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Birkhäuser

Advances in Degradation Modeling

Applications to Reliability, Survival Analysis, and Finance

  • Book
  • © 2010

Overview

Editors:
  1. M.S. Nikulin

    1. Université Victor Segalen Bordeaux 2, I’lnstitut de Mathématiques de Bordeaux, Bordeaux Cedex, France

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  2. Nikolaos Limnios

    1. Département Génie Informatique, Labo. Mathématiques Appliquées Compiègne, Université de Technologie de Compiègne, Compiègne, France

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  3. N. Balakrishnan

    1. McMaster University, Department of Mathematics and Statistics, Hamilton, Canada

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  4. Waltraud Kahle

    1. Fak. Mathematik, Inst. Mathematische Stochastik, Otto-von-Guericke-Universität, Magdeburg, Germany

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  5. Catherine Huber-Carol

    1. Laboratoire de Statistique Medicale, Université René Descartes, Paris 5, Paris, France

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  • Covers a wide range of applications to areas such as reliability, quality control, the health sciences, economics, and finance
  • For a broad audience of researchers and practitioners in applied probability and statistics, industrial statistics, the health sciences, quality control, economics, and finance
  • Includes supplementary material: sn.pub/extras

Part of the book series: Statistics for Industry and Technology (SIT)

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Table of contents (26 chapters)

  1. Front Matter

    Pages i-xxxviii
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  2. Review, Tutorials, and Perspective

    1. Front Matter

      Pages 1-1
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    2. Trends in the Statistical Assessment of Reliability

      • William Q. Meeker
      Pages 3-16

    3. Degradation Processes: An Overview

      • Mohamed Abdel-Hameed
      Pages 17-25

    4. Defect Initiation, Growth, and Failure – A General Statistical Model and Data Analyses

      • Wayne B. Nelson
      Pages 27-37

    5. Properties of Lifetime Estimators Based on Warranty Data Consisting only of Failures

      • Kazuyuki Suzuki, Watalu Yamamoto, Takashi Hara, Md. Mesbahul Alam
      Pages 39-55

  3. Shock Models

    1. Front Matter

      Pages 56-56
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    2. Shock Models

      • Allan Gut, Jürg Hüsler
      Pages 59-76

    3. Parametric Shock Models

      • Waltraud Kahle, Heide Wendt
      Pages 77-104

    4. Poisson Approximation of Processes with Locally Independent Increments and Semi-Markov Switching – Toward Application in Reliability

      • V.S. Koroliuk, N. Limnios, I.V. Samoilenko
      Pages 105-116

    5. On Some Shock Models of Degradation

      • Maxim Finkelstein, Ji Hwan Cha
      Pages 117-124

  4. Degradation Models

    1. Front Matter

      Pages 125-125
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    2. The Wiener Process as a Degradation Model: Modeling and Parameter Estimation

      • Waltraud Kahle, Axel Lehmann
      Pages 127-146

    3. On the General Degradation Path Model: Review and Simulation

      • Firoozeh Haghighi, Nazanin Nooraee, Narges Nazeri Rad
      Pages 147-155

    4. A Closer Look at Degradation Models: Classical and Bayesian Approaches

      • Marta A. Freitas, Thiago R. dos Santos, Magda C. Pires, Enrico A. Colosimo
      Pages 157-180

    5. Optimal Prophylaxis Policy Under Non-monotone Degradation

      • S.S. Rasova, B.P. Harlamov
      Pages 181-194

    6. Deterioration Processes With Increasing Thresholds

      • S. Zacks
      Pages 195-208

    7. Failure Time Models Based on Degradation Processes

      • Axel Lehmann
      Pages 209-233

    8. Degradation and Fuzzy Information

      • R. Viertl
      Pages 235-240

    9. A New Perspective on Damage Accumulation, Marker Processes, and Weibull’s Distribution

      • Nozer D. Singpurwalla
      Pages 241-249
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Keywords

About this book

William Q. Meeker has made pioneering and phenomenal contributions to the general areaofreliabilityand,inparticular,tothetopicsofdegradationandacceleratedtesting. Hisresearchpublicationsandthenumerouscitationshehasreceivedoverthepastthree decades provide an ample testimony to this fact. Statistical methods have become critical in analyzing reliability and survival data. Highly reliable products have necessitated the development of accelerated testing and degradation models and their analyses. This volume has been put together in order to (i) review some of the recent advances on accelerated testing and degradation, (ii) highlight some new results and discuss their applications, and (iii) suggest possible directions for future research in these topics. With these speci?c goals in mind, many authors were invited to write a chapter for this volume. These authors are not only experts in lifetime data analysis, but also form a representative group from former students, colleagues, and other close professional associates of William Meeker. All contributions have been peer reviewed and organized into 26 chapters. For the convenience of readers, the volume has been divided into the following six parts: • Review, Tutorials, and Perspective • Shock Models • Degradation Models • Reliability Estimation and ALT • Survival Function Estimation • Competing Risk and Chaotic Systems Itneedstobeemphasizedherethatthisvolumeisnotaproceedings,butacarefully anddeliberatelyplannedvolumecomprisingchaptersconsistentwiththeeditorialgoals and purposes mentioned above. Our thanks go to all the authors who have contributed to this volume. Thanks are also due to Mrs. Debbie Iscoe for the excellent typesetting of the entire volume.SpecialthanksgotoMs.ReginaGorenshteynandMr.TomGrasso(Editor,Birkh¨ auser, Boston) for their interest and support for this project.

Reviews

From the reviews:

“The topics covered are of current interest and include accelerated life testing and degradation models. … The volume covers a host of applications to the field, including reliability, quality control, economics and finance. The volume is well organized, structured and presented, and the chapters appear in a logical order. It contains a lot of useful information and applications. … the volume would be a useful resource for researchers and graduate students involved in this arena.” (Technometrics, Vol. 52 (4), November, 2010)

Editors and Affiliations

  • Université Victor Segalen Bordeaux 2, I’lnstitut de Mathématiques de Bordeaux, Bordeaux Cedex, France

    M.S. Nikulin

  • Département Génie Informatique, Labo. Mathématiques Appliquées Compiègne, Université de Technologie de Compiègne, Compiègne, France

    Nikolaos Limnios

  • McMaster University, Department of Mathematics and Statistics, Hamilton, Canada

    N. Balakrishnan

  • Fak. Mathematik, Inst. Mathematische Stochastik, Otto-von-Guericke-Universität, Magdeburg, Germany

    Waltraud Kahle

  • Laboratoire de Statistique Medicale, Université René Descartes, Paris 5, Paris, France

    Catherine Huber-Carol

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