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<p class="MsoNormal" style="text-align:justify;text-justify:inter-ideograph"><b><span style="font-size:12.0pt;mso-bidi-font-size:
11.0pt;line-height:107%">Ph.<a name="OLE_LINK18"></a><a name="OLE_LINK17">D. Defense Announcement<o:p></o:p></a></span></b></p>
<p class="MsoNormal" style="text-align:justify;text-justify:inter-ideograph">10am-12
Thursday, July 28 2016, located at IE conference room, E214, Engineering
Building 2<o:p></o:p></p>
<p class="MsoNormal" style="text-align:justify;text-justify:inter-ideograph">Dissertation
Title: Lévy, Non-Gaussian Ornstein-Uhlenbeck, and Markov Additive Processes in
Reliability Analysis<o:p></o:p></p>
<p class="MsoNormal" style="text-align:justify;text-justify:inter-ideograph">Yin
Shu, Ph.D. Candidate, Department of Industrial Engineering, University of
Houston<o:p></o:p></p>
<p class="MsoNormal">Committee members: <a name="OLE_LINK20"></a><a name="OLE_LINK19">Dr. Qianmei Feng</a>,
<a name="OLE_LINK22"></a><a name="OLE_LINK21">Dr.
Hao Liu</a>, <a name="OLE_LINK24"></a><a name="OLE_LINK23">Dr. Gino Lim</a>, <a name="OLE_LINK26"></a><a name="OLE_LINK25">Dr. Jiming Peng</a>,
<a name="OLE_LINK28"></a><a name="OLE_LINK27">Dr.
Edward P.C. Kao</a><o:p></o:p></p>
<p class="MsoNormal" style="text-align:justify;text-justify:inter-ideograph">Abstract:
Unavoidable degradation is one of the major failure mechanisms of many systems
due to internal properties (mechanical, thermal, electrical, or chemical) and
external influences (temperature, humidity, or vibration). Such degradation in
critical engineering systems (e.g., pipelines, wind turbines, power/smart
grids, and mechanical devices, etc.) takes the form of corrosion, erosion,
fatigue crack, deterioration or wear that may lead to the loss of structural
integrity and catastrophic failure. Therefore, developing stochastic
degradation models based on appropriate stochastic processes becomes imperative
in the reliability and statistics research communities.<o:p></o:p></p>
<p class="MsoNormal" style="text-align:justify;text-justify:inter-ideograph">This
dissertation aims to develop a new research framework to integrally handle the
complexities in degradation processes (the intrinsic/extrinsic stochastic
properties, complex jump mechanisms and dependence) based on general stochastic
processes including Lévy, non-Gaussian Ornstein-Uhlenbeck (OU), and Markov
additive processes; and to develop a new systematic methodology for reliability
analysis that provides compact and explicit results for reliability function
and lifetime characteristics. First, to handle the intrinsic stochastic
properties and complex jumps, we use Lévy subordinators and their functional
extensions, Lévy driven non-Gaussian OU processes, to model the cumulative
degradation with jumps that occur at random times and have random sizes. We
then integrally handle the complexities of a degradation process including both
intrinsic and extrinsic stochastic properties with complex jump mechanisms, by
constructing general Markov additive processes. Moreover, the models are
extended to multi-dimensional cases for multiple dependent degradation
processes under dynamic environments, where the Lévy copulas are studied to
construct Markov-modulated multi-dimensional Lévy processes. The Fokker-Planck
equations for such general stochastic processes are developed, based on which
we derive the explicit results for reliability function and lifetime moments,
represented by the Lévy measures, the infinitesimal generator matrices and the
Lévy copulas. To analyze the degradation data series from such degradation
phenomena of interest, we propose a systematic statistical estimation method
using linear programming estimators and empirical characteristic functions. We
also construct bootstrap procedures for the confidence intervals. Simulation
studies for Lévy measures of gamma processes, compound Poisson processes,
positive stable processes and positive tempered stable processes are performed.
The framework can be recognized as a general approach that can be used to
flexibly handle stylized features of widespread classes of degradation data
series such as jumps, linearity/nonlinearity, symmetry/asymmetry, and
light/heavy tails, etc. The results are expected to provide accurate reliability
prediction and estimation that can be used to assist the mitigation of risk and
property loss associated with system failures.<o:p></o:p></p>
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