M.S. Nikulin & Nikolaos Limnios 
Advances in Degradation Modeling 
Applications to Reliability, Survival Analysis, and Finance

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.Specialthanksgoto Ms.Regina Gorenshteynand Mr.Tom Grasso(Editor, Birkh¨ auser, Boston) for their interest and support for this project.

Table of Content

Review, Tutorials, and Perspective.- Trends in the Statistical Assessment of Reliability.- Degradation Processes: An Overview.- Defect Initiation, Growth, and Failure – A General Statistical Model and Data Analyses.- Properties of Lifetime Estimators Based on Warranty Data Consisting only of Failures.- Shock Models.- Shock Models.- Parametric Shock Models.- Poisson Approximation of Processes with Locally Independent Increments and Semi-Markov Switching – Toward Application in Reliability.- On Some Shock Models of Degradation.- Degradation Models.- The Wiener Process as a Degradation Model: Modeling and Parameter Estimation.- On the General Degradation Path Model: Review and Simulation.- A Closer Look at Degradation Models: Classical and Bayesian Approaches.- Optimal Prophylaxis Policy Under Non-monotone Degradation.- Deterioration Processes With Increasing Thresholds.- Failure Time Models Based on Degradation Processes.- Degradation and Fuzzy Information.- A New Perspective on Damage Accumulation, Marker Processes, and Weibull’s Distribution.- Reliability Estimation and ALT.- Reliability Estimation of Mechanical Components Using Accelerated Life Testing Models.- Reliability Estimation from Failure-Degradation Data with Covariates.- Asymptotic Properties of Redundant Systems Reliability Estimators.- An Approach to System Reliability Demonstration Based on Accelerated Test Results on Components.- Survival Function Estimation.- Robust Versus Nonparametric Approaches and Survival Data Analysis.- Modelling Recurrent Events for Repairable Systems Under Worse Than Old Assumption.- Survival Models for Step-Stress Experiments With Lagged Effects.- Estimation of Density on Censored Data.- Competing Risk and Chaotic Systems.- Toward a Test for Departure of a Trajectory froma Neighborhood of a Chaotic System.- Probability Plotting with Independent Competing Risks.