published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

This thesis provides a stochastic modeling tool to assist in the component selection process for Army Aviation's Condition-Based Maintenance Plus (CBM+) program. This work is in conjunction with the Operations Research Center of Excellence (ORCEN) at the United States Military Academy to assist in providing insight for the U.S. Aviation and Missile Command (AMCOM). The component selected for this thesis is the AH-64/UH-60 T701C Turbine Helicopter Engine. Data analysis of the failure data indicated that a nonhomogeneous Poisson process appropriately modeled the failure characteristics of this engine. A Microsoft Excel simulation utilizing Crystal Ball version 5.5 compares an engine monitored by CBM+ versus the traditional Legacy system of maintenance. This simulation provides information on diagnosed faults, mission aborts, repair times, false positives, and logistical implications. This simulation is generic and can be used in comparing CBM+ candidate components for future inclusion into the CBM+ program. Results suggest when considering a component for inclusion in the CBM+ program important factors to consider are even the smallest false positive rate can invalidate process, large sensor probability of detection isn't necessary for beneficial results, and by entering a component into the CBM+ the on hand component requirements can be greatly reduced. / US Army (USA) author.

by Lau Chung Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1980. / Bibliography: leaf 90.

So-Kuen Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 99-102). / Chapter Chapter One --- Preview --- p.1 / Chapter Section 1 --- Introduction --- p.1 / Chapter Section 2 --- The Life Time Distribution --- p.4 / Chapter 2.1 --- Exponential Distribution --- p.5 / Chapter 2.2 --- Gamma Distribution --- p.6 / Chapter 2.3 --- Weibull Distribution --- p.7 / Chapter 2.4 --- Lognormal Distribution --- p.10 / Chapter Section 3 --- Nonparametric Inference for Geometric Process --- p.13 / Chapter 3.1 --- Test for Geometric Process --- p.13 / Chapter 3.2 --- Nonparametric Estimation Method --- p.17 / Chapter Section 4 --- Test for Distribution --- p.20 / Chapter 4.1 --- Graphical Method --- p.20 / Chapter 4.2 --- KS-test --- p.22 / Chapter 4.3 --- x2 GOF-test --- p.27 / Chapter 4.4 --- F-test (Exponential Dist.) --- p.28 / Chapter Chapter Two --- Parametric Inference for Geometric Process --- p.29 / Chapter Chapter Three --- Simulations --- p.39 / Chapter Chapter Four --- Examples --- p.49 / Chapter Chapter Five --- Comparison and Conclusion --- p.57 / Tables and Graphs --- p.61 / References --- p.99

The thesis is devoted to non-stationary point process models as generalizations of the standard homogeneous Poisson process. The work can be divided in two parts. In the first part, we introduce a fractional non-homogeneous Poisson process (FNPP) by applying a random time change to the standard Poisson process. We characterize the FNPP by deriving its non-local governing equation. We further compute moments and covariance of the process and discuss the distribution of the arrival times. Moreover, we give both finite-dimensional and functional limit theorems for the FNPP and the corresponding fractional non-homogeneous compound Poisson process. The limit theorems are derived by using martingale methods, regular variation properties and Anscombe's theorem. Eventually, some of the limit results are verified via a Monte-Carlo simulation. In the second part, we analyze statistical point process models for durations between trades recorded in financial high-frequency trading data. We consider parameter settings for models which are non-stationary or very close to non-stationarity which is quite typical for estimated parameter sets of models fitted to financial data. Simulation, parameter estimation and in particular model selection are discussed for the following three models: a non-homogeneous normal compound Poisson process, the exponential autoregressive conditional duration model (ACD) and a Hawkes process model. In a Monte-Carlo simulation, we test the performance of the following information criteria for model selection: Akaike's information criterion, the Bayesian information criterion and the Hannan-Quinn information criterion. We are particularly interested in the relation between the rate of correct model selection and the underlying sample size. Our numerical results show that the model selection for the compound Poisson type model works best for small parameter numbers. Moreover, the results for Hawkes processes confirm the theoretical asymptotic distributions of model selection whereas for the ACD model the model selection exhibits adverse behavior in certain cases.

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Bibliography: leaves 146-152 / vi, 152 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1987

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 125-135).

Thesis (Ph. D.)--Ohio State University, 1967. / Includes bibliographical references. Available online via OhioLINK's ETD Center

Thesis (Ph. D.)--Ohio State University, 1968. / Includes bibliographical references (leaves 76-77). Available online via OhioLINK's ETD Center