Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent Univ., 2004.Thesis (Ph.D.) -- Bilkent University, 2004.Includes bibliographical references leaves 96-100.In this thesis, we suggest an approach to statistical parameter estimation
when an estimator is constructed by the trajectory observations of a stochastic
system and apply the approach to reliability models. We analyze the asymptotic
properties of the estimators constructed by the trajectory observations using moments
method, maximum likelihood method and least squares method. Using
limit theorems for Switching Processes and the results for parameter estimation
by trajectory observations, we study the behavior of moments method estimators
which are constructed by the observations of a trajectory of a switching process
and prove the consistency and asymptotic normality of such estimators. We consider
four different reliability models with large number of devices. For each of the
models, we represent the system process as a Switching Process and prove that
the system process converges to the solution of a differential equation. We also
prove the consistency of the moments method estimators for each model. Simulation
results are also provided to support asymptotic results and to indicate the
applicability of the approach to finite sample case for reliability models.Güleryüz, GüldalPh.D
