3.4.7 Smallest Extreme Value Distribution, 103 3.4.8 Lognormal Distribution, 104 3.4.9 F Distribution, 104 3.5 General Distribution Fitting, 106 3.6 How to Select a Distribution, 107 3.7 Summary, 108 References, 109 Exercises, 109 68 contents Point Estimation vii 121 4.1 Point Estimators and Point Estimates, 121 4.2 Desirable Properties of Point Estimators, 121 4.2.1 Unbiasedness and Consistency, 121 4.2.2 Minimum Variance, 122 4.2.3 Estimators Whose Properties Depend on the Assumed Distribution, 124 4.2.4 Comparing Biased and Unbiased Estimators, 124 4.3 Distributions of Sampling Statistics, 125 4.3.1 Central Limit Theorem, 126 4.3.1.1 Illustration of Central Limit Theorem, 126 4.3.2 Statistics with Nonnormal Sampling Distributions, 128 4.4 Methods of Obtaining Estimators, 128 4.4.1 Method of Maximum Likelihood, 128 4.4.2 Method of Moments, 130 4.4.3 Method of Least Squares, 131 4.5 Estimating σθˆ , 132 4.6 Estimating Parameters Without Data, 133 4.7 Summary, 133 References, 134 Exercises, 134 Confidence Intervals and Hypothesis Tests—One Sample 5.1 Confidence Interval for µ: Normal Distribution, σ Not Estimated from Sample Data, 140 5.1.1 Sample Size Determination, 142 5.1.2 Interpretation and Use, 143 5.1.3 General Form of Confidence Intervals, 145 5.2 Confidence Interval for µ: Normal Distribution, σ Estimated from Sample Data, 146 5.2.1 Sample Size Determination, 146 5.3 Hypothesis Tests for µ: Using Z and t, 147 5.3.1 Null Hypotheses Always False?, 147 5.3.2 Basic Hypothesis Testing Concepts, 148 5.3.3 Two-Sided Hypothesis Tests Vis-`a-Vis Confidence Intervals, 152 5.3.4 One-Sided Hypothesis Tests Vis-`a-Vis One-Sided Confidence Intervals, 153 5.3.5 Relationships When the t-Distribution is Used, 155 5.3.6 When to Use t or Z (or Neither)?, 155 5.3.7 Additional Example, 156 5.4 Confidence Intervals and Hypothesis Tests for a Proportion, 157 5.4.1 Approximate Versus Exact Confidence Interval for a Proportion, 158 140 572 c4 0.7979 0.8862 0.9213 0.9400 0.9515 0.9594 0.9650 0.9693 0.9727 0.9823 0.9869 0.9896 n 10 15 20 25 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078 3.472 3.735 3.931 d2 For Estimating Sigma 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.223 0.180 0.153 A2 2.659 1.954 1.628 1.427 1.287 1.182 1.099 1.032 0.975 0.789 0.680 0.606 A3 For X Chart TABLE F Control Chart Constants 2.121 1.732 1.500 1.342 1.225 1.134 1.061 1.000 0.949 0.775 0.671 0.600 A For X Chart (Standard Given) 0 0 0.076 0.136 0.184 0.223 0.348 0.414 0.459 D3 3.267 2.575 2.282 2.115 2.004 1.924 1.864 1.816 1.777 1.652 1.586 1.541 D4 For R Chart 0 0 0.205 0.387 0.546 0.687 1.207 1.548 1.804 D1 3.686 4.358 4.698 4.918 5.078 5.203 5.307 5.394 5.469 5.737 5.922 6.058 D2 For R Chart (Standard Given) 0 0 0.030 0.118 0.185 0.239 0.284 0.428 0.510 0.565 B3 3.267 2.568 2.266 2.089 1.970 1.882 1.815 1.761 1.716 1.572 1.490 1.435 B4 0 0 0.029 0.113 0.179 0.232 0.276 0.421 0.504 0.559 B5 For s chart (Standard Given) 2.606 2.276 2.088 1.964 1.874 1.806 1.751 1.707 1.669 1.544 1.470 1.420 B6 Author Index Abate, M L., 382, 384, 390 Ackerman, H., 221 Affie, E., 267 Agresti, A., 158, 159, 489, 521 Albin, S L., 450 Allen, T T., Aloko, D F., 439 Amster, S J., 464 Anand, K N., 386 Anderson-Cook, C., 428 Anscombe, F J., 237 Anthony, J., 423 Apley, D W., 365 Arrhenius, S A., 464 Barad, M., 237, 248, 291 Barker, L., 165 Barlow, R E., 481 Bartelink, H H., 316 Basu, A P., 463 Bates, D M., 250, 302 Batson, R G., 54 Bauer, R., 367 Bement, T R., 480 Benedict, J., 32 Berettoni, J., 103 Bergman, A., 411 Berk, K N., 296 Bernoulli, J., 80 Birnbaum, P., 25 Birnbaum, Z W., 472 Bisgaard, S., 359, 361, 383, 422, 441, 456, 497, 526 Bishop, T A., 386 Blishke, W R., 481 Blumstein, A., 32 Bohning, D., 355 Booker, J M., 480 Borror, C M., 442, 445, 456 Bowen, J D., 328 Box, G E P., 15, 148, 245, 263, 314, 316, 317, 366, 382, 383, 409, 414, 421, 422, 507, 511 Boyett, J H., 367 Bradley, D M., 482 Brady, J E., Brown, L D., 159 Brown, M B., 194, 386 Buckner, J., 442, 450, 459 Bullington, R G., 475-477 Burdick, R K., 442, 444, 445, 456 Butler, R W., 294 Cai, T T., 159 Caroni, C., 317–319, 327 Carroll, R J., 247, 324 Carter, C W., 400, 401 Case, K E., 368 Chaganty, N G., 120 Champ, C W., 358 Charnes, J., 331, 373 Chen, J C., 438, 530 Chernick, M R., 168 Chernoff, H., Chevan, A., 289 Chin, B L., 442, 450, 459 Chou, C.-Y., 530 Chou, Y.-L., 343 Christensen, R., 497 Clark, J B., 383 Cleveland, W S., 519–520 Modern Engineering Statistics By Thomas P Ryan Copyright C 2007 John Wiley & Sons, Inc 573 574 Clopper, C J., 158 Cochran, W G., 90, 355, 422 Coehlo, C M., 455 Coen, P J., 245 Cook, R D., 301 Cooley, B J., 424 Cornell, J., 64 Corrall, R J M., 267 Coull, B., 158, 159 Cox, D R., 250 Cressie, N A C., 193, 324 Croarkin, C., 22, 362, 456, 463, 464, 466, 472, 473, 477 Cryer, J., 508 Czitrom, V., 3, 279, 434, 445 Dahiya, R C., 120, 262 Daniel, C., 297, 400, 401, 407, 408 Das, J C., 474 Das Gupta, A., 159 Daskin, M S., 365 Davies, T D., 316 Davis, J C., 254 Davison, A C., 168 de Mast, J., 420 De Walle, D P., 316 Dean, A., 407 Deane, B., 25 Dechert, J., 368 Deming, W E., 3, 221, 356 Derringer, G., 418 Devlin, S J., 519 Dhillon, B S., 468 Dodge, H F., 368 Does, R J M M., 338, 378, 420 Doganaksoy, N., 478 Doviak, M J., 120 Draper, N R., 292, 294, 422 Duane, J T., 463 Dudewicz, E J., 386, 391, 408 Eberhardt, K R., 263 Efron, B., 133, 168, 527 Elrod, G., 424 Escobar, L A., 479–481 Eshleman, K N., 316 Fang, Y., 90 Feinberg, W E., 172 Finney, D J., 409 Fisher, R A., 382, 489, 505 Fluharty, D A., 457, 462 author index Forsythe, A B, 194, 386 Franklin, L A., 424 Freedman, D A., 294 Freedman, L S., 294 Friedman, D J., 355 Freidman, H., 172 Fung, C., 383 Furnival, G M., 296 Galton, F., 232 Ganju, J., 417 Gawande, B N., 429 Geary, R C., 93 Gelman, A., 77 Gertsbakh, I., 455, 497 Ghosh, B K., 335 Giesbrecht, F., 148 Gitlow, H., 331, 373 Gochnour, D J., 186 Gomme, E., 245 Gong, G., 133 Good, P I., 130, 132, 192 Goodman, A., 275 Gorenflo, R., 440 Gossain, V., 316 Gosset, W S., 98, 99 Grage, H., 402 Green, T P., 450 Gunst, R F., 140, 207 Gupta, A., 432 Gupta, R C., 482 Guttman, I., 222 Gyurcsik, R S., 254 Hahn, G J., 175, 184, 216, 220, 221, 224228, 382, 478 Hahn-Hăagerdal, B., 402 Haimes, Y Y., 68 Haith, D A., 306, 307 Halverson, G D., 343 Hamada, M., 464, 474, 476, 477 Hamed, K H, 131 Hardin, J W., 130, 132, 192 Hare, L B., 434 Haugh, L D., 275, 279, 434 Henri, J., 442, 450, 459 Hegemann, V., 15 Hess, W., 68 Hinkley, D V., 168 Hoaglin, D C., 9, 19, 20 Hoeting, J A., 275 Hooper, J H., 464 575 author index Horrell, K., 456 Horton, R., 411 Hosmer, D W., Jr., 301 Howe, W G., 216, 217 Høyland, A., 460 Huang, L., 438 Huang, P.-T., 530 Hughes-Oliver, J M., 254 Hui, Y V., 335 Hunter, J S., 14, 15, 409 Hunter, W G., 15, 423 Hutchinson, T P., 256 Inman, J., 444, 458 Ishikawa, K., 20 Iyer, H., 456 James, P C., 513 Jiang, R., 103 Jilek, M., 221 Johnson, N L., 366 Jones, S., 414 Joseph, V R., 417 Juran, J M., 420 Kang, L., 450 Kautiainen, T L., 368 Keane, M A., 326 Kendall, M G., 245 Kennard, R W., 299 Kerscher, W J., 480 Khattree, R., 444 Khurshid, A., 165 Kim, B S., 355 Kim, K., 450 Kim, K P., 369 King, E N., 301 Kotz, S., 366 Kuczek, T., 382, 384, 390 Kulahci, M., 359, 361 Kv˚alseth, T O., 321 Kvam, P H., 473 Lai, C D., 256 Larsen, G A., 444 Layard, M W J., 193 Ledolter, J., 418, 444, 458 Lee, C., 103 Lee, S., 355 Lemeshow, S., 301 Lenth, R.V., 3, 404, 407, 444, 458 Levene, H., 193, 386 Lieblein, J., 317, 318, 327 Lighthall, F F., 1, 34 Lin, D K J., 416 Lin, J.-H., 108 Lindsey, J K., 497 Liu, K C., 25 Liu, S., 54 Loader, C., 519 Lovin, G S., 475–477 Lu, J C., 254 Lucas, J M., 417 Luce˜no, A., 365 Lynch, J D., 441, 462 Lynch, R O., 362, 364 Madanat, S M., 317 Mahmoud, M A., 369, 450 Mallows, C., 297 Mandraccia, S T., 343 Mann, N R., 480 Manning, G B., 455 Manuel, L., 316 Markle, R J., 362, 364 Marshall, K C., 317, 327 Martinez, R A., 165 Matzo, G A D., 103 McCabe, G P., 147, 156 McCoun, V E., McKeon, J J., 262 Mee, R W., 263 Meeker, W Q., 175, 184, 216, 220, 221, 224–228, 478–481 Meinander, N Q., 402 Mess, L E., 186 Meyer, M A., 480 Miller, D M., 475–477 Miller, J G., 473 Mitchell, T., 15 Montgomery, D C., 336, 419, 422, 442, 443, 445, 456 Moore, D S., 147, 156 Morgan, J P., 120 Morrow, M C., 382, 384, 390 Murdoch, P S., 316 Murthy, D N P., 103, 481 Murzin, D Y., 326 Myers, R H., 419 Natrella, M G., 227 Nelson, L S., 19 Nelson, P R., 391, 408 Nelson, W., 225, 228, 316, 466, 469, 477, 481 576 Nemeth, L., 420 Nester, M R., 148 Neumann, D W., 520 Newbold, P., 245 Newrick, P G., 267 Niemi, L., 444, 458 Noether, G., 521 Nolan, D., 77 Nordman, D J., 225 Odeh, R E., 174, 216, 219 Olsen, A R., 275 Onifade, K R., 439 Osborne, C., 263 Osterwise, L., 367 Ott, E R., 9, 343, 390, 526 Owen, D B., 174, 182, 216, 219 Palmqvist, E., 402 Pankratz, P C., 449 Park, C., 355 Patel, J K., 221, 225, 226 Patkar, A Y., 429 Pearson, E S., 147, 156, 158 Peck, R., 275 Pee, D., 294 Peters, N E., 316 Pettersson, M., 380 Phadke, M S., 317 Pinault, S C., 294 Please, N W., 147, 156 Poisson, S., 89 Pope, P T., 294 Porte, A., 316 Posten, H O., 193 Proffi, J A., 317 Prozzi, J A., 316 Qasrawi, H Y., 229 Qu, X., 418 Quesenberry, C P., 333 Rajagopalan, B., 520 Rao, A R., 131 Ratkowsky, D A., 325 Rausand, M., 460 Rayner, J C W., 256 Raz, T., 237, 248, 291 Reeve, R., 148 Reynolds, M R., Jr., 335 Rigdon, S E., 463 Rocke, D M., 53 author index Roes, K C B., 338, 378, 420 Rousseeuw, P J., 25 Ruppert, D., 234, 247 Rutledge, J., 181 Ryan, T P., 22, 29, 220, 246–248, 259, 260, 279, 281, 290, 301, 302, 316, 336, 350, 351, 358, 362, 365, 366, 383, 401, 414, 415, 422, 435, 444 Sahai, H., 165 Samaranayake, V A., 225, 226 Saunders, S C., 472 Schafer, R E., 480 Schechtman, E., 262 Schilling, E G., 368 Schurink, Y., 338 Schwartz, S., 367 Schwertman, N C., 165, 350, 351 Scott, D W., 16, 499 Seber, G A F., 297, 299 Seder, L A., 420 Shainin, D., 418, 420 Shewhart, W A., 336, 527 Shon, Y., 327 Silknitter, K O., 422 Singhal, S C., 379 Singpurwalla, N D., 480 Smith, H., 292, 294 Snedecor, G W., 90, 355, 422 Sniegowski, J., 279, 434 Speigelman, C., 262 Spence, H., 464 Stewart, W E., 316 Suich, R., 418 Sutherland, M., 289 Swersey, A., 418 Taguchi, G., 308, 325, 327, 419 Tan, Y., 317, 326 Taylor, J R., 456 Terrell, G R., 16 Thayer, P C., 455 Thomas, E H., 456 Thorn, J., 25 Tiao, G C., 317 Tibshirani, R J., 168 Tiffany, T O., 455 Tobias, P., 22, 362, 456, 463, 464, 466, 472, 473, 477 Tocher, K D., 494 Trantner, M., 316 Trindade, D C., 477 577 author index Tripp, T B., 400, 401 Tsung, F., 365 Tufte, E R., 14 Tukey, J W., 9, 148 van den Heuvel, E R., 458 Van Sickle, J., 316 Van Zomeren, B C., 25 Vardeman, S B., 214 Velleman, P V., 9, 19, 20 Von Alven, W H., 468 Voss, D., 407 Wallis, W A., 221 Wang, F K., 166, 167 Wang, Y., 44, 462 Wang, Z.-X., 317, 326 Warner, B., 181 Watkins, D., 411 Watts, D G., 250, 302 Webster, J., 294, 474 Weibull, W., 470 Weisberg, S., 248, 301 Wen, C C., 108 Whitford, H J., 193 Wigginton, P J Jr., 316 Wilson, E B., 159 Wilson, R W., 296 Wisnowski, J W., 422 Wludyka, P S., 391, 408 Wolfram, S., 329 Woodall, W H., 336, 358, 369, 450, 456, 475–477 Wu, C F J., 418, 464, 474, 476, 477 Xie, M., 103 Yashchin, E., 456 Yeh, H C., 193 Young, A., 133 Young, J C., 405 Zaciewski, R D., 420 Zanoga, E A., 520 Zelen, M., 317, 318, 327 Subject Index Acceptance sampling, 368 Accreditation Board of Engineering and Technology (ABET), American Society for Quality (ASQ), 473 American Statistical Association, 49, 65 Analysis of Covariance, 422 Analysis of Means (ANOM), 383, 390, 391, 404, 420, 526 for one factor, 390–391 normality assumption, 387 with unequal variances (HANOM), 408–409 Analysis of Variance (ANOVA), 383–386, 388, 390, 402, 420, 442, 526 computing formulas, 424–425 heteroscedastic (unequal variances), 386 homoscedasticity, 386, 389 tests for homoscedasticity, 386–387 Bartlett’s test, 387 Levene’s test, 386–387, 390 nonparametric, Kruskal–Wallis method, 386, 388, 391 normality assumption, 387, 389 Analytic studies, Autocorrelation, 12, 341, 390 defined, 508 plot, 360, 510 Automotive Industry Action Group, 445, 447, 455 Bayes’ theorem, 74, 76 applications, 76 definition, 76 Box–Cox transformation, 167, 220, 224, 250, 299, 341 Box–Tidwell transformation, 284 Boxplot, 20–22, 57, 58 estimating μ and σ , 57, 58 skeletal, 20 Calibration, 257–263 classical theory of, 257 hypothesis test, 257 interval, 262 inverse regression, 257 California Institute of Technology, 288 Categorical data, 487 design of experiments, 497 goodness-of-fit tests, 498 Anderson–Darling, 500 Kolmogorov–Smirnov tests, 500 Ryan–Joiner, 500 Shapiro–Wilk test, 500 Central Limit Theorem, 126–128, 136, 156, 191, 507, 511 illustration, 126–128 Chance magazine, 181 Chance News, 27, 32 Confidence intervals, 141 assumptions, validity of, 143 connection with hypothesis tests, 140, 153 defined, 141 for a mean, unknown distribution, 174 for a normal mean, σ known, 140–142 illustration, 143–145 interpretation, 145 for a normal mean, σ unknown, 146 sample size determination, 146 Modern Engineering Statistics By Thomas P Ryan Copyright C 2007 John Wiley & Sons, Inc 579 580 Confidence intervals (Continued ) for a proportion, 157, 175 approximate versus exact interval, 158 Clopper–Pearson approach, 158 illustration of approximate approach, 159–160 for the difference of two means, normality assumed, variances known, 191 for the difference of two proportions, 202 for the Poisson mean, 164–165, 175 for the ratio of two variances, 203–204 for σ and σ , 161–163, 175 assumption, 162 examples, 161–163 general form, 145 obtained using bootstrap methods, 166 sample size determination, 142–143 used to test hypotheses, 152–155 Contingency tables, 487–490 degrees of freedom, 490 exact analysis, 493 StatXact, 494–496 expected frequencies, 488 Fisher’s exact test, 494, 496 limitations, 496 Tocher’s modification, 494, 496 null hypothesis, 488 test statistic, 489 with more than two factors, 497 Control chart, 11, 24 assignable causes, 330 detecting, 359–362 assumptions, 334 independence, 334 normality, 334 attributes charts, 349 average run length (ARL), 335 in control, 335 parameter change, 335 basic principles, 330–331 c-chart, 351 regression-based limits, 352–353 robustness considerations, 354 3-sigma limits, 354 case study, 362–364 testing for nonnormality, 362 common causes, 330 limits, 11, 332–333 recomputing, 333 trial, 332 subject index moving average chart, 344 multivariate charts, 362 nonconformities and nonconforming units, 349 used in conjunction with measurement charts, 349 nonparametric, 334 np-chart, 350 regression-based limits, 350, 351 p-chart, 336, 350 overdispersion, 351 R-chart, 346–349, 448 probability limits, 347 3-sigma limits, 347–348 rational subgroups, 344 s-chart, 347, 363 Shewhart-type, 335, 336, 356 alternatives, 356–359 CUSUM procedures, 357–358 fast initial response, 358 Shewhart-CUSUM, 358 EWMA procedures, 358 Shewhart-EWMA, 358 stages of use, 331–332 Phase I, 331–333, 336–338, 449 Phase II, 331–333, 336–338, 449 u-chart, 354–355 overdispersion, 355 tests for Poisson overdispersion, 355 regression-based limits, 355 using with designed experiments, 349 X -chart (I -chart), 336–343 importance of checking for nonnormality, 339 impossible computed LCL, 340 nonparametric approach, 341 transforming data, 343 X -chart, 344–347, 363, 448 Central Limit Theorem, 344 failure to indicate assignable cause, 361 parameter estimation, 347 runs rules, 358 trial control limits, 345 suggested minimum number of observations, 345 Correlation, 254–256 Pearson correlation coefficient, 254, 514 spurious, 256 Cree Research, 466 Cytel Software Corp., 494 subject index Data, bivariate, 24 multivariate, univariate, Data mining, 23 DATAPLOT, 227 Degrees of freedom, 101 Design-Ease r , 423 Designed experiments, 3–4, 382 processes should be in statistical control, 383 Design-Expert r , 422–423 Digidot plot, 14 Distribution-free (nonparametric) procedures, 507 asymptotic relative efficiency (A.R.E.), 508 Mann–Whitney test, 512–513 asymptotic relative efficiency, 513 nonparametric analysis of variance, 514 Kruskal–Wallis method for one factor, 514–515, 518 asymptotic relative efficiency, 516 Friedman test for two factors, 516–518 exact test, 518 StatXact, 518 runs test, 509 sign test, 510–511 Spearman rank correlation coefficient, 513–514 Wilcoxon one-sample test, 511–512 asymptotic relative efficiency, 512 Dotplot, 14, 24 limitations, 15 Earned run averages, 25 Eastman Chemical Company, 384 Eaton Corporation, 475 Emcore, 466 Empirical-mechanistic model, 316–318, 325 Energy Information Administration, 139 Engineering process control (EPC), 364, 365 contrasted with statistical process control (SPC), 364, 365 Enumerative studies, Estimates interval, 140 point, 121 Estimating parameters without data, 133 Estimators mean squared error of, 124, 125 point, 121 biased, 124–125 desirable properties, 121 581 consistency, 121 minimum variance, 122 minimum variance unbiased (MVUE), 124 unbiasedness, 121, 122, 125 methods of obtaining, 128–131 least squares, 131 maximum likelihood, 128–130 method of moments, 130–131 Events, 71 composite, 71 dependent, 72 independent, 71, 72 multiple, 73 mutually exclusive, 72 Evolutionary Operation (EVOP), 421–422, 497 Experiment, 4, 70 Experimental designs complete randomization, 385 expected mean squares, 407 factorial (crossed), 396, 405 ANOM, 407–408 blocking, 404, 405 conditional effects, 399, 402 interaction effects, 401 effect estimates, 398 relationship with regression coefficients, 426 interaction plot, 396, 399 mixed, 404 regression model coefficients, 398 three factors, 400 treatment combinations, 397 unreplicated, 403 normal probability plot analysis, 403–404 Pareto chart, 404 fixed factors, 406 for binary data, 420 fractional factorials, 409–413 2k –1 , 409–412 confounded (aliased) effects, 411 defining contrast, 411 highly fractionated, 412–413 principal fraction, 411 resolution, 409 hard-to-change factors, 416–417 multifactor, 395 multiple response optimization, 418–419 desirability function, 418 582 Experimental designs (Continued ) nested, 405–406 nonorthogonal, 383 one-at-a-time plans, 396, 417–418 nonorthogonality, 418 weakness, 396 one blocking factor, 392–395 randomized complete block (RCB), 392–395 assumptions, 393 one-factor experiments, 384–389 orthogonal, 383, 397 main effect plans, 413 Plackett–Burman, 419, 475, 476 random factors, 406 raw form analysis versus coded form analysis, 415 multicollinearity, 416 response surface designs, 414 central composite, 414 orthogonality, 414 rotatability, 414 split-plot, 413–414 Taguchi methods, 419, 438 training for use of, 423 two blocking factors, 395 Latin square design, 395 Exploratory data analysis (EDA), Finite population correction factor, 52, 123 Fitting probability distributions, 106–107 moments, 106–107 Florida Department of Highway and Safety, 506 General Electric, 466 Georgia Tech, Grouped data, 56 Sheppard’s correction, 56 subject index for two means dependent samples, paired-t test, 197–200, 204, 512 variances assumed known, 189, 190 variances assumed unknown, 192, 193, 197 for two proportions, 200–201, 204 for two variances, 194, 202, 204 F-test, 202, 203 Levene’s test, 194, 195, 204, 386 Brown–Forsythe modification, 194, 204 for σ and σ , 163–164 for a Poisson mean, 175 null hypothesis, 147, 148, 172 p-value, 151, 170–171, 175 power of the test, 168–171 practical significance, 172–173, 257 versus statistical significance, 172 rejection region, 151 relationship with confidence intervals, 147, 152 selection of the proper test statistic, 155 significance level, 170–171 Type I and Type II errors, 168, 171, 172 Wilcoxon two-sample test, 197 IGOR, 325 Inferential statistics, International Standards Organization, 317 Interquartile range, 21 Institute for Scientific Information, 315, 528 Web of Science, 315, 528 JMP, 19, 147, 217, 320, 325, 419, 420, 456, 465, 480 Journal of Environmental Engineering, 520 Journal of Statistics Education, 3, 423 Lag plot, 11 Histogram, 16–20, 23, 24 class boundaries, 17 number of classes, 16 power-of-two rule, 16, 17 square root rule, 16, 23 Hypothesis tests alternative hypothesis, 148, 149 always false?, 147 basic concepts, 148 for a mean, 149–154 for normality, 195 Anderson–Darling, 195 Mathematica, 329 Measurement error, 422 Measurement systems, 441 attribute gage study, 452–453 calibration, 449 designs for, 454 designed experiments, 442 gage linearity and bias study, 450-452 gage reproducibility and repeatability (R&R) study, 442, 446–448, 455, 456 number of distinct categories, 447 583 subject index instrument bias, 449–450 monitoring, 449 simple linear regression, 449–450 precision over tolerance ratio, 445 propagation of error, 454–455 repeatability, 442, 443 reproducibility, 442, 443 software, 455–456 tolerance analysis, 444–445 variance components, 442, 443 confidence intervals, 445 negative estimates, 444 Measurement Systems Analysis Reference Manual, 41, 445, 451 Measures of location (center), 45 mean, 45 median, 45 Measures of variability (dispersion), 45 coefficient of variation, 53 range, 45 standard deviation, 45 variance, 45 Mechanistic models, 303, 314, 315 in accelerated life testing, 315–316, 464 Arrhenius model, 316 MINITAB, 10, 13, 18, 25, 26, 30, 31, 35, 37, 41, 55, 58, 61, 85, 97, 107, 127, 136, 147, 156, 164, 169, 180, 194, 197, 202, 207, 216, 240, 244, 246, 284, 296, 326, 331, 336, 340, 341, 352, 355, 359, 383, 384, 386–390, 398, 404, 407, 408, 410, 412, 419, 420, 422, 446, 448 , 451–453, 455, 472, 476, 478–480, 490, 493, 495, 496, 500, 512, 515, 517–518, 520, 530 NONLIN macro, 325–326 TOLINT macro, 216, 217, 219 Multi-vari chart, 22, 420, 421 National Basketball Association (NBA), National Institute of Standards and Technology, 2, 259, 449 National Oceanic and Atmospheric Administration (NOAA), 331 National Weather and Climate Center, 40 New York’s Land Use and Natural Resource Laboratory, 307 NIST/SEMATECH e-Handbook of Statistical Methods, 2, 22, 195, 227, 258, 259, 263, 273, 362, 379, 449, 454–456, 460, 462, 464 465 Nonlinear least squares, 324 Nonlinear model, 315 Michaelis–Menten, 324 Observational data, Ogive, 22 Outlier, 22 Pareto chart, 22, 23 Pie chart, 22 Poisson process, 355, 463 Population, finite, Prediction intervals, 221–227 distribution-free, 226–227 for multiple future observations, 225 for number of failures, 225 known parameters, 222 nonnormal distributions, 224 one-sided prediction bounds, 225–226 for certain discrete distributions, 226 unknown parameters, normality assumed, 223 sensitivity to normality, 223–224 used in civil engineering, 222 width, 224 Probability, 68 Bayes probabilities, 75 conditional, 73, 74 exceedance, 174 joint, 72 law of total probability, 74 plot, 107 probability mass function (pmf), 76 manufacturing application, 70 multiplication rule, 73 relative frequency approach, 70, 71, 73 Probability distributions, 50, 68 continuous Birnbaum–Saunders, 472 bivariate normal, 256 chi-square, 100–101,104, 347, 348 exponential, 101–102 in reliability applications, 469–470 extreme value distribution, 471 in reliability applications, 471 F, 104–106 gamma, 100 in reliability applications, 471, 473 other applications, 100 half-normal, 195 584 Probability distributions (Continued ) lognormal, 104 in reliability applications, 471, 473 three-parameter, 472 normal, 93–97 standard normal, 95 testing normality, 97 smallest extreme value, 103–104 used in reliability applications, 103–104 t, 97–100 Weibull, 102–103, 104, 340, 341 in reliability applications, 470–473, 479 three-parameter, 472, 473 cumulative distribution function, 77 discrete, 76 binomial, 80–86, 107 Bernoulli trials, 80, 84, 85 testing for appropriateness of, 86–87 used in quality improvement work, 86 geometric, 91–92 hypergeometric, 87, 88 Poisson, 88–91, 107, 352 applications, 88–89 testing for the appropriateness of, 90–91 uniform, 77 heavy tails, 50 skewed, 50 Process capability, 20, 365–366 approximate confidence interval, 366 studies, 20 Process performance indices, 333 Purdue University, 503 Quality control, 50, 51 Random variable, continuous, determining probabilities for, 92–93 expected value, 92 rules, 123 variance, 92 rules, 123, 124 covariance, 85 discrete, expected value, 78, 79 standard deviation, 78 variance, 78 Regression, 232 checking assumptions, 245 constant error variance, 246, 290 subject index independent errors, 245–246, 290-291 normality, 247–248, 289–290 confidence intervals, 250–252 fixed versus random regressors, 249 for control, 263 indicator variables, 300 inverse, 257–258 logistic, 301 measurement error, 263 method of least squares, 235–236, 244 model validation, 254 multiple linear, 276 adjusted R , 296 fixed regressors, 279 example, 279–281 graphical methods, 300–301 partial residual plot, 301 interpreting regression coefficients, 278 outliers, 283 random regressors, 281 example, 281–291 use of scatterplot matrix, 282–283 total squared error, 297 total standardized squared error, 298 transformations, 299–300 unusual observations, 287–288 using scatter plots, 277 variable selection, 283–287, 293 all possible regressions, 296 Mallows’ C p , 297–299 backward elimination, 295, 296 forward selection, 294–295, 296 nominal versus actual significance levels, 294 stepwise regression, 284–287, 295 significance levels, 295–296 “wrong” signs of coefficients, 278–279 nonlinear, 301–302 nonparametric, 302, 519– 521 locally weighted regression (loess), 302, 519, 520 neighborhood size, 519 Mallows’ C p statistic, 519 piecewise linear, 271 prediction intervals, 250-252 R , 242, 243 coefficient of determination, 256 simple linear, 232 assumptions, 237 degrees of freedom, 243 example with college data, 239–248 fitted values, 234 585 subject index model definition, 233 parameter estimation, 234–237 prediction equation, 234 sequence of steps, 237 standardized residual, 244–245 transformations, 249 model, 249–250 Y and/or X , 250 Reliability, 460 accelerated testing, 463 acceleration factor, 464 acceleration models, 463 Arrhenius equation, 464 inverse power function, 465 censored data, 466 interval censoring, 467 left (Type II) censoring, 467 right (Type I) censoring, 467 competing risk model, 462 conditional survivor function, 468 confidence intervals, 477–478 defined, 460 degradation data, 465 designed experiments, 477 used in extrapolation, 465 designed experiments, 474–475 Duane model, 463, 473 failure mode and effects analysis (FMEA), 462 example, 474 failure rate (hazard function), 467 bathtub curve, 469–470 mean residual life (MRL), 468 mean time between failures (MTBF), 463 mean time to failure (MTTF), 467, 468 nonrepairable systems, 462 parallel system, 462, 469 PREDICT, 480 reliability function, 467 defined, 468 repairable system, 462 series system, 462, 469 for dependent components, 469 Reliability engineering, 473 availability, 473 maintainability, 473 prediction, 473–474 Reliability growth and demonstration testing, 479–480 Robust statistics, 53, 123 Royal Statistical Society, 27, 35, 314 RSS News, 314 Sample, convenience, 6, 144 frame, 5, 144 random, 5, 143 representative, space, 70 systematic sampling, SAS Software r , 496 SAT scores, 12, 13 Scatter plot, 12, 24 Scatterplot matrix, 14 SEMATECH, Six Sigma, 219, 365, 367–368, 458 Software engineering, 68 St James Gate Brewery, 98 Statistic (sample), 4, 46, 84 coefficient of variation, 53 correlation coefficient, 55 covariance, 55 interquartile range, 53 mean (average), 47, 54 median, 47, 48 moving average, 47 moving range, 50, 51 nonnormal sampling distributions, 128 range, 50, 51 sampling distributions, 125 standard deviation, 51, 52, 54 standard error, 125, 132 estimated, 132 bootstrapping, 132 trimmed average, 49 trimmed standard deviation, 53 trimmed variance, 53 variance, 51, 52, 54 weighted average, 56 Statistical hydrology, 131 Statistical inference, defined, 143 Statistical process control (SPC), 368 measurement error, 368 Stem-and-leaf display, 9, 24 Texaco, Inc., 431 Time sequence plot, Tolerance intervals, 214 approximations, 217 assuming normality, 215 importance of testing assumption, 220 determining sample size, 221 distribution free, 219–220 lower tolerance bound, 214 586 Tolerance intervals (Continued ) one-sided bound, 218, 219 two-sided interval, 216 possibly unequal tails, 218 U S Consumer Product Safety Commission U S Energy Information Administration, 67 U S Environmental Protection Agency, 224 U S Food and Drug Administration, 166 U S Geological Survey, 66 U S News and World Report, 12, 13, 133, 281 University of California-Berkeley, 245 subject index University of Georgia, 211 University of Tennessee, 473 Variable, random, continuous, discrete, Variation, 50 abnormal, 50 normal, 50 Western Mine Engineering, Inc., 49, 59, 62, 115, 205, 206 Wiley Encyclopedia of Electrical and Electronics Engineering, 474 .. .Modern Engineering Statistics THOMAS P RYAN Acworth, Georgia A JOHN WILEY & SONS, INC., PUBLICATION Modern Engineering Statistics Modern Engineering Statistics THOMAS P RYAN Acworth,... Cataloging-in-Publication Data: Ryan, Thomas P., 1945– Modern engineering statistics / Thomas P Ryan p cm Includes bibliographical references and index ISBN 978-0-470-08187-7 Engineering Statistical... that failure to properly analyze available engineering data or failure to collect necessary data can endanger Modern Engineering Statistics By Thomas P Ryan Copyright C 2007 John Wiley & Sons,