Análise de confiabilidade dependente do tempo usando modelos de séries temporais

Abstract

This thesis presents conceptual and computational comparisons between EOLE (Expansion Optimal Linear Estimation) and ARMA (Autoregressive Moving Average) models to represent stochastic processes in the context of time-dependent reliability analysis. It is demonstrated that similar results for time-dependent reliability can be obtained using the two approaches. Even though expansion techniques, such as EOLE, are appropriate for problems where the properties of the stochastic process are explicitly known, such information is rarely available in practical situations. On the other hand, time series models, such as ARMA, are widely employed to represent stochastic processes from real time monitoring or available historical data. Two new approaches, that are complementary to the previous ones, are presented in this thesis: i) appropriate calibration of ARMA models when the properties of the stochastic process are explicitly known, but no data sample is available; ii) employment of EOLE using information that can be obtained from real data samples, but without explicit knowledge of the properties of the stochastic process. These two novel approaches complement the approaches available until now. This is an important contribution for the field and allows the employment of ARMA and EOLE models in cases where it was not possible until now. With these two new approaches, ARMA and EOLE models were applied to five problems concerning time-dependent reliability. The results are notably consistent, demonstrating that the new approaches are valid and that time-dependent reliability analysis problems can be addressed using both ARMA and EOLE techniques.