Hybrid Stochastic Models for Remaining Lifetime Prognosis Dissertation

<p>This dissertation is concerned with the development of implementable analytical models for the estimation of the remaining lifetime probability distribution of a component subject to a randomly evolving environment. The models incorporate estimated parameters via environmental or degradation measures obtained from component sensors. We consider three distinct stochastic process models for the random environment: a temporally nonhomogeneous Markov environment a temporally homogeneous Markov environment and a temporally homogeneous semi-Markov environment. The hybrid approach unites real environment state or degradation measures with analytical stochastic failure models to numerically compute the distributions and their moments. Additionally it is shown that the lifetime distributions resulting from the homogeneous Markov environment and a special case of the nonhomogeneous Markov environment are distributions of the matrix-exponential type. Because the lifetime distribution in the semi-Markov case is computationally intensive we instead utilize phase-type (PH) approximations that transform the semi-Markov environment to a time-homogeneous Markov environment. The numerical experiments indicate that the analytical techniques developed in this research hold great promise for remaining lifetime prognosis in a variety of contexts.</p><p>This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact and remains as true to the original work as possible. Therefore you will see the original copyright references library stamps (as most of these works have been housed in our most important libraries around the world) and other notations in the work.</p><p>This work is in the public domain in the United States of America and possibly other nations. Within the United States you may freely copy and distribute this work as no entity (individual or corporate) has a copyright on the body of the work.</p><p>As a reproduction of a historical artifact this work may contain missing or blurred pages poor pictures errant marks etc. Scholars believe and we concur that this work is important enough to be preserved reproduced and made generally available to the public. We appreciate your support of the preservation process and thank you for being an important part of keeping this knowledge alive and relevant.</p>