Springer Handbook of Engineering Statistics978-1-84628-288...School of Mathematical and Geospatial...
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Springer Handbook of Engineering Statistics
Transcript of Springer Handbook of Engineering Statistics978-1-84628-288...School of Mathematical and Geospatial...
Springer Handbookof Engineering Statistics
Springer Handbooks providea concise compilation of approvedkey information on methods ofresearch, general principles, andfunctional relationships in physicsand engineering. The world’s lead-ing experts in the fields of physicsand engineering will be assigned byone or several renowned editors towrite the chapters comprising eachvolume. The content is selected bythese experts from Springer sources(books, journals, online content)and other systematic and approvedrecent publications of physical andtechnical information.
The volumes will be designed tobe useful as readable desk referencebooks to give a fast and comprehen-sive overview and easy retrieval ofessential reliable key information,including tables, graphs, and bibli-ographies. References to extensivesources are provided.
123
HandbookSpringerof Engineering Statistics
Hoang Pham (Ed.)
With CD-ROM, 377 Figures and 204 Tables
Hoang PhamRutgers the State University of New JerseyPiscataway, NJ 08854, USA
British Library Cataloguing in Publication Data
Springer Handbook of Engineering Statistics1. Engineering - Statistical methodsI. Pham, Hoang620’.0072 ISBN-13: 9781852338060ISBN-10: 1852338067
Library of Congress Control Number: 2006920465
ISBN-10: 1-85233-806-7 e-ISBN: 1-84628-288-8ISBN-13: 978-1-85233-806-0 Printed on acid free paper
c© 2006, Springer-Verlag London LimitedApart from any fair dealing for the purposes of research or private study, orcriticism or review, as permitted under the Copyright, Designs and PatentsAct 1988, this publication may only be reproduced, stored or transmitted,in any form or by any means, with the prior permission in writing of thepublishers, or in the case of reprographic reproduction in accordance withthe terms of licences issued by the Copyright Licensing Agency. Enquiriesconcerning reproduction outside those terms should be sent to the publishers.
The use of registered names, trademarks, etc. in this publication does notimply, even in the absence of a specific statement, that such names are ex-empt from the relevant laws and regulations and therefore free for general use.
The publisher makes no representation, express or implied, with regard tothe accuracy of the information contained in this book and cannot acceptany legal responsibility or liability for any errors or omissions that may bemade.
Production and typesetting: LE-TeX GbR, LeipzigHandbook coordinator: Dr. W. Skolaut, HeidelbergTypography, layout and illustrations: schreiberVIS, SeeheimCover design: eStudio Calamar Steinen, BarcelonaCover production: design&production GmbH, HeidelbergPrinting and binding: Stürtz GmbH, WürzburgPrinted in Germany
SPIN 10956779 100/3100/YL 5 4 3 2 1 0
V
for Michelle, Hoang Jr., and David
VII
Preface
The Springer Handbook of Engineering Statistics, al-together 54 chapters, aims to provide a comprehensivestate-of-the-art reference volume that covers both funda-mental and theoretical work in the areas of engineeringstatistics including failure time models, accelerated lifetesting, incomplete data analysis, stochastic processes,Bayesian inferences, data collection, Bootstrap models,burn-in and screening, competing risk models, cor-related data analysis, counting processes, proportionalhazards regression, design of experiments, DNA se-quence analysis, empirical Bayes, genetic algorithms,evolutionary model, generalized linear model, geo-metric process, life data analysis, logistic regressionmodels, longitudinal data analysis, maintenance, datamining, six sigma, Martingale model, missing data,influential observations, multivariate analysis, multi-variate failure model, nonparametric regression, DNAsequence evolution, system designs, optimization, ran-dom walks, partitioning methods, resampling method,financial engineering and risks, scan statistics, semi-parametric model, smoothing and splines, step-stress lifetesting, statistical process control, statistical inferences,statistical design and diagnostics, process control andimprovement, biological statistical models, samplingtechnique, survival model, time-series model, uniformexperimental designs, among others.
The chapters in this handbook have outlined into sixparts, each contains nine chapters except Part E and F, as
Prof. Hoang Pham
follows:Part A Fundamental Statistics
and Its ApplicationsPart B Process Monitoring
and ImprovementPart C Reliability Models
and Survival AnalysisPart D Regression Methods
and Data MiningPart E Statistical Methods
and ModelingPart F Applications in Engineering StatisticsAll the chapters are written by over 100 outstanding
scholars in their fields of expertise. I am deeply indebtedand wish to thank all of them for their contributions andcooperation. Thanks are also due to the Springer stafffor their patience and editorial work. I hope that prac-titioners will find this Handbook useful when lookingfor solutions to practical problems; researchers, statis-ticians, scientists and engineers, teachers and studentscan use it for quick access to the background, recentresearch and trends, and most important references re-garding certain topics, if not all, in the engineeringstatistics.
January 2006 Hoang PhamPiscataway, New Jersey
IX
List of Authors
Susan L. AlbinRutgers UniversityDepartment of Industrialand Systems Engineering96 Frelinghuysen RoadPiscataway, NJ 08854, USAe-mail: [email protected]
Suprasad V. AmariSenior Reliability EngineerRelex Software Corporation540 Pellis RoadGreensburg, PA 15601, USAe-mail: [email protected]
Y. Alp AslandoganThe University of Texas at ArlingtonComputer Science and Engineering416 Yates St., 206 Nedderman HallArlington, TX 76019-0015, USAe-mail: [email protected]
Jun BaiJP Morgan ChaseCard ServicesDE1-1073, 301 Walnut StreetWilmington, DE 19801, USAe-mail: [email protected]
Jaiwook BaikKorea National Open UniversityDepartment of Information StatisticsJong Ro Gu, Dong Sung Dong 169Seoul, South Koreae-mail: [email protected]
Amit K. BardhanUniversity of Delhi – South CampusDepartment of Operational ResearchBenito Juarez RoadNew Delhi, 110021, Indiae-mail: [email protected]
Anthony BedfordRoyal Melbourne Institute of Technology UniversitySchool of Mathematical and Geospatial SciencesBundoora East Campus, Plenty RdBundoora, Victoria 3083, Australiae-mail: [email protected]
James BrobergRoyal Melbourne Institute of Technology UniversitySchool of Computer Science & InformationTechnologyGPO Box 2476VMelbourne, Victoria 3001, Australia
Michael BulmerUniversity of QueenslandDepartment of MathematicsBrisbane, Qld 4072, Australiae-mail: [email protected]
Zhibin CaoArizona State UniversityComputer Science & Engineering DepartmentPO Box 878809Tempe, AZ 85287-8809, USAe-mail: [email protected]
Philippe CastagliolaUniversité de Nantes and IRCCyN UMR CNRS 6597Institut Universitaire de Technologie de NantesQualité Logistique Industrielle et Organisation2 avenue du Professeur Jean RouxelBP 539-44475 Carquefou, Francee-mail: [email protected]
Giovanni CelanoUniversity of CataniaDipartimento di Ingegneria Industrialee MeccanicaViale Andrea Doria 6Catania, 95125, Italye-mail: [email protected]
X List of Authors
Ling-Yau ChanThe University of Hong KongDepartment of Industrial and ManufacturingSystems EngineeringPokfulam RoadHong Konge-mail: [email protected]
Ted ChangUniversity of VirginiaDepartment of StatisticsKerchhof Hall, PO Box 400135Charlottesville, VA 22904-4135, USAe-mail: [email protected]
Victoria ChenUniversity of Texas at ArlingtonIndustrial and Manufacturing Systems EngineeringCampus Box 19017Arlington, TX 76019-0017, USAe-mail: [email protected]
Yinong ChenArizona State UniversityComputer Science and Engineering DepartmentPO Box 878809Tempe, AZ 85287-8809, USAe-mail: [email protected]
Peter DimopoulosRoyal Melbourne Institute of Technology UniversityComputer Science and IT376-392 Swanston StreetMelbourne, 3001, Australiae-mail: [email protected]
Fenghai DuanDepartment of Preventiveand Societal Medicine984350 Nebraska Medical CenterOmaha, NE 68198-4350, USAe-mail: [email protected]
Veronica EsaulovaOtto-von-Guericke-University MagdeburgDepartment of MathematicsUniversitätsplatz 2Magdeburg, 39016, Germanye-mail: [email protected]
Luis A. EscobarLouisiana State UniversityDepartment of Experimental Statistics159-A Agricultural Administration Bldg.Baton Rouge, LA 70803, USAe-mail: [email protected]
Chun FanArizona State UniversityComputer Science & Engineering DepartmentPO Box 878809Tempe, AZ 85287-8809, USAe-mail: [email protected]
Kai-Tai FangHong Kong Baptist UniversityDepartment of MathematicsKowloon Tong, Hong Konge-mail: [email protected]
Qianmei FengUniversity of HoustonDepartment of Industrial EngineeringE206 Engineering Bldg 2Houston, TX 77204, USAe-mail: [email protected]
Emilio FerrariUniversity of BolognaDepartment of Industrialand Mechanical Engineering (D.I.E.M.)viale Risorgimento, 2Bologna, 40136, Italye-mail: [email protected]
Sergio FicheraUniversity of CataniaDepartment Industrialand Mechanical Engineeringavenale Andrea Doria 6Catania, 95125, Italye-mail: [email protected]
Maxim FinkelsteinUniversity of the Free StateDepartment of Mathematical StatisticsPO Box 339Bloemfontein, 9300, South Africae-mail: [email protected]
List of Authors XI
Mitsuo GenWaseda UniversityGraduate School of Information,Production & Systems2-7 Hibikino, Wakamatsu-KuKitakyushu, 808-0135, Japane-mail: [email protected]
Amrit L. GoelSyracuse UniversityDepartment of Electrical Engineeringand Computer ScienceSyracuse, NY 13244, USAe-mail: [email protected]
Thong N. GohNational University of SingaporeIndustrial and Systems Engineering Dept.10 Kent Ridge CrescentSingapore, 119260, Republic of Singaporee-mail: [email protected]
Raj K. GovindarajuMassey UniversityInstitute of Information Sciencesand TechnologyPalmerston North, 5301, New Zealande-mail: [email protected]
Xuming HeUniversity of Illinois at Urbana-ChampaignDepartment of Statistics725 S. Wright StreetChampaign, IL 61820, USAe-mail: [email protected]
Chengcheng HuHarvard School of Public HealthDepartment of Biostatistics655 Huntington AvenueBoston, MA 02115, USAe-mail: [email protected]
Feifang HuUniversity of VirginiaDepartment of StatisticsCharlottesville, VA 22904, USAe-mail: [email protected]
Hai HuangIntel Corp CH3-20Component Automation Systems5000 W. Chandler Blvd.Chandler, AZ 85226, USAe-mail: [email protected]
Jian HuangUniversity of IowaDepartment of Statistics and Actuarial Science241 Schaeffler HallIowa City, IA 52242, USAe-mail: [email protected]
Tao HuangYale University, School of MedicineDepartment of Epidemiology and Public Health60 College StreetNew Haven, CT 06520, USAe-mail: [email protected]
Wei JiangStevens Institute of TechnologyDepartment of Systems Engineeringand Engineering ManagementCastle Point of HudsonHoboken, NJ 07030, USAe-mail: [email protected]
Richard JohnsonUniversity of Wisconsin – MadisonDepartment of Statistics1300 University AvenueMadison, WI 53706-1685, USAe-mail: [email protected]
Kailash C. KapurUniversity of WashingtonIndustrial EngineeringBox 352650Seattle, WA 98195-2650, USAe-mail: [email protected]
P. K. KapurUniversity of DelhiDepartment of Operational ResearchDelhi, 110007, Indiae-mail: [email protected]
XII List of Authors
Kyungmee O. KimKonkuk UniversityDepartment of Industrial Engineering1 Hwayang-dong, Gwangjin-guSeoul, 143-701, S. Koreae-mail: [email protected]
Taeho KimKorea TelecomStrategic Planning Office221 Jungja-dong, Bundang-kuSungnam, Kyonggi-do, 463-711, S. Koreae-mail: [email protected]
Way KuoUniversity of TennesseeDepartment of Electricaland Computer Engineering124 Perkins HallKnoxville, TN 37996-2100, USAe-mail: [email protected]
Paul KvamGeorgia Institute of TechnologySchool of Industrial and Systems Engineering755 Ferst DriveAtlanta, GA 30332-0205, USAe-mail: [email protected]
Chin-Diew LaiMassey UniversityInstitute of Information Sciences and TechnologyTuritea CampusPalmerston North, New Zealande-mail: [email protected]
Jae K. LeeUniversity of VirginiaPublic Health SciencesPO Box 800717Charlottesville, VA 22908, USAe-mail: [email protected]
Kit-Nam F. LeungCity University of Hong KongDepartment of Management SciencesTat Chee AvenueKowloon Tong, Hong Konge-mail: [email protected]
Ruojia LiGlobal Statistical SciencesLilly Corporate CenterDC 3844Indianapolis, IN 46285, USAe-mail: [email protected]
Wenjian LiJavelin Direct, Inc.Marketing Science7850 Belt Line RoadIrving, TX 75063, USAe-mail: [email protected]
Xiaoye LiYale UniversityDepartment of Applied Mathematics300 George StreetNew Heaven, CT 06511, USAe-mail: [email protected]
Yi LiHarvard UniversityDepartment of Biostatistics44 Binney Street, M232Boston, MA 02115, USAe-mail: [email protected]
Hojung LimKorea Electronics Technology Institute (KETI)Ubiquitous Computing Research Center68 Yatap-dong, Bundang-GuSeongnam-Si, Gyeonggi-Do 463-816, Koreae-mail: [email protected]
Haiqun LinYale University School of MedicineDepartment of Epidemiologyand Public Health60 College StreetNew Haven, CT 06520, USAe-mail: [email protected]
Nan LinWashington University in Saint LouisDepartment of MathematicsCampus Box 1146, One Brookings DriveSt. Louis, MO 63130, USAe-mail: [email protected]
List of Authors XIII
Wei-Yin LohUniversity of Wisconsin – MadisonDepartment of Statistics1300 University AvenueMadison, WI 53706, USAe-mail: [email protected]
Jye-Chyi LuThe School of Industrial and SystemsEngineeringGeorgia Institute of Technology765 Ferst Drive, Campus Box 0205Atlanta, GA 30332, USAe-mail: [email protected]
William Q. Meeker, Jr.Iowa State UniversityDepartment of Statistics304C Snedecor HallAmes, IA 50011-1210, USAe-mail: [email protected]
Mirjam MoerbeekUtrecht UniversityDepartment of Methodology and StatisticsPO Box 80140Utrecht, 3508 TC, Netherlandse-mail: [email protected]
Terrence E. MurphyYale University School of MedicineDepartment of Internal Medicine1 Church StNew Haven, CT 06437, USAe-mail: [email protected]
D.N. Pra MurthyThe University of QueenslandDivision of Mechanical EngineeringBrisbane, QLD 4072, Australiae-mail: [email protected]
H. N. NagarajaOhio State UniversityDepartment of Statistics404 Cockins Hall, 1958 Neil AvenueColumbus, OH 43210-1247, USAe-mail: [email protected]
Toshio NakagawaAichi Institute of TechnologyDepartment of Marketing and Information Systems1247 Yachigusa, Yagusa-choToyota, 470-0392, Japane-mail: [email protected]
Joseph NausRutgers UniversityDepartment of StatisticsHill Center for the Mathematical SciencesPiscataway, NJ 08855, USAe-mail: [email protected]
Harriet B. NembhardPennsylvania State UniversityHarold and Inge Marcus Department of Industrialand Manufacturing EngineeringUniversity Park, PA 16802, USAe-mail: [email protected]
Douglas NoeUniversity of Illinois at Urbana-ChampaignDepartment of Statistics725 S. Wright St.Champaign, IL 61820, USAe-mail: [email protected]
Arrigo PareschiUniversity of BolognaDepartment of Industrial and MechanicalEngineering (D.I.E.M.)viale Risorgimento, 2Bologna, 40136, Italye-mail: [email protected]
Francis PascualWashington State UniversityDepartment of MathematicsPO Box 643113Pullman, WA 99164-3113, USAe-mail: [email protected]
Raymond A. PaulC2 PolicyU.S. Department of Defense (DoD)3400 20th Street NEWashington, DC 20017, USAe-mail: [email protected]
XIV List of Authors
Alessandro PersonaUniversity of PaduaDepartment of Industrialand Technology ManagementStradella S. Nicola, 3Vicenza, 36100, Italye-mail: [email protected]
Daniel PeñaUniversidad Carlos III de MadridDepartamento de EstadisticaC/Madrid 126Getafe (Madrid), 28903, Spaine-mail: [email protected]
Hoang PhamRutgers UniversityDepartment of Industrialand Systems Engineering96 Frelinghuysen RoadPiscataway, NJ 08854, USAe-mail: [email protected]
John QuigleyUniversity of StrathclydeDepartment of Management Science40 George StreetGlasgow, G1 1QE, Scotlande-mail: [email protected]
Alberto RegattieriBologna UniversityDepartment of Industrialand Mechanical Engineeringviale Risorgimento, 2Bologna, 40136, Italye-mail: [email protected]
Miyoung ShinKyungpook National UniversitySchool of Electrical Engineeringand Computer Science1370 Sankyuk-dong, Buk-guDaegu, 702-701, Republic of Koreae-mail: [email protected]
Karl SigmanColumbia University in the City of New York,School of Engineering and Applied ScienceCenter for Applied Probability (CAP)500 West 120th St., MC: 4704New York, NY 10027, USAe-mail: [email protected]
Loon C. TangNational University of SingaporeDepartment of Industrialand Systems Engineering1, Engineering Drive 2Singapore, 117576, Singaporee-mail: [email protected]
Charles S. TapieroPolytechnic UniversityTechnology Managementand Financial EngineeringSix MetroTech CenterBrooklyn, NY 11201, USAe-mail: [email protected]
Zahir TariRoyal Melbourne Institute of Technology UniversitySchool of Computer Scienceand Information TechnologyGPO Box 2476VMelbourne, Victoria 3001, Australiae-mail: [email protected]
Xiaolin TengTime Warner Inc.Research Department135 W 50th Street, 751-ENew York, NY 10020, USAe-mail: [email protected]
Wei-Tek TsaiArizona State UniversityComputer Science & Engineering DepartmentPO Box 878809Tempe, AZ 85287-8809, USAe-mail: [email protected]
List of Authors XV
Kwok-Leung TsuiGeorgia Institute of TechnologySchool of Industrial and Systems Engineering765 Ferst DriveAtlanta, GA 30332, USAe-mail: [email protected]
Fugee TsungHong Kong University of Scienceand TechnologyDepartment of Industrial Engineeringand Logistics ManagementClear Water BayKowloon, Hong Konge-mail: [email protected]
Lesley WallsUniversity of StrathclydeDepartment of Management Science40 George StreetGlasgow, G1 1QE, Scotlande-mail: [email protected]
Wei WangDana-Farber Cancer InstituteDepartment of Biostatisticsand Computational Biology44 Binney StreetBoston, MA 02115, USAe-mail: [email protected]
Kenneth WilliamsYale UniversityMolecular Biophysics and Biochemistry300 George Street, G005New Haven, CT 06520, USAe-mail: [email protected]
Richard J. WilsonThe University of QueenslandDepartment of MathematicsBrisbane, 4072, Australiae-mail: [email protected]
Baolin WuUniversity of Minnesota, School of Public HealthDivision of BiostatisticsA460 Mayo Building,MMC 303, 420 Delaware St SEMinneapolis, MN 55455, USAe-mail: [email protected]
Min XieNational University of SingaporeDept. of Industrial & Systems EngineeringKent Ridge CrescentSingapore, 119 260, Singaporee-mail: [email protected]
Chengjie XiongWashington University in St. LouisDivision of Biostatistics660 South Euclid Avenue, Box 8067St. Louis, MO 63110, USAe-mail: [email protected]
Di XuAmercian ExpressDept. of Risk Managementand Decision Science200 Vesey StreetNew York, NY 10285, USAe-mail: [email protected]
Shigeru YamadaTottori UniversityDepartment of Social Systems EngineeringMinami, 4-101 KoyamaTottori-shi, 680-8552, Japane-mail: [email protected]
Jun YanUniversity of IowaDepartment of Statistics and Actuarial Science241 Shaeffer HallIowa City, IA 52242, USAe-mail: [email protected]
XVI List of Authors
Shang-Kuo YangDepartment of Mechanical EngineeringNational ChinYi Institute of TechnologyNo. 35, Lane 215, Sec. 1, Jungshan Rd.Taiping City, 411, Taiwan, R.O.C.e-mail: [email protected]
Kai YuWashington University in St. Louis,School of MedicineDivision of BiostatisticsBox 8067St. Louis, MO 63110, USAe-mail: [email protected]
Weichuan YuYale Center for Statistical Genomicsand Proteomics, Yale UniversityDepartment of Molecular Biophysicsand Biochemistry300 George StreetNew Haven, CT 06511, USAe-mail: [email protected]
Panlop ZeephongsekulRoyal Melbourne Institute of Technology UniversitySchool of Mathematical and Geospatial SciencesGPO Box 2467VMelbourne, Victoria 3000, Australiae-mail: [email protected]
Cun-Hui ZhangRutgers UniversityDepartment of StatisticsHill Center, Busch CampusPiscataway, NJ 08854, USAe-mail: [email protected]
Heping ZhangYale University School of MedicineDepartment of Epidemiology and Public Health60 College StreetNew Haven, CT 06520-8034, USAe-mail: [email protected]
Hongyu ZhaoYale University School of MedicineDepartment of Epidemiology and Public Health60 College StreetNew Haven, CT 06520-8034, USAe-mail: [email protected]
Kejun ZhuChina University of GeosciencesSchool of ManagementNo. 388 Lumo RoadWuhan, 430074, Peoples Republic of Chinae-mail: [email protected]
XVII
Contents
List of Tables.............................................................................................. XXXIList of Abbreviations ................................................................................. XLI
Part A Fundamental Statistics and Its Applications
1 Basic Statistical ConceptsHoang Pham ........................................................................................... 31.1 Basic Probability Measures ............................................................. 31.2 Common Probability Distribution Functions .................................... 71.3 Statistical Inference and Estimation ............................................... 171.4 Stochastic Processes ...................................................................... 321.5 Further Reading ............................................................................ 42References............................................................................................... 421.A Appendix: Distribution Tables ........................................................ 431.B Appendix: Laplace Transform ......................................................... 47
2 Statistical Reliability with ApplicationsPaul Kvam, Jye-Chyi Lu ............................................................................ 492.1 Introduction and Literature Review ................................................ 492.2 Lifetime Distributions in Reliability ................................................ 502.3 Analysis of Reliability Data ............................................................. 542.4 System Reliability .......................................................................... 56References............................................................................................... 60
3 Weibull Distributions and Their ApplicationsChin-Diew Lai, D.N. Pra Murthy, Min Xie ................................................... 633.1 Three-Parameter Weibull Distribution ............................................ 643.2 Properties ..................................................................................... 643.3 Modeling Failure Data ................................................................... 673.4 Weibull-Derived Models ................................................................ 703.5 Empirical Modeling of Data ............................................................ 733.6 Applications .................................................................................. 74References............................................................................................... 76
4 Characterizations of Probability DistributionsH.N. Nagaraja ......................................................................................... 794.1 Characterizing Functions ................................................................ 804.2 Data Types and Characterizing Conditions ....................................... 814.3 A Classification of Characterizations................................................ 834.4 Exponential Distribution ................................................................ 844.5 Normal Distribution ....................................................................... 854.6 Other Continuous Distributions ...................................................... 87
XVIII Contents
4.7 Poisson Distribution and Process .................................................... 884.8 Other Discrete Distributions ........................................................... 904.9 Multivariate Distributions and Conditional Specification.................. 904.10 Stability of Characterizations.......................................................... 924.11 Applications .................................................................................. 924.12 General Resources ......................................................................... 93References............................................................................................... 94
5 Two-Dimensional Failure ModelingD.N. Pra Murthy, Jaiwook Baik, Richard J. Wilson, Michael Bulmer............. 975.1 Modeling Failures .......................................................................... 985.2 Black-Box Modeling Process .......................................................... 985.3 One-Dimensional Black-Box Failure Modeling ................................ 995.4 Two-Dimensional Black-Box Failure Modeling ................................ 1035.5 A New Approach to Two-Dimensional Modeling .............................. 1075.6 Conclusions ................................................................................... 110References............................................................................................... 110
6 Prediction Intervals for Reliability Growth Modelswith Small Sample SizesJohn Quigley, Lesley Walls ........................................................................ 1136.1 Modified IBM Model – A Brief History ............................................. 1146.2 Derivation of Prediction Intervals for the Time to Detection
of Next Fault ................................................................................. 1156.3 Evaluation of Prediction Intervals for the Time to Detect Next Fault . 1176.4 Illustrative Example....................................................................... 1196.5 Conclusions and Reflections ........................................................... 122References............................................................................................... 122
7 Promotional Warranty Policies: Analysis and PerspectivesJun Bai, Hoang Pham .............................................................................. 1257.1 Classification of Warranty Policies .................................................. 1267.2 Evaluation of Warranty Policies ...................................................... 1297.3 Concluding Remarks ...................................................................... 134References............................................................................................... 134
8 Stationary Marked Point ProcessesKarl Sigman ............................................................................................ 1378.1 Basic Notation and Terminology ..................................................... 1388.2 Inversion Formulas ........................................................................ 1448.3 Campbell’s Theorem for Stationary MPPs ........................................ 1458.4 The Palm Distribution: Conditioning in a Point at the Origin ............ 1468.5 The Theorems of Khintchine, Korolyuk, and Dobrushin.................... 1468.6 An MPP Jointly with a Stochastic Process......................................... 1478.7 The Conditional Intensity Approach ................................................ 1488.8 The Non-Ergodic Case .................................................................... 1508.9 MPPs in R
d .................................................................................... 150References............................................................................................... 152
Contents XIX
9 Modeling and Analyzing Yield, Burn-In and Reliabilityfor Semiconductor Manufacturing: OverviewWay Kuo, Kyungmee O. Kim, Taeho Kim .................................................... 1539.1 Semiconductor Yield ...................................................................... 1549.2 Semiconductor Reliability .............................................................. 1599.3 Burn-In ........................................................................................ 1609.4 Relationships Between Yield, Burn-In and Reliability ..................... 1639.5 Conclusions and Future Research ................................................... 166References............................................................................................... 166
Part B Process Monitoring and Improvement
10 Statistical Methods for Quality and Productivity ImprovementWei Jiang, Terrence E. Murphy, Kwok-Leung Tsui....................................... 17310.1 Statistical Process Control for Single Characteristics ......................... 17410.2 Robust Design for Single Responses ................................................ 18110.3 Robust Design for Multiple Responses ............................................ 18510.4 Dynamic Robust Design ................................................................. 18610.5 Applications of Robust Design ........................................................ 187References............................................................................................... 188
11 Statistical Methods for Product and Process ImprovementKailash C. Kapur, Qianmei Feng................................................................ 19311.1 Six Sigma Methodology and the (D)MAIC(T) Process .......................... 19511.2 Product Specification Optimization ................................................. 19611.3 Process Optimization ..................................................................... 20411.4 Summary ...................................................................................... 211References............................................................................................... 212
12 Robust Optimization in Quality EngineeringSusan L. Albin, Di Xu ................................................................................ 21312.1 An Introduction to Response Surface Methodology .......................... 21612.2 Minimax Deviation Method to Derive Robust Optimal Solution ......... 21812.3 Weighted Robust Optimization ....................................................... 22212.4 The Application of Robust Optimization in Parameter Design ........... 224References............................................................................................... 227
13 Uniform Design and Its Industrial ApplicationsKai-Tai Fang, Ling-Yau Chan ................................................................... 22913.1 Performing Industrial Experiments with a UD ................................. 23113.2 Application of UD in Accelerated Stress Testing ................................ 23313.3 Application of UDs in Computer Experiments .................................. 23413.4 Uniform Designs and Discrepancies ................................................ 23613.5 Construction of Uniform Designs in the Cube .................................. 23713.6 Construction of UDs for Experiments with Mixtures ......................... 240
XX Contents
13.7 Relationships Between Uniform Design and Other Designs .............. 24313.8 Conclusion .................................................................................... 245References............................................................................................... 245
14 Cuscore Statistics: Directed Process Monitoringfor Early Problem DetectionHarriet B. Nembhard................................................................................ 24914.1 Background and Evolution of the Cuscore in Control Chart
Monitoring .................................................................................... 25014.2 Theoretical Development of the Cuscore Chart ................................. 25114.3 Cuscores to Monitor for Signals in White Noise ................................ 25214.4 Cuscores to Monitor for Signals in Autocorrelated Data .................... 25414.5 Cuscores to Monitor for Signals in a Seasonal Process ...................... 25514.6 Cuscores in Process Monitoring and Control .................................... 25614.7 Discussion and Future Work ........................................................... 258References............................................................................................... 260
15 Chain SamplingRaj K. Govindaraju .................................................................................. 26315.1 ChSP-1 Chain Sampling Plan ........................................................... 26415.2 Extended Chain Sampling Plans ..................................................... 26515.3 Two-Stage Chain Sampling ............................................................ 26615.4 Modified ChSP-1 Plan ..................................................................... 26815.5 Chain Sampling and Deferred Sentencing ....................................... 26915.6 Comparison of Chain Sampling with Switching Sampling Systems .... 27215.7 Chain Sampling for Variables Inspection ......................................... 27315.8 Chain Sampling and CUSUM ............................................................ 27415.9 Other Interesting Extensions .......................................................... 27615.10 Concluding Remarks ...................................................................... 276References............................................................................................... 276
16 Some Statistical Models for the Monitoringof High-Quality ProcessesMin Xie, Thong N. Goh ............................................................................. 28116.1 Use of Exact Probability Limits ....................................................... 28216.2 Control Charts Based on Cumulative Count of Conforming Items ....... 28316.3 Generalization of the c-Chart ........................................................ 28416.4 Control Charts for the Monitoring of Time-Between-Events ............. 28616.5 Discussion ..................................................................................... 288References............................................................................................... 289
17 Monitoring Process Variability Using EWMAPhilippe Castagliola, Giovanni Celano, Sergio Fichera................................ 29117.1 Definition and Properties of EWMA Sequences ................................ 29217.2 EWMA Control Charts for Process Position ........................................ 29517.3 EWMA Control Charts for Process Dispersion..................................... 298
Contents XXI
17.4 Variable Sampling Interval EWMA Control Charts for ProcessDispersion..................................................................................... 310
17.5 Conclusions ................................................................................... 323References............................................................................................... 324
18 Multivariate Statistical Process Control Schemesfor Controlling a MeanRichard A. Johnson, Ruojia Li ................................................................... 32718.1 Univariate Quality Monitoring Schemes .......................................... 32818.2 Multivariate Quality Monitoring Schemes ........................................ 33118.3 An Application of the Multivariate Procedures ................................ 33618.4 Comparison of Multivariate Quality Monitoring Methods ................. 33718.5 Control Charts Based on Principal Components ............................... 33818.6 Difficulties of Time Dependence in the Sequence
of Observations ............................................................................. 341References............................................................................................... 344
Part C Reliability Models and Survival Analysis
19 Statistical Survival Analysis with ApplicationsChengjie Xiong, Kejun Zhu, Kai Yu ............................................................ 34719.1 Sample Size Determination to Compare Mean or Percentile
of Two Lifetime Distributions ......................................................... 34919.2 Analysis of Survival Data from Special Cases
of Step-Stress Life Tests ................................................................. 355References............................................................................................... 365
20 Failure Rates in Heterogeneous PopulationsMaxim Finkelstein, Veronica Esaulova....................................................... 36920.1 Mixture Failure Rates and Mixing Distributions ............................... 37120.2 Modeling the Impact of the Environment ....................................... 37720.3 Asymptotic Behaviors of Mixture Failure Rates ................................ 380References............................................................................................... 385
21 Proportional Hazards Regression ModelsWei Wang, Chengcheng Hu ...................................................................... 38721.1 Estimating the Regression Coefficients β ......................................... 38821.2 Estimating the Hazard and Survival Functions ................................ 38921.3 Hypothesis Testing ........................................................................ 39021.4 Stratified Cox Model ...................................................................... 39021.5 Time-Dependent Covariates ........................................................... 39021.6 Goodness-of-Fit and Model Checking ............................................ 39121.7 Extension of the Cox Model ............................................................ 39321.8 Example ....................................................................................... 394References............................................................................................... 395
XXII Contents
22 Accelerated Life Test Models and Data AnalysisFrancis Pascual, William Q. Meeker, Jr., Luis A. Escobar.............................. 39722.1 Accelerated Tests ........................................................................... 39822.2 Life Distributions ........................................................................... 40022.3 Acceleration Models ...................................................................... 40022.4 Analysis of Accelerated Life Test Data .............................................. 40722.5 Further Examples .......................................................................... 41222.6 Practical Considerations for Interpreting the Analysis of ALT Data ..... 42122.7 Other Kinds of ATs ......................................................................... 42122.8 Some Pitfalls of Accelerated Testing ................................................ 42322.9 Computer Software for Analyzing ALT Data ...................................... 424References............................................................................................... 425
23 Statistical Approaches to Planning of Accelerated ReliabilityTestingLoon C. Tang............................................................................................ 42723.1 Planning Constant-Stress Accelerated Life Tests .............................. 42823.2 Planning Step-Stress ALT (SSALT) ..................................................... 43223.3 Planning Accelerated Degradation Tests (ADT) ................................. 43623.4 Conclusions ................................................................................... 439References............................................................................................... 440
24 End-to-End (E2E) Testing and Evaluation of High-AssuranceSystemsRaymond A. Paul, Wei-Tek Tsai, Yinong Chen, Chun Fan, Zhibin Cao,Hai Huang............................................................................................... 44324.1 History and Evolution of E2E Testing and Evaluation........................ 44424.2 Overview of the Third and Fourth Generations of the E2E T&E .......... 44924.3 Static Analyses .............................................................................. 45124.4 E2E Distributed Simulation Framework ........................................... 45324.5 Policy-Based System Development ................................................. 45924.6 Dynamic Reliability Evaluation ....................................................... 46524.7 The Fourth Generation of E2E T&E on Service-Oriented
Architecture .................................................................................. 47024.8 Conclusion and Summary............................................................... 473References............................................................................................... 474
25 Statistical Models in Software Reliabilityand Operations ResearchP.K. Kapur, Amit K. Bardhan .................................................................... 47725.1 Interdisciplinary Software Reliability Modeling ............................... 47925.2 Release Time of Software ............................................................... 48625.3 Control Problem ............................................................................ 48925.4 Allocation of Resources in Modular Software ................................... 491References............................................................................................... 495
Contents XXIII
26 An Experimental Study of Human Factors in Software ReliabilityBased on a Quality Engineering ApproachShigeru Yamada ...................................................................................... 49726.1 Design Review and Human Factors ................................................. 49826.2 Design-Review Experiment ............................................................ 49926.3 Analysis of Experimental Results .................................................... 50026.4 Investigation of the Analysis Results .............................................. 50126.5 Confirmation of Experimental Results ............................................. 50226.6 Data Analysis with Classification of Detected Faults ......................... 504References............................................................................................... 506
27 Statistical Models for Predicting Reliability of Software Systemsin Random EnvironmentsHoang Pham, Xiaolin Teng....................................................................... 50727.1 A Generalized NHPP Software Reliability Model ............................... 50927.2 Generalized Random Field Environment (RFE) Model ....................... 51027.3 RFE Software Reliability Models ...................................................... 51127.4 Parameter Estimation .................................................................... 513References............................................................................................... 519
Part D Regression Methods and Data Mining
28 Measures of Influence and Sensitivity in Linear RegressionDaniel Peña............................................................................................. 52328.1 The Leverage and Residuals in the Regression Model ...................... 52428.2 Diagnosis for a Single Outlier ......................................................... 52528.3 Diagnosis for Groups of Outliers ..................................................... 52828.4 A Statistic for Sensitivity for Large Data Sets .................................... 53228.5 An Example: The Boston Housing Data ........................................... 53328.6 Final Remarks ............................................................................... 535References............................................................................................... 535
29 Logistic Regression Tree AnalysisWei-Yin Loh............................................................................................. 53729.1 Approaches to Model Fitting .......................................................... 53829.2 Logistic Regression Trees ................................................................ 54029.3 LOTUS Algorithm ............................................................................ 54229.4 Example with Missing Values ......................................................... 54329.5 Conclusion .................................................................................... 549References............................................................................................... 549
30 Tree-Based Methods and Their ApplicationsNan Lin, Douglas Noe, Xuming He ............................................................ 55130.1 Overview....................................................................................... 55230.2 Classification and Regression Tree (CART) ........................................ 55530.3 Other Single-Tree-Based Methods .................................................. 561
XXIV Contents
30.4 Ensemble Trees ............................................................................. 56530.5 Conclusion .................................................................................... 568References............................................................................................... 569
31 Image Registration and Unknown Coordinate SystemsTed Chang ............................................................................................... 57131.1 Unknown Coordinate Systems and Their Estimation ........................ 57231.2 Least Squares Estimation ............................................................... 57531.3 Geometry of O(p) and SO(p) ......................................................... 57831.4 Statistical Properties of M-Estimates .............................................. 58031.5 Diagnostics ................................................................................... 587References............................................................................................... 590
32 Statistical Genetics for Genomic Data AnalysisJae K. Lee ................................................................................................ 59132.1 False Discovery Rate ...................................................................... 59232.2 Statistical Tests for Genomic Data ................................................... 59332.3 Statistical Modeling for Genomic Data ............................................ 59632.4 Unsupervised Learning: Clustering ................................................. 59832.5 Supervised Learning: Classification ................................................. 599References............................................................................................... 603
33 Statistical Methodologies for Analyzing Genomic DataFenghai Duan, Heping Zhang .................................................................. 60733.1 Second-Level Analysis of Microarray Data ....................................... 60933.2 Third-Level Analysis of Microarray Data .......................................... 61133.3 Fourth-Level Analysis of Microarray Data ........................................ 61833.4 Final Remarks ............................................................................... 618References............................................................................................... 619
34 Statistical Methods in ProteomicsWeichuan Yu, Baolin Wu, Tao Huang, Xiaoye Li, Kenneth Williams,Hongyu Zhao ........................................................................................... 62334.1 Overview....................................................................................... 62334.2 MS Data Preprocessing ................................................................... 62534.3 Feature Selection .......................................................................... 62834.4 Sample Classification ..................................................................... 63034.5 Random Forest: Joint Modelling of Feature Selection
and Classification .......................................................................... 63034.6 Protein/Peptide Identification ........................................................ 63334.7 Conclusion and Perspective ............................................................ 635References............................................................................................... 636
35 Radial Basis Functions for Data MiningMiyoung Shin, Amrit L. Goel ..................................................................... 63935.1 Problem Statement ....................................................................... 64035.2 RBF Model and Parameters ............................................................ 641
Contents XXV
35.3 Design Algorithms ......................................................................... 64235.4 Illustrative Example....................................................................... 64335.5 Diabetes Disease Classification ....................................................... 64535.6 Analysis of Gene Expression Data ................................................... 64735.7 Concluding Remarks ...................................................................... 648References............................................................................................... 648
36 Data Mining Methods and ApplicationsKwok-Leung Tsui, Victoria Chen, Wei Jiang, Y. Alp Aslandogan .................. 65136.1 The KDD Process ............................................................................ 65336.2 Handling Data ............................................................................... 65436.3 Data Mining (DM) Models and Algorithms ....................................... 65536.4 DM Research and Applications ....................................................... 66436.5 Concluding Remarks ...................................................................... 667References............................................................................................... 667
Part E Modeling and Simulation Methods
37 Bootstrap, Markov Chain and Estimating FunctionFeifang Hu .............................................................................................. 67337.1 Overview....................................................................................... 67337.2 Classical Bootstrap ......................................................................... 67537.3 Bootstrap Based on Estimating Equations ....................................... 67837.4 Markov Chain Marginal Bootstrap ................................................... 68137.5 Applications .................................................................................. 68237.6 Discussion ..................................................................................... 684References............................................................................................... 684
38 Random EffectsYi Li......................................................................................................... 68738.1 Overview....................................................................................... 68738.2 Linear Mixed Models...................................................................... 68838.3 Generalized Linear Mixed Models ................................................... 69038.4 Computing MLEs for GLMMs ............................................................ 69238.5 Special Topics: Testing Random Effects for Clustered Categorical
Data ............................................................................................. 69738.6 Discussion ..................................................................................... 701References............................................................................................... 701
39 Cluster Randomized Trials: Design and AnalysisMirjam Moerbeek ..................................................................................... 70539.1 Cluster Randomized Trials .............................................................. 70639.2 Multilevel Regression Model and Mixed Effects ANOVA Model ........... 70739.3 Optimal Allocation of Units ............................................................ 70939.4 The Effect of Adding Covariates ...................................................... 71239.5 Robustness Issues.......................................................................... 713
XXVI Contents
39.6 Optimal Designs for the Intra-Class Correlation Coefficient .............. 71539.7 Conclusions and Discussion ............................................................ 717References............................................................................................... 717
40 A Two-Way Semilinear Model for Normalization and Analysisof Microarray DataJian Huang, Cun-Hui Zhang..................................................................... 71940.1 The Two-Way Semilinear Model ..................................................... 72040.2 Semiparametric M-Estimation in TW-SLM ....................................... 72140.3 Extensions of the TW-SLM .............................................................. 72440.4 Variance Estimation and Inference for β ......................................... 72540.5 An Example and Simulation Studies ............................................... 72740.6 Theoretical Results ........................................................................ 73240.7 Concluding Remarks ...................................................................... 734References............................................................................................... 734
41 Latent Variable Models for Longitudinal Data with FlexibleMeasurement ScheduleHaiqun Lin .............................................................................................. 73741.1 Hierarchical Latent Variable Models for Longitudinal Data ............... 73841.2 Latent Variable Models for Multidimensional Longitudinal Data....... 74141.3 Latent Class Mixed Model for Longitudinal Data .............................. 74341.4 Structural Equation Model with Latent Variables
for Longitudinal Data .................................................................... 74441.5 Concluding Remark: A Unified Multilevel Latent Variable Model ....... 746References............................................................................................... 747
42 Genetic Algorithms and Their ApplicationsMitsuo Gen .............................................................................................. 74942.1 Foundations of Genetic Algorithms................................................. 75042.2 Combinatorial Optimization Problems ............................................ 75342.3 Network Design Problems .............................................................. 75742.4 Scheduling Problems ..................................................................... 76142.5 Reliability Design Problem ............................................................. 76342.6 Logistic Network Problems ............................................................. 76642.7 Location and Allocation Problems .................................................. 769References............................................................................................... 772
43 Scan StatisticsJoseph Naus ............................................................................................ 77543.1 Overview....................................................................................... 77543.2 Temporal Scenarios ....................................................................... 77643.3 Higher Dimensional Scans.............................................................. 78443.4 Other Scan Statistics ...................................................................... 786References............................................................................................... 788
Contents XXVII
44 Condition-Based Failure PredictionShang-Kuo Yang ..................................................................................... 79144.1 Overview....................................................................................... 79244.2 Kalman Filtering ........................................................................... 79444.3 Armature-Controlled DC Motor ....................................................... 79644.4 Simulation System ......................................................................... 79744.5 Armature-Controlled DC Motor Experiment ..................................... 80144.6 Conclusions ................................................................................... 804References............................................................................................... 804
45 Statistical Maintenance Modeling for Complex SystemsWenjian Li, Hoang Pham ......................................................................... 80745.1 General Probabilistic Processes Description ..................................... 80945.2 Nonrepairable Degraded Systems Reliability Modeling .................... 81045.3 Repairable Degraded Systems Modeling.......................................... 81945.4 Conclusions and Perspectives ......................................................... 83145.5 Appendix A ................................................................................... 83145.6 Appendix B ................................................................................... 832References............................................................................................... 833
46 Statistical Models on MaintenanceToshio Nakagawa .................................................................................... 83546.1 Time-Dependent Maintenance....................................................... 83646.2 Number-Dependent Maintenance .................................................. 83846.3 Amount-Dependent Maintenance .................................................. 84246.4 Other Maintenance Models ............................................................ 843References............................................................................................... 847
Part F Applications in Engineering Statistics
47 Risks and Assets PricingCharles S. Tapiero .................................................................................... 85147.1 Risk and Asset Pricing .................................................................... 85347.2 Rational Expectations, Risk-Neutral Pricing and Asset Pricing .......... 85747.3 Consumption Capital Asset Price Model and Stochastic Discount
Factor ........................................................................................... 86247.4 Bonds and Fixed-Income Pricing ................................................... 86547.5 Options ......................................................................................... 87247.6 Incomplete Markets and Implied Risk-Neutral Distributions ............ 880References............................................................................................... 898
48 Statistical Management and Modeling for Demand of Spare PartsEmilio Ferrari, Arrigo Pareschi, Alberto Regattieri, Alessandro Persona ....... 90548.1 The Forecast Problem for Spare Parts .............................................. 90548.2 Forecasting Methods ..................................................................... 90948.3 The Applicability of Forecasting Methods to Spare-Parts Demands ... 911
XXVIII Contents
48.4 Prediction of Aircraft Spare Parts: A Case Study ............................... 91248.5 Poisson Models ............................................................................. 91548.6 Models Based on the Binomial Distribution .................................... 91748.7 Extension of the Binomial Model Based on the Total Cost Function .. 92048.8 Weibull Extension ......................................................................... 923References............................................................................................... 928
49 Arithmetic and Geometric ProcessesKit-Nam F. Leung .................................................................................... 93149.1 Two Special Monotone Processes .................................................... 93449.2 Testing for Trends .......................................................................... 93649.3 Estimating the Parameters ............................................................. 93849.4 Distinguishing a Renewal Process from an AP (or a GP).................... 93949.5 Estimating the Means and Variances .............................................. 93949.6 Comparison of Estimators Using Simulation .................................... 94549.7 Real Data Analysis ......................................................................... 94649.8 Optimal Replacement Policies Determined Using
Arithmetico-Geometric Processes ................................................... 94749.9 Some Conclusions on the Applicability of an AP and/or a GP ............ 95049.10 Concluding Remarks ...................................................................... 95149.A Appendix ...................................................................................... 953References............................................................................................... 954
50 Six SigmaFugee Tsung ............................................................................................ 95750.1 The DMAIC Methodology ................................................................. 96050.2 Design for Six Sigma ...................................................................... 96550.3 Six Sigma Case Study ..................................................................... 97050.4 Conclusion .................................................................................... 971References............................................................................................... 971
51 Multivariate Modeling with Copulas and Engineering ApplicationsJun Yan ................................................................................................... 97351.1 Copulas and Multivariate Distributions ........................................... 97451.2 Some Commonly Used Copulas ....................................................... 97751.3 Statistical Inference ....................................................................... 98151.4 Engineering Applications ............................................................... 98251.5 Conclusion .................................................................................... 98751.A Appendix ...................................................................................... 987References............................................................................................... 989
52 Queuing Theory Applications to Communication Systems:Control of Traffic Flows and Load BalancingPanlop Zeephongsekul, Anthony Bedford, James Broberg,Peter Dimopoulos, Zahir Tari .................................................................... 99152.1 Brief Review of Queueing Theory .................................................... 99452.2 Multiple-Priority Dual Queue (MPDQ) .............................................. 1000
Contents XXIX
52.3 Distributed Systems and Load Balancing......................................... 100552.4 Active Queue Management for TCP Traffic ........................................ 101252.5 Conclusion .................................................................................... 1020References............................................................................................... 1020
53 Support Vector Machines for Data Modeling with SoftwareEngineering ApplicationsHojung Lim, Amrit L. Goel ........................................................................ 102353.1 Overview....................................................................................... 102353.2 Classification and Prediction in Software Engineering ..................... 102453.3 Support Vector Machines ............................................................... 102553.4 Linearly Separable Patterns............................................................ 102653.5 Linear Classifier for Nonseparable Classes ....................................... 102953.6 Nonlinear Classifiers ...................................................................... 102953.7 SVM Nonlinear Regression .............................................................. 103253.8 SVM Hyperparameters .................................................................... 103353.9 SVM Flow Chart .............................................................................. 103353.10 Module Classification ..................................................................... 103453.11 Effort Prediction ............................................................................ 103553.12 Concluding Remarks ...................................................................... 1036References............................................................................................... 1036
54 Optimal System DesignSuprasad V. Amari ................................................................................... 103954.1 Optimal System Design .................................................................. 103954.2 Cost-Effective Designs.................................................................... 104754.3 Optimal Design Algorithms ............................................................. 105154.4 Hybrid Optimization Algorithms ..................................................... 1055References............................................................................................... 1063
Acknowledgements ................................................................................... 1065About the Authors ..................................................................................... 1067Detailed Contents ...................................................................................... 1085Subject Index ............................................................................................. 1113
XXXI
List of Tables
Part A Fundamental Statistics and Its Applications
1 Basic Statistical ConceptsTable 1.1 Results from a twelve-component life duration test ............... 6Table 1.2 Main rotor blade data ........................................................... 22Table 1.3 Successive inter-failure times (in s) for a real-time command
system ................................................................................. 25Table 1.4 Sample observations for each cell boundary .......................... 26Table 1.5 Confidence limits for θ .......................................................... 29Table 1.6 Cumulative areas under the standard normal distribution ...... 43Table 1.7 Percentage points for the t-distribution (tα,r ) ......................... 44Table 1.8 Percentage points for the F-distribution F0.05, ν2/ν1 .............. 45Table 1.9 Percentage points for the χ2 distribution ............................... 46Table 1.10 Critical values dn,α for the Kolmogorov–Smirnov test .............. 47
2 Statistical Reliability with ApplicationsTable 2.1 Common lifetime distributions used in reliability data
analysis ................................................................................ 52Table 2.2 Minimum cut sets and path sets for the systems in Fig. 2.3 ..... 57
3 Weibull Distributions and Their ApplicationsTable 3.1 Data set of failure test (data set 2) ......................................... 74Table 3.2 A sample of reliability applications ........................................ 75Table 3.3 A sample of other applications .............................................. 76
6 Prediction Intervals for Reliability Growth Modelswith Small Sample SizesTable 6.1 Values of the mean of the distribution of R ........................... 118Table 6.2 Values of the median of the distribution of R ........................ 118Table 6.3 Percentiles of the distribution of R ........................................ 119Table 6.4 Predictions of fault detection times based on model .............. 120Table 6.5 Expected faults remaining undetected ................................... 120Table 6.6 Probability of having detected all faults ................................ 121Table 6.7 Observed ratios ..................................................................... 121Table 6.8 Prediction errors ................................................................... 122
9 Modeling and Analyzing Yield, Burn-In and Reliabilityfor Semiconductor Manufacturing: OverviewTable 9.1 Industry sales expectations for IC devices ............................... 154
XXXII List of Tables
Part B Process Monitoring and Improvement
11 Statistical Methods for Product and Process ImprovementTable 11.1 Noise factor levels for optimum combination ......................... 210Table 11.2 Comparison of results from different methods ....................... 211
12 Robust Optimization in Quality EngineeringTable 12.1 22 factorial design for paper helicopter example .................... 217Table 12.2 Experiments along the path of steepest ascent ...................... 217Table 12.3 Central composite design for paper helicopter example .......... 217Table 12.4 Comparison of performance responses using canonical
and robust optimization approaches (true optimalperformance: −19.6) ............................................................ 226
Table 12.5 Comparison of performance responses using canonical,robust, and weighted robust optimization ............................. 226
13 Uniform Design and Its Industrial ApplicationsTable 13.1 Experiment for the production yield y ................................... 232Table 13.2 ANOVA for a linear model ...................................................... 232Table 13.3 ANOVA for a second-degree model......................................... 233Table 13.4 ANOVA for a centered second-degree model........................... 233Table 13.5 The set up and the results of the accelerated stress test ......... 233Table 13.6 ANOVA for an inverse responsive model ................................. 234Table 13.7 Experiment for the robot arm example .................................. 235Table 13.8 A design in U(6; 32 × 2) .......................................................... 237Table 13.9 Construction of UD in S3−1
a,b ..................................................... 242
15 Chain SamplingTable 15.1 ChSP-1 plans indexed by AQL and LQL (α = 0.05, β = 0.10)
for fraction nonconforming inspection .................................. 265Table 15.2 Limits for deciding unsatisfactory variables plans ................... 274
16 Some Statistical Models for the Monitoringof High-Quality ProcessesTable 16.1 A set of defect count data ..................................................... 285
17 Monitoring Process Variability Using EWMATable 17.1 Standard-deviation σ(Z) of the normal (0, 1) sample median,
for n ∈ {3, 5, . . . , 25} .............................................................. 296Table 17.2 Optimal couples (λ∗, K∗) and optimal ARL∗ of the
EWMA-X (half top) and EWMA-X (half bottom) control charts,for τ ∈ {0.1, 0.2, . . . , 2}, n ∈ {1, 3, 5, 7, 9} and ARL0 = 370.4...... 297
Table 17.3 Constants AS2 (n), BS2 (n), CS2 (n), Y0, E(Tk), σ(Tk), γ3(Tk) andγ4(Tk) for the EWMA-S2 control chart, for n ∈ {3, . . . , 15} ......... 300
Table 17.4 Optimal couples (λ∗, K∗) and optimal ARL∗ for the EWMA-S2
control chart, for τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . ,2}, n ∈ {3, 5, 7, 9} and ARL0 = 370.4 ....................................... 300
List of Tables XXXIII
Table 17.5 Constants AS(n), BS(n), CS(n), Y0, E(Tk), σ(Tk), γ3(Tk) andγ4(Tk) for the EWMA-S control chart, for n ∈ {3, . . . , 15} .......... 304
Table 17.6 Optimal couples (λ∗, K∗) and optimal ARL∗ for the EWMA-Scontrol chart, for τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2,. . . , 2}, n ∈ {3, 5, 7, 9} and ARL0 = 370.4 ................................ 306
Table 17.7 Expectation E(R), variance V (R) and skewness coefficientγ3(R) of R............................................................................. 307
Table 17.8 Constants AR(n), BR(n), CR(n), Y0, E(Tk), σ(Tk), γ3(Tk) andγ4(Tk) for the EWMA-R control chart, for n ∈ {3, . . . , 15} .......... 307
Table 17.9 Optimal couples (λ∗, K∗) and optimal ARL∗ for the EWMA-Rcontrol chart, for τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2,. . . , 2}, n ∈ {3, 5, 7, 9} and ARL0 = 370.4 ................................ 309
Table 17.10 Optimal out-of-control ATS∗ of the VSI EWMA-S2 forτ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, n ∈ {3, 5},hS ∈ {0.1, 0.5}, W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4 ................. 311
Table 17.11 Optimal out-of-control ATS∗ of the VSI EWMA-S2 forτ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, n ∈ {7, 9},hS ∈ {0.1, 0.5}, W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4 ................. 312
Table 17.12 Optimal h∗L values of the VSI EWMA-S2 for n ∈ {3, 5, 7, 9},
τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, hS ∈ {0.1, 0.5},W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4....................................... 313
Table 17.13 Optimal couples (λ∗, K∗) of the VSI EWMA-S2 for n ∈ {3, 5},τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, hS ∈ {0.1, 0.5},W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4....................................... 314
Table 17.14 Optimal couples (λ∗, K∗) of the VSI EWMA-S2 for n ∈ {7, 9},τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, hS ∈ {0.1, 0.5},W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4....................................... 315
Table 17.15 Subgroup number, sampling interval (hS or hL), total elapsedtime from the start of the simulation and statistics S2
k , Tk
and Yk .................................................................................. 317Table 17.16 Optimal out-of-control ATS∗ of the VSI EWMA-R for
τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, n ∈ {3, 5},hS ∈ {0.1, 0.5}, W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4 ................. 318
Table 17.17 Optimal out-of-control ATS∗ of the VSI EWMA-R forτ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, n ∈ {7, 9},hS ∈ {0.1, 0.5}, W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4 ................. 319
Table 17.18 Optimal h∗L values of the VSI EWMA-R for n ∈ {3, 5, 7, 9},
τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, hS ∈ {0.1, 0.5},W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4....................................... 320
Table 17.19 Optimal couples (λ∗, K∗) of the VSI EWMA-R for n ∈ {3, 5},τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, hS ∈ {0.1, 0.5},W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4....................................... 321
Table 17.20 Optimal couples (λ∗, K∗) of the VSI EWMA-R for n ∈ {7, 9},τ ∈ {0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, . . . , 2}, hS ∈ {0.1, 0.5},W = {0.1, 0.3, 0.6, 0.9}, ATS0 = 370.4....................................... 322
XXXIV List of Tables
18 Multivariate Statistical Process Control Schemesfor Controlling a MeanTable 18.1 ARL comparison with bivariate normal data (uncorrelated) ..... 337Table 18.2 ARL comparison with bivariate normal data (correlated) ......... 338Table 18.3 Eigenvectors and eigenvalues from the 30 stable observations 340Table 18.4 Probability of false alarms when the process is in control.
Normal populations and X-bar chart ..................................... 342Table 18.5 The estimated ARL for Page’s CUSUM when the process is in
control. Normal populations ................................................. 342Table 18.6 The h value to get in-control ARL ≈ 200, k = 0.5. Page’s CUSUM 342Table 18.7 The estimate in-control ARL using Crosier’s multivariate
scheme ................................................................................ 343
Part C Reliability Models and Survival Analysis
19 Statistical Survival Analysis with ApplicationsTable 19.1 Sample size per group based on the method of Rubinstein,
et al. [19.18] α = 5%, β = 20% ............................................... 352Table 19.2 Sample size per group based on the method of
Freedman [19.22] (Weibull distribution with a shapeparameter 1.5 assumed) α = 5%, β = 20% .............................. 353
Table 19.3 Sample size per group based on (19.8); The lognormal caseα = 5%, β = 20%, σ = 0.8 ...................................................... 353
Table 19.4 Sample size per group based on (19.8); the Weibull caseα = 5%, β = 20%, σ = 0.8 ...................................................... 353
Table 19.5 Step-stress pattern after step 4 ............................................. 360Table 19.6 Count data ........................................................................... 360Table 19.7 Parameter estimates ............................................................. 360Table 19.8 Percentiles of S3 and S5 ........................................................ 364
21 Proportional Hazards Regression ModelsTable 21.1 Data table for the example ................................................... 393Table 21.2 Model fitting result ............................................................... 394
22 Accelerated Life Test Models and Data AnalysisTable 22.1 GAB insulation data .............................................................. 403Table 22.2 GAB insulation data. Weibull ML estimates for each voltage
stress ................................................................................... 409Table 22.3 GAB insulation data. ML estimates for the inverse power
relationship Weibull regression model ................................... 409Table 22.4 GAB insulation data. Quantiles ML estimates at 120 V/mm ...... 412Table 22.5 IC device data ....................................................................... 412Table 22.6 IC device data. Lognormal ML estimates for each temperature 414Table 22.7 IC device data. ML estimates for the Arrhenius lognormal
regression model .................................................................. 414
List of Tables XXXV
Table 22.8 Laminate panel data. ML estimates for the inverse powerrelationship lognormal regression model ............................... 415
Table 22.9 LED device subset data. ML estimates for the lognormalregression models (22.12) and (22.13) ...................................... 417
Table 22.10 Spring fatigue data. ML estimates for the Weibull regressionmodel .................................................................................. 419
Table 22.11 Spring fatigue data. Quantiles ML estimates at (20 mil, 600 ◦F)for the Old and New processing methods ............................... 420
23 Statistical Approaches to Planning of Accelerated ReliabilityTestingTable 23.1 A summary of the characteristics of literature on optimal
design of SSALT ..................................................................... 432
24 End-to-End (E2E) Testing and Evaluation of High-AssuranceSystemsTable 24.1 Evolution of E2E T&E techniques ............................................ 445Table 24.2 Automatically generated code example ................................. 457Table 24.3 Examples of obligation policies ............................................. 461Table 24.4 Examples of specifying system constraints ............................. 463Table 24.5 Policy registration ................................................................. 464Table 24.6 Reliability definition of ACDATE entities .................................. 467Table 24.7 The most reliable services and their forecast .......................... 469Table 24.8 ANOVA significance analysis ................................................... 469Table 24.9 Cooperative versus traditional ontology ................................. 472
25 Statistical Models in Software Reliabilityand Operations ResearchTable 25.1 Fitting of testing effort data .................................................. 485Table 25.2 Parameter estimation of the SRGM ........................................ 485Table 25.3 Estimation result on DS-3 ...................................................... 486Table 25.4 Release-time problems ......................................................... 489
26 An Experimental Study of Human Factors in Software ReliabilityBased on a Quality Engineering ApproachTable 26.1 Controllable factors in the design-review experiment ............ 499Table 26.3 Controllable factors in the design-review experiment ............ 500Table 26.2 Input and output tables for the two kinds of error ................. 500Table 26.4 The result of analysis of variance using the SNR ..................... 502Table 26.5 The comparison of SNR and standard error rates .................... 503Table 26.6 The optimal and worst levels of design review ....................... 503Table 26.7 The SNRs in the optimal levels for the selected inducers ......... 503Table 26.8 The comparison of SNRs and standard error rates between the
optimal levels for the selected inducers ................................. 503Table 26.9 The orthogonal array L18(21 × 37) with assigned human
factors and experimental data .............................................. 504Table 26.10 The result of analysis of variance (descriptive-design faults) .. 505
XXXVI List of Tables
Table 26.11 The result of analysis of variance (symbolic-design faults) ...... 505Table 26.12 The result of analysis of variance by taking account of
correlation among inside and outside factors ........................ 505
27 Statistical Models for Predicting Reliability of Software Systemsin Random EnvironmentsTable 27.1 Summary of NHPP software reliability models ........................ 508Table 27.2 Normalized cumulative failures and times during software
testing ................................................................................. 513Table 27.3 Normalized cumulative failures and their times
in operation ......................................................................... 513Table 27.4 MLE solutions for the γ-RFE model ........................................ 514Table 27.5 MLE solutions for the β-RFE model ........................................ 514Table 27.6 The mean-value functions for both RFEs models .................... 515Table 27.7 MLEs and fitness comparisons ............................................... 518
Part D Regression Methods and Data Mining
28 Measures of Influence and Sensitivity in Linear RegressionTable 28.1 Three sets of data which differ in one observation ................. 527Table 28.2 Some statistics for the three regressions fitted to the data
in Table 28.1 ......................................................................... 527Table 28.3 A simulated set of data ......................................................... 531Table 28.4 Eigen-analysis of the influence matrix for the data
from Table 28.3. The eigenvectors and eigenvaluesare shown ............................................................................ 531
Table 28.5 Values of the t statistics for testing each point as an outlier ... 531Table 28.6 Eigenvalues of the sensitivity matrix for the data
from Table 28.3..................................................................... 532
29 Logistic Regression Tree AnalysisTable 29.1 Indicator variable coding for the species variable S ................ 539Table 29.2 Predictor variables in the crash-test dataset. Angular
variables crbang, pdof, and impang are measured indegrees clockwise (from -179 to 180) with 0 being straightahead .................................................................................. 544
Table 29.3 Split at node 7 of the tree in Fig. 29.8 .................................... 546Table 29.4 Split at node 9 of the tree in Fig. 29.8.................................... 547
30 Tree-Based Methods and Their ApplicationsTable 30.1 Electronic mail characteristics ............................................... 552Table 30.2 Seismic rehabilitation cost-estimator variables ...................... 553Table 30.3 Characteristics of CPUs ........................................................... 559Table 30.4 Comparison of tree-based algorithms .................................... 564Table 30.5 Data-mining software for tree-based methods ...................... 565
List of Tables XXXVII
31 Image Registration and Unknown Coordinate SystemsTable 31.1 12 digitized locations on the left and right hand .................... 573Table 31.2 Calculation of residual lengths for data from Table 31.1 ........... 583
32 Statistical Genetics for Genomic Data AnalysisTable 32.1 Outcomes when testing m hypotheses ................................... 593Table 32.2 Classification results of the classification rules and the
corresponding gene model.................................................... 603
33 Statistical Methodologies for Analyzing Genomic DataTable 33.1 The numbers of genes belonging to the intersects of the five
k-means clusters and the 13 PMC clusters ............................... 614
35 Radial Basis Functions for Data MiningTable 35.1 Dataset for illustrative example ............................................. 643Table 35.2 Data description for the diabetes example ............................. 645Table 35.3 RBF models for the diabetes example .................................... 646Table 35.4 Selected models and error values for the diabetes example .... 647Table 35.5 Classification results for the cancer gene example .................. 647
Part E Modeling and Simulation Methods
37 Bootstrap, Markov Chain and Estimating FunctionTable 37.1 Minimum Lq distance estimator (q = 1.5). Simulated coverage
probabilities and average confidence intervals (fixed design) . 683
39 Cluster Randomized Trials: Design and AnalysisTable 39.1 Values for the mixed effects ANOVA model.............................. 708Table 39.2 Changes in the variance components due to the inclusion of
a covariate ........................................................................... 713Table 39.3 Assumptions about the intra-class correlation coefficient,
with associated power with 86 groups and required numberof groups for a power level of 0.9 .......................................... 714
Table 39.4 Empirical type I error rate α and power 1−β for the standarddesign and re-estimation design for three values of theprior ρ. The true ρ = 0.05 ...................................................... 715
40 A Two-Way Semilinear Model for Normalization and Analysisof Microarray DataTable 40.1 Simulation results for model 1. 10 000 × Summary of MSE. The
true normalization curve is the horizontal line at 0. Theexpression levels of up- and down-regulated genes aresymmetric: α1 = α2, where α1 +α2 = α ................................... 731
Table 40.2 Simulation results for model 2. 10 000 × Summary of MSE. Thetrue normalization curve is the horizontal line at 0. But thepercentages of up- and down-regulated genes are different:α1 = 3α2, where α1 +α2 = α .................................................. 731
XXXVIII List of Tables
Table 40.3 Simulation results for model 3. 10 000 × Summary of MSE.There are nonlinear and intensity-dependent dye biases. Theexpression levels of up- and down-regulated genes aresymmetric: α1 = α2, where α1 +α2 = α ................................... 731
Table 40.4 Simulation results for model 4. 10 000 × Summary of MSE.There are nonlinear and intensity-dependent dye biases. Thepercentages of up- and down-regulated genes are different:α1 = 3α2, where α1 +α2 = α .................................................. 731
42 Genetic Algorithms and Their ApplicationsTable 42.1 Failure modes and probabilities in each subsystem ................ 764Table 42.2 Coordinates of Cooper and Rosing’s example ......................... 770Table 42.3 Comparison results of Cooper and Rosing’s example ............... 770
44 Condition-Based Failure PredictionTable 44.1 Mean values, standard deviations, and variances for
different T ........................................................................... 803
45 Statistical Maintenance Modeling for Complex SystemsTable 45.1 Optimal values I and L ......................................................... 824Table 45.2 The effect of L on Pc for I = 37.5 ........................................... 825Table 45.3 Nelder–Mead algorithm results ............................................. 830Table 45.4 The effect of (L1, L2) on Pp for a given inspection sequence ... 830Table 45.5 The effect of the inspection sequence on Pp for fixed PM
values .................................................................................. 830
46 Statistical Models on MaintenanceTable 46.1 Optimum T∗, N∗ for T = 1 and percentile Tp when
F(t) = 1− exp(−t/100)2 .......................................................... 839Table 46.2 Optimum replacement number K∗, failed element number
N∗, and the expected costs C1(K∗) and C2(N∗) ...................... 847
Part F Applications in Engineering Statistics
47 Risks and Assets PricingTable 47.1 Comparison of the log-normal and bi-log-normal model ...... 890
48 Statistical Management and Modeling for Demand of Spare PartsTable 48.1 A summary of selected forecasting methods ........................... 907Table 48.2 Classification of forecasting methods, corresponding testing
ground and applications ....................................................... 909Table 48.3 Summary of the better forecasting methods........................... 911Table 48.4 Comparison among some methods ........................................ 913Table 48.5 Ranking based on performance evaluation (MAD)................... 914Table 48.6 Example of N evaluation for a specific item (code 0X931: pin
for fork gear levers) ............................................................. 918
List of Tables XXXIX
Table 48.7 LS % and minimum cost related to Tsd and Rt/(Cmd)− no. ofemployments n = 5 ............................................................... 921
Table 48.8 LS % and minimum cost related to Tsd and Rt/(Cmd)− no. ofemployments n = 15 ............................................................. 921
Table 48.9 Optimization of Ts for fixed number of spare parts N ............. 922
49 Arithmetic and Geometric ProcessesTable 49.1 Recommended estimators for µA1 and σ2
A1............................. 945
Table 49.2 Recommended estimators for µG1 and σ2G1
............................ 945Table 49.3 Recommended estimators for µ A1
and σ2A1
, and µG1and σ2
G1. 946
Table 49.4 Estimated values of common difference and ratio, and meansfor the 6LXB engine .............................................................. 950
Table 49.5 Estimated values of common difference and ratio, and meansfor the Benz gearbox ............................................................ 950
Table 49.6 Summary of useful results of both AP and GP processes .......... 951
50 Six SigmaTable 50.1 Final yield for different sigma levels in multistage processes .. 958Table 50.2 Number of Six Sigma black belts certified by the American
Society for Quality (ASQ) internationally (ASQ record up toApril, 2002) ........................................................................... 959
51 Multivariate Modeling with Copulas and EngineeringApplicationsTable 51.1 Some one-parameter (α) Archimedean copulas ...................... 980Table 51.2 Comparison of T 2 percentiles when the true copula is normal
and when the true copula is Clayton with various Kendall’s τ.The percentiles under Clayton copulas are obtained from100 000 simulations ............................................................... 984
Table 51.3 IFM fit for all the margins using normal and gammadistributions, both parameterized by mean and standarddeviation. Presented results are log-likelihood (Loglik),estimated mean, and estimated standard deviation (StdDev)for each margin under each model........................................ 985
Table 51.4 IFM and CML fit for single-parameter normal copulas withdispersion structures: AR(1), exchangeable, and Toeplitz ......... 986
Table 51.5 Maximum-likelihood results for the disk error-rate data.Parameter estimates, standard errors and log-likelihood areprovided for both the multivariate normal model and themultivariate gamma model with a normal copula. The secondentry of each cell is the corresponding standard error ............ 986
52 Queuing Theory Applications to Communication Systems:Control of Traffic Flows and Load BalancingTable 52.1 Some heavy-tail distributions ............................................... 1016Table 52.2 Scheduling variables ............................................................. 1016Table 52.3 DPRQ parameters .................................................................. 1018
XL List of Tables
Table 52.4 States of the DPRQ ................................................................ 1019
53 Support Vector Machines for Data Modeling with SoftwareEngineering ApplicationsTable 53.1 Data points for the illustrative example ................................. 1028Table 53.2 Three common inner-product kernels ................................... 1030Table 53.4 Classification results ............................................................. 1034Table 53.3 List of metrics from NASA database ........................................ 1034Table 53.5 Performance of effort prediction models ................................ 1036
54 Optimal System DesignTable 54.1 Exhaustive search results ...................................................... 1052Table 54.2 Dynamic programming solution............................................. 1054Table 54.3 Parameters for a series system .............................................. 1059Table 54.4 Parameters for optimization of a series system ...................... 1059Table 54.5 Parameters for a hypothetical reliability block diagram .......... 1060Table 54.6 Parameters for the optimization of a hypothetical reliability
block diagram ...................................................................... 1060Table 54.7 Parameters for a bridge network ........................................... 1062
XLI
List of Abbreviations
A
ABC approximated bootstrap confidenceACK acknowledgmentADDT accelerated destructive degradation testsADI average inter-demand intervalADT accelerated degradation testAF acceleration factorAGP arithmetico-geometric processALM accelerated life modelALT accelerated life testingAMA arithmetic moving-averageANN artificial neural networksANOVA analysis of variationsAP arithmetic processAPC automatic process controlAQL acceptable quality levelAQM active queue managementAR autoregressive processARI adjusted Rand indexARL average run lengthARMA autoregressive and moving averageARMDT accelerated repeated measures degradation
testsARRSES adaptive response rate single-exponential
smoothingART accelerated reliabilityASN average sample numberASQ American Society for QualityATI average total inspectionAUC area under the receiver operating
characteristics curveAW additive Winter
B
BIB burn-in boardBIR built-in reliabilityBLAST Berkeley lazy abstraction software
verification toolBLUP best linear unbiased predictorBM binomial modelBVE bivariate exponential
C
CART classification and regression treeCBFQ credit-based fair queueingCBQ class-based queuesCCD central composite designCDF cumulative distribution function
CE classification errorCF characteristic functionCFE Cauchy functional equationCFF call for fireCHAID chi-square automatic interaction detectionCID collision-induced dissociationCIM cluster-image mapCLT central limit theoremCM corrective maintenanceCML canonical maximum likelihoodCMW combination warrantyCNM customer needs mappingCOPQ cost of poor qualityCOT cumulative sum of TcPLP capacitated plant location problemCRC cumulative results criterionCRUISE classification rule with unbiased interaction
selection and estimationCS-CQ cycle stealing with central queueCS-ID cycle stealing with immediate dispatchCSALT constant-stress accelerated life testCSS conditional single-samplingCTQ critical-to-qualityCUSUM cumulative sumCV coefficient of varianceCV cross-validationCVP critical value pruningCX cycle crossoverCdf cumulative distribution functionCuscore cumulative scoreCusum cumulative sum
D
DBI dynamic burn-inDBSCAN Density-based clusteringDCCDI define, customer concept, design,
and implementDES double-exponential smoothingdf degrees of freedomDFM design for manufacturabilityDFR decreasing failure rateDFR design for reliabilityDFSS design for Six SigmaDFY design for yieldDLBI die-level burn-inDLBT die-level burn-in and testingDM Data miningDMADV define, measure, analyze, design and verifyDMAIC define, measure, analyze, improve, and
control
XLII List of Abbreviations
DMAICT define, measure, analyze, improve, controland technology transfer
DOE design of experimentsDP dynamic programmingDP design parametersDPMO defects per million opportunitiesDQ dual-queueDQLT dual queue length thresholdDRD dynamic robust designDRR deficit round-robinDSSP dependent stage sampling planDUT device under testDWC discounted warranty costDoD Department of Defense
E
EBD equivalent business daysEBP error-based pruningEDWC expected discounted warranty costEF estimating functionEM expectation maximizationEOQ economic order quantityEOS electrical-over-stressEQL expected quality lossES exponential smoothingESC expected scrap costESD electrostatic dischargeETC expected total costEWC expected warranty costEWMA exponentially weighted moving averageEWMAST exponentially weighted moving average
chart for stationary processes
F
FCFS first-come first-servedFDR false discovery rateFIR fast initial responseFMEA failure modes and effects analysisFR failure rateFR functional requirementsFRPW free repair warrantyFRW free replacement warrantyFSI fixed sampling intervalFSW full-service warrantyFTP file transfer protocolFWER family-wise error rate
G
GA genetic algorithmsGAB generator armature barsGAM generalized additive modelGAOT genetic algorithm optimization toolboxGEE generalized estimating equation
GERT graphical evaluation and review techniqueGLM general linear modelGLM generalized linear modelGLMM generalized linear mixed modelGLRT generalized likelihood ratio testGP geometric processGUIDE generalized, unbiased interaction detection
and estimation
H
HALT highly accelerated life testsHCF highest class firstHDL high-density lipoproteinHEM heterogeneous error modelHEM hybrid evolutionary methodHLA/RTI high level architecture/runtime
infrastructureHPP homogeneous Poisson processHR human resourceHTTP hypertext transfer protocol
I
IC inspection costICOV identify, characterize, optimize, verifyIDOV identify, design, optimize, validateIETF internet engineering task forceIFM inference functions for marginsIFR increasing failure ratei.i.d. of independent and identically distributediid independent identically distributedIM improvement maintenanceIT information technology
K
KDD knowledge discovery in databasesKGD known good diesKNN k-nearest neighbors
L
LAC lack of anticipation conditionLCEM linear cumulative exposure modelLCF lowest class firstLCL lower control limitsLDA linear discriminant analysisLED light emitting deviceLIFO last-in first-outLLF least loaded firstLLP log-linear processLMP lack-of-memory propertyLOC lines of codeLOF lack-of-fitLPE local pooled error
List of Abbreviations XLIII
LQL limiting quality levelLR logistic regressionLSL lower specification limitLTI low-turnaround-indexLTP linear transportation problem
M
MAD mean absolute deviationMAD median absolute deviationMAPE mean absolute percentage errorMARS multivariate adaptive regression splinesMART multiple additive regression treeMC/DC modified condition/decision coverageMCF minimum-cost-flow problemMCMB Markov chain marginal bootstrapMCNR Monte Carlo Newton–RaphsonMCS Monte Carlo simulationMCUSUM multivariate cumulative sumMDMSP multidimensional mixed sampling plansMDS multiple dependent (deferred) stateMEP minimum error pruningMEWMA multivariate exponentially weighted moving
averageMGF moment generating functionMILP mixed integer linear programming modelML maximum-likelihoodMLDT mean logistic delay timeMLE maximum likelihood estimationMME method of moment estimatesMMSE minimum mean squared errorMOLAP multidimensional OLAPMPDQ multiple-priority dual queuesMPP marked point processMPP multistage process planningMRL mean residual lifeMS mass spectrometryMSA measurement system analysisMSE mean square errorsMST minimum spanning treeMTBF mean time before failureMTBR mean time between replacementMTEF marginal testing effort functionmTP multiobjective transportation problemMTS Mahalanobis–Taguchi systemMTTF mean time to failureMTTR mean time to repairMVN multivariate normalMW multiplicative WinterMiPP misclassification penalized posterior
N
NBM nonoverlapping batch meansNHPP nonhomogeneous Poisson processNLP nonlinear programming
NN nearest neighborNPC nutritional prevention of cancerNTB nominal-the-best caseNUD new, unique, and difficult
O
OBM overlapping batch meansOC operating characteristicOLAP online analytical processingOX order crossover
P
PAR phased array radarPCB printed circuit boardPDF probability density functionpdf probability density functionPEP pessimistic error pruningpFDR proposed positive FDRPH proportional hazardsPID proportional-integral-derivativePLBI package-level burn-inPM preventive maintenancePMC probabilistic model-based clusteringPMX partial-mapped crossoverPOF physics-of-failurePQL penalized quasi-likelihoodPRM probabilistic rational modelPRW pro-rata warrantyPV process variable
Q
QCQP quadratically constrained quadraticprogramming
QDA quadratic discriminant analysisQFD quality function deploymentQML qualified manufacturing lineQSS quick-switching samplingQUEST quick, unbiased and efficient
statistical treeQoS quality of service
R
RBF radial basis functionRCL rate conservation lawRCLW repair-cost-limit warrantyRD Robust designRED random early-detection queueREP reduced error pruningRF random forestRGS repetitive group samplingRIO RED in/outRNLW repair-number-limit warranty
XLIV List of Abbreviations
RP renewal processRPC remote procedure callRPN priority numberRPN risk priority numberRSM response surface methodRSM response surface methodologyRSM response surface modelsRTLW repair-time-limit warrantyRV random variable
S
SA simulated annealingSAFT scale-accelerated failure-timeSAM significance analysis of microarraySAR split and recombineSBI steady-state or static burn-inSCC special-cause chartsSCFQ as self-clocked fair queueingSCM supply-chain managements.d. standard deviationSDLC software development life cycleSDP semidefinite programSE standard errorsSEM structural equation modelsSES single-exponential smoothingSEV standard smallest extreme valueSF survival functionSIMEX simulation extrapolationSIPOC suppliers, inputs, process, outputs
and customerSIRO service in random orderSMD surface-mount devicesSMT surface-mount technologySNR signal-to-noise ratiosSOAP simple object access protocolSOF special operations forcesSOM self-organizing mapsSOM self-organizing (feature) mapSPC statistical process controlSQL structured query languageSRGM software reliability growth modelsSRM seasonal regression modelSSBB Six Sigma black beltsSSE sum of squared errorsSSM surface-to-surface missileSTS standardized time series
SVM support vector machineSoS system of systems
T
TAAF test, analyse and fixTAES forecasting time series data that have
a linear trendTCP transmission control protocolTCP/IP transmission control protocol/internet
protocolTDBI test during burn-inTDF temperature differential factorTQM total quality managementTS tracking signalTSP traveling-salesman problem
U
UBM unified batch meanUCL upper control limitsUML unified modeling languageUSL upper specification limit
V
VOC voice of customerVSI variable sampling intervalsVaR value at risk
W
WBM weighted batch meanWLBI wafer-level burn-inWLBT wafer-level burn-in and testingWLR wafer-level reliabilityWPP Weibull probability plotWRED weighted REDWRR weighted round-robinWSDL web services description language
X
XML extensible markup language
Y
Y2K year 2000
