The Weibull Distribution: A Handbook - Index of

More documents

Recommendations

Info

XXIV List of Tables 22/7 Percentage points � W ∗ n,P . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 22/8 Upper percentage points of Z = n � 1 − R2 (X,T) � . . . . . . . . . . . . . 673 22/9 22/10 Recommended values for k . . . . . . . . . . . . . . . . . . . . . . . . . . Percentage points λα such that Pr 675 � � λ < λα = α . . . . . . . . . . . . . . 678 22/11 Probability of correct selection (Gamma versus WEIBULL) . . . . . . . . . 680 22/12 Probability of correct selection (Lognormal versus WEIBULL) . . . . . . . 683 22/13 Probability of correct selection between gamma, lognormal and WEIBULL models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686 22/14 Probability of correct selection of the better of two WEIBULL distributions 688 22/15 Sample size n required for given PCS to select the better of two WEIBULL distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689 © 2009 by Taylor & Francis Group, LLC
© 2009 by Taylor & Francis Group, LLC I Genesis, theory and description
Page 1 and 2: © 2009 by Taylor & Francis Group,
Page 3 and 4: Chapman & Hall/CRC Taylor & Francis
Page 5 and 6: IV Contents 2.7 Aging criteria . .
Page 7 and 8: VI Contents 6.2 WEIBULL characteriz
Page 9 and 10: VIII Contents 11 Parameter estimati
Page 11 and 12: X Contents 15.1.1 The key ideas . .
Page 13 and 14: XII Contents 22 WEIBULL goodness-of
Page 15 and 16: XIV Preface by the three parameters
Page 17 and 18: List of Figures 1/1 Densities of th
Page 19 and 20: List of Figures XIX 9/7 Dataset #1
Page 21 and 22: List of Tables 1/1 Comparison of th
Page 23: List of Tables XXIII 12/6 Elements
Page 27 and 28: 4 1 History and meaning of the WEIB
Page 33 and 34: 10 1 History and meaning of the WEI
Page 51 and 52: 28 2 Definition and properties of t
Page 75 and 76:
52 2 Definition and properties of t
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
3 Related distributions This chapte
Page 123 and 124:
100 3 Related distributions Figure
Page 125 and 126:
102 3 Related distributions Whereas
Page 127 and 128:
104 3 Related distributions The adv
Page 129 and 130:
106 3 Related distributions and the
Page 131 and 132:
108 3 Related distributions Unfortu
Page 133 and 134:
110 3 Related distributions Type-II
Page 135 and 136:
112 3 Related distributions The DF
Page 137 and 138:
114 3 Related distributions Using T
Page 139 and 140:
116 3 Related distributions Table 3
Page 141 and 142:
118 3 Related distributions With n
Page 143 and 144:
120 3 Related distributions viewpoi
Page 145 and 146:
122 3 Related distributions The typ
Page 147 and 148:
124 3 Related distributions is the
Page 149 and 150:
126 3 Related distributions This le
Page 151 and 152:
Page 153 and 154:
130 3 Related distributions The haz
Page 155 and 156:
132 3 Related distributions with ©
Page 157 and 158:
134 3 Related distributions truncat
Page 159 and 160:
136 3 Related distributions The fir
Page 161 and 162:
138 3 Related distributions by link
Page 163 and 164:
140 3 Related distributions c=3 f2(
Page 165 and 166:
142 3 Related distributions for ind
Page 167 and 168:
144 3 Related distributions The DF
Page 169 and 170:
146 3 Related distributions but has
Page 171 and 172:
Page 173 and 174:
150 3 Related distributions discret
Page 175 and 176:
152 3 Related distributions From (3
Page 177 and 178:
Page 179 and 180:
156 3 Related distributions Let ©
Page 181 and 182:
158 3 Related distributions Var(X |
Page 183 and 184:
160 3 Related distributions The cor
Page 185 and 186:
162 3 Related distributions • λ
Page 187 and 188:
164 3 Related distributions • λ
Page 189 and 190:
166 3 Related distributions We ment
Page 191 and 192:
168 3 Related distributions 3.3.8 W
Page 193 and 194:
170 3 Related distributions where (
Page 195 and 196:
172 3 Related distributions popular
Page 197 and 198:
174 3 Related distributions There i
Page 199 and 200:
176 3 Related distributions Three i
Page 201 and 202:
178 3 Related distributions The are
Page 203 and 204:
180 3 Related distributions LU (198
Page 205 and 206:
182 3 Related distributions Differe
Page 207 and 208:
184 3 Related distributions 3.3.9.2
Page 209 and 210:
186 3 Related distributions The joi
Page 211 and 212:
188 3 Related distributions They di
Page 213 and 214:
190 4 WEIBULL processes and WEIBULL
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
224 5 Order statistics and related
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
6 Characterizations 1 Characterizat
Page 279 and 280:
256 6 Characterizations Proof of Pr
Page 281 and 282:
258 6 Characterizations has the sam
Page 283 and 284:
260 6 Characterizations Integration
Page 285 and 286:
262 6 Characterizations Theorem 8 (
Page 287 and 288:
264 6 Characterizations Theorem 9 (
Page 289 and 290:
266 6 Characterizations Tn Xn:n), f
Page 291 and 292:
268 6 Characterizations Theorem 16
Page 293 and 294:
270 6 Characterizations i.e., u,v,w
Page 295 and 296:
272 6 Characterizations and the com
Page 297 and 298:
7 WEIBULL applications and aids in
Page 299 and 300:
7.1 A survey of WEIBULL application
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
7.2 Aids in WEIBULL analysis 285 7.
Page 309 and 310:
8.2 Parameters of a life test plan
Page 311 and 312:
8.2 Parameters of a life test plan
Page 313 and 314:
8.3 Types of life test plans 291 in
Page 315 and 316:
8.3 Types of life test plans 293 Th
Page 317 and 318:
8.3 Types of life test plans 295 Ta
Page 319 and 320:
8.3 Types of life test plans 297 be
Page 321 and 322:
8.3 Types of life test plans 299 an
Page 323 and 324:
8.3 Types of life test plans 301 As
Page 325 and 326:
8.3 Types of life test plans 303
Page 327 and 328:
8.3 Types of life test plans 305 4.
Page 329 and 330:
8.3 Types of life test plans 307 wh
Page 331 and 332:
8.3 Types of life test plans 309 No
Page 333 and 334:
8.3 Types of life test plans 311 Fi
Page 335 and 336:
9 Parameter estimation — Graphica
Page 337 and 338:
9.1 General remarks on parameter es
Page 339 and 340:
9.2 Motivation for and types of gra
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
Page 349 and 350:
Page 351 and 352:
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
9.3 WEIBULL plotting techniques 335
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
Page 375 and 376:
Page 377 and 378:
10 Parameter estimation — Least s
Page 379 and 380:
10.1 From OLS to linear estimation
Page 381 and 382:
10.2 BLUEs for the Log-WEIBULL dist
Page 383 and 384:
Page 385 and 386:
Page 387 and 388:
Page 389 and 390:
Page 391 and 392:
10.3 BLIEs for Log-WEIBULL paramete
Page 393 and 394:
Page 395 and 396:
Page 397 and 398:
10.4 Approximations to BLUEs and BL
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
Page 405 and 406:
Page 407 and 408:
Page 409 and 410:
10.5 Linear estimation with a few o
Page 411 and 412:
Table 10/8: BLUES of a ∗ and b
Page 413 and 414:
Page 415 and 416:
Page 417 and 418:
10.6 Linear estimation of a subset
Page 419 and 420:
10.6 Linear estimation of a subset
Page 421 and 422:
10.7 Miscellaneous problems of line
Page 423 and 424:
10.7 Miscellaneous problems of line
Page 425 and 426:
11.1 Likelihood functions and likel
Page 427 and 428:
11.2 Statistical and computational
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
Page 437 and 438:
Page 439 and 440:
11.3 Uncensored samples with non-gr
Page 441 and 442:
Page 443 and 444:
Page 445 and 446:
Page 447 and 448:
Page 449 and 450:
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
11.4 Uncensored samples with groupe
Page 459 and 460:
11.5 Samples censored on both sides
Page 461 and 462:
11.6 Samples singly censored on the
Page 463 and 464:
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
11.7 Samples progressively censored
Page 473 and 474:
11.7 Samples progressively censored
Page 475 and 476:
11.8 Randomly censored samples 453
Page 477 and 478:
12 Parameter estimation — Methods
Page 479 and 480:
12.1 Traditional method of moments
Page 481 and 482:
Page 483 and 484:
Page 485 and 486:
Page 487 and 488:
Page 489 and 490:
12.2 Modified method of moments 467
Page 491 and 492:
12.2 Modified method of moments 469
Page 493 and 494:
12.3 W. WEIBULL’s approaches to e
Page 495 and 496:
12.4 Method of probability weighted
Page 497 and 498:
12.5 Method of fractional moments 4
Page 499 and 500:
13.1 Method of percentiles 477 For
Page 501 and 502:
13.1 Method of percentiles 479 dete
Page 503 and 504:
13.1 Method of percentiles 481 It f
Page 505 and 506:
13.1 Method of percentiles 483 size
Page 507 and 508:
13.2 Minimum distance estimators 48
Page 509 and 510:
13.2 Minimum distance estimators 48
Page 511 and 512:
13.3 Some hybrid estimation methods
Page 513 and 514:
13.4 Miscellaneous approaches 491
Page 515 and 516:
13.4 Miscellaneous approaches 493 E
Page 517 and 518:
13.4 Miscellaneous approaches 495 A
Page 519 and 520:
13.4 Miscellaneous approaches 497 (
Page 521 and 522:
13.5 Further estimators for only on
Page 523 and 524:
Page 525 and 526:
Page 527 and 528:
Page 529 and 530:
Page 531 and 532:
13.6 Comparisons of classical estim
Page 533 and 534:
14 Parameter estimation — BAYESIA
Page 535 and 536:
14.1 Foundations of BAYESIAN infere
Page 537 and 538:
14.1 Foundations of BAYESIAN infere
Page 539 and 540:
14.2 Two-parameter WEIBULL distribu
Page 541 and 542:
Page 543 and 544:
Page 545 and 546:
Page 547 and 548:
Page 549 and 550:
Page 551 and 552:
14.3 Empirical BAYES estimation 529
Page 553 and 554:
15 Parameter estimation — Further
Page 555 and 556:
15.2 Structural inference 533 15.2.
Page 557 and 558:
15.2 Structural inference 535 In th
Page 559 and 560:
16.1 Life-stress relationships 537
Page 561 and 562:
16.1 Life-stress relationships 539
Page 563 and 564:
16.2 ALT using constant stress mode
Page 565 and 566:
Page 567 and 568:
Page 569 and 570:
Page 571 and 572:
16.3 ALT using step-stress models 5
Page 573 and 574:
16.4 ALT using progressive stress m
Page 575 and 576:
16.5 Models for PALT 553 tions is F
Page 577 and 578:
16.5 Models for PALT 555 and the co
Page 579 and 580:
17 Parameter estimation for mixed W
Page 581 and 582:
17.1 Classical estimation approache
Page 583 and 584:
Page 585 and 586:
Page 587 and 588:
Page 589 and 590:
17.2 BAYESIAN estimation approaches
Page 591 and 592:
17.2 BAYESIAN estimation approaches
Page 593 and 594:
18 Inference of WEIBULL processes T
Page 595 and 596:
18.1 Failure truncation 573 as note
Page 597 and 598:
18.1 Failure truncation 575 distrib
Page 599 and 600:
18.1 Failure truncation 577 18.1.2
Page 601 and 602:
18.2 Time truncation 579 18.2 Time
Page 603 and 604:
18.3 Other methods of collecting da
Page 605 and 606:
18.4 Estimation based on DUANE’s
Page 607 and 608:
19 Estimation of percentiles and re
Page 609 and 610:
19.1 Percentiles, reliability and t
Page 611 and 612:
19.2 Classical methods of estimatin
Page 613 and 614:
Page 615 and 616:
Page 617 and 618:
Page 619 and 620:
Page 621 and 622:
Page 623 and 624:
19.4 Tolerance intervals 601 each i
Page 625 and 626:
19.4 Tolerance intervals 603 Table
Page 627 and 628:
19.4 Tolerance intervals 605 by whe
Page 629 and 630:
19.5 BAYESIAN approaches 607 Assumi
Page 631 and 632:
19.5 BAYESIAN approaches 609 When s
Page 633 and 634:
20.1 Classical prediction 611 calle
Page 635 and 636:
20.1 Classical prediction 613 The s
Page 637 and 638:
20.1 Classical prediction 615 Examp
Page 639 and 640:
20.1 Classical prediction 617 for s
Page 641 and 642:
20.1 Classical prediction 619 Sect.
Page 643 and 644:
20.1 Classical prediction 621 The F
Page 645 and 646:
20.2 BAYESIAN prediction 623 where
Page 647 and 648:
21.1 Testing hypotheses on function
Page 649 and 650:
Page 651 and 652:
Page 653 and 654:
Page 655 and 656:
Page 657 and 658:
Page 659 and 660:
Page 661 and 662:
Page 663 and 664:
Page 665 and 666:
Page 667 and 668:
Page 669 and 670:
Page 671 and 672:
Page 673 and 674:
22 WEIBULL goodness-of-fit testing
Page 675 and 676:
22.1 Goodness-of-fit testing 653 (s
Page 677 and 678:
22.1 Goodness-of-fit testing 655 Th
Page 679 and 680:
22.1 Goodness-of-fit testing 657 Re
Page 681 and 682:
22.1 Goodness-of-fit testing 659 Ta
Page 683 and 684:
Page 685 and 686:
22.1 Goodness-of-fit testing 663 Fi
Page 687 and 688:
22.1 Goodness-of-fit testing 665 3.
Page 689 and 690:
22.1 Goodness-of-fit testing 667 Co
Page 691 and 692:
Page 693 and 694:
22.1 Goodness-of-fit testing 671 Th
Page 695 and 696:
Page 697 and 698:
22.2 Discrimination between WEIBULL
Page 699 and 700:
Page 701 and 702:
Page 703 and 704:
Page 705 and 706:
Page 707 and 708:
Page 709 and 710:
22.3 Selecting the better of severa
Page 711 and 712:
22.3 Selecting the better of severa
Page 713 and 714:
Table of the gamma, digamma and tri
Page 715 and 716:
Abbreviations 695 Abbreviations ABL
Page 717 and 718:
Abbreviations 697 RP renewal proces
Page 719 and 720:
Mathematical and statistical notati
Page 721 and 722:
Bibliography A-A-A-A-A ABDEL-GHALY,
Page 723 and 724:
Bibliography 703 AROIAN, L.A. / ROB
Page 725 and 726:
Bibliography 705 BALASOORIYA, U. /
Page 727 and 728:
Bibliography 707 BHATTACHARYYA, G.K
Page 729 and 730:
Bibliography 709 CALABRIA, R. / PUL
Page 731 and 732:
Bibliography 711 CHRISTOPEIT, N. (1
Page 733 and 734:
Bibliography 713 DALLAS, A.C. (1982
Page 735 and 736:
Bibliography 715 DUFOUR, R. / MAAG,
Page 737 and 738:
Bibliography 717 ESCOBAR, L.A. / ME
Page 739 and 740:
Bibliography 719 GALAMBOS, J. (1981
Page 741 and 742:
Bibliography 721 density functions;
Page 743 and 744:
Bibliography 723 HASSANEIN, K.M. (1
Page 745 and 746:
Bibliography 725 HUGHES, D.W. (1978
Page 747 and 748:
Bibliography 727 KAGAN, A.M. / LINN
Page 749 and 750:
Bibliography 729 KIM, B.H. / CHANG,
Page 751 and 752:
Bibliography 731 tion and Computati
Page 753 and 754:
Bibliography 733 LOVE, G.E. / GUO,
Page 755 and 756:
Bibliography 735 MANN, N.R. / FERTI
Page 757 and 758:
Bibliography 737 MEEKER, W.Q. JR. (
Page 759 and 760:
Bibliography 739 MUDHOLKAR, G.S. /
Page 761 and 762:
Bibliography 741 NEWBY, M.J. (1982)
Page 763 and 764:
Bibliography 743 PANCHANG, V.G. / G
Page 765 and 766:
Bibliography 745 PROSCHAN, F. (1963
Page 767 and 768:
Bibliography 747 RIGDON, S.E. / BAS
Page 769 and 770:
Bibliography 749 SALVIA, A.A. (1996
Page 771 and 772:
Bibliography 751 SHESHADRI, V. (196
Page 773 and 774:
Bibliography 753 SOLAND, R.M. (1968
Page 775 and 776:
Bibliography 755 TALKNER, P. / WEBE
Page 777 and 778:
Bibliography 757 U-U-U-U-U UMBACH,
Page 779 and 780:
Bibliography 759 WHITE, J.S. (1964a
Page 781:
Bibliography 761 YILDIRIM, F. (1996
show all

The Weibull Distribution: A Handbook - Index of

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?