Resumo:
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.
