Browsing by Subject "Reliability (Engineering)--Mathematical models."

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Open Access
Parameter estimation in switching stochastic models
(2004) Güleryüz, Güldal
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.
Open Access
A policy for the maintenance of a multistate multicomponent series system
(1997) Kaya, Alev
In real life situations various levels of performance for both systems and components are identified. Deterioration of systems and components has been considered by many maintenance and replacement models in the literature, but most of these models are for single component. Our study concerns a multistate multicomponent maintenance model. We extended the model studied by Van der Duyn Schouten and Vanneste (1993) with four states, (0,1,2,3), to a multistate system with 5 + 1 states, (0, 1,..., S). While classifying these S +1 states, we use two different classification schemes corresponding to different real life situations. Then, we analyze our model under both exponential and Erlang sojourn time distributions for both state classification schemes. As a result of our analysis, we derive expressions for the long-run average cost per unit time. We used the randomization method to evaluate the transient state probabilities during the implementation of the average cost expressions.