Desenvolvimento de metodologias estatísticas para modelagem da degradação da performance de sistemas reparáveis.

Abstract

Reliability and maintenance have become crucial in industrial systems, leading to the develop ment of associated theories and methodologies. In a globalized and highly competitive market, producing highly reliable products is essential to maximize profits and meet consumer demand. Traditional reliability analysis, which often relies on failure data to select lifetime models, faces challenges with modern products. Recent advances in monitoring techniques and the increasing reliability of systems have shifted the focus to degradation modeling, which can provide valuable information even in the absence of failures. Degradation-based reliability analysis posits that monitoring quality characteristics over time can reveal important informa tion about equipment condition. Various stochastic processes, such as the Gamma Process and the Wiener Process, have been used to model this deterioration. Although these models have been generalized to incorporate covariates, random effects, and maintenance impacts, and recent studies investigate different observation schemes, a gap remains in applying models that consider varying maintenance effects to prognostics problems with real-world data. This dissertation, therefore, proposes an extension of the degradation model based on the Wiener Process with imperfect maintenance of the Arithmetic Reduction of Degradation with memory one (ARD1) type. The main contribution is the generalization of the model to incorporate time-varying maintenance effects, allowing for a more realistic representation of aging systems. A complete methodology for statistical inference was developed, including the derivation of Maximum Likelihood Estimators (MLE), the proof of their bias properties, and the formal construction of confidence intervals. Additionally, the distribution of the Remaining Useful Life (RUL) was derived, demonstrating that it follows an Inverse Gaussian distribution. The robustness of the estimators was validated through an extensive simulation study, which confirmed their good asymptotic properties. Finally, the methodology was applied to a case study with data from an industrial bag filter. The fitted model showed good adherence and was used as a prognostic tool to estimate the equipment’s reliability curve and RUL, providing a quantitative basis for maintenance planning. This work, therefore, connects statistical inference theory with the practical application of prognostics, offering a validated methodology for the analysis of repairable systems.