Análise de confiabilidade de sistemas reparáveis: abordagens para dados de tempo de falha, degradação e degradação acelerada

Abstract

Reliability analysis aims to understand and predict the behavior of systems over time, using both failure data and degradation data. In repairable systems, these two types of information are particularly relevant, as they allow one to characterize the evolution of failure risk and the impact of maintenance actions throughout the life cycle. Therefore, it is possible to develop more realistic models to support maintenance decisions and optimize operational costs, reflecting the actual conditions to which the systems are subjected. In this thesis, we present three statistical models focused on the analysis of repairable systems from different perspectives. Initially, we propose a frailty model for failure times in systems operating under minimal repair, accounting for unobserved heterogeneity among units. The failure intensity function follows a Power Law Process, while the frailty term is assumed to follow a non‑central Gamma distribution. Through simulation studies and applications to real datasets, we demonstrate that this approach yields more accurate estimates and reliability functions that are better adjusted to the variability among systems. Subsequently, we advance to models based on degradation trajectories, investigating processes in which the system condition deteriorates over time and can be partially restored by imperfect maintenance actions. We adopt the inverse Gaussian process associated with the order-one Arithmetic Reduction of Degradation ARD1 mechanism, which captures the variable effects of maintenance actions and provides more faithful representations of system behavior. Simulation studies and applications confirm the model's effectiveness. Finally, we propose an accelerated degradation model that combines the inverse Gaussian process with an exponential acceleration factor and the imperfect maintenance mechanism. This formulation allows for the simultaneous assessment of the effects of external stress variables and maintenance actions, providing estimates of the mean time to failure and reliability functions that are more consistent with dynamic operating conditions. Across all models, we adopt a classical approach to construct likelihood functions, estimate parameters via maximum likelihood, and investigate asymptotic properties through simulation studies. Applications demonstrate the potential of the proposed methodologies to support more effective maintenance policies and provide technical insights for managing of repairable systems operating under variable and heterogeneous conditions.