Dynamic general path models for degradation data

• Autor(a) principal: Guilherme Augusto Veloso
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/40486; https://orcid.org/0000-0002-5348-3793
• topic: Degradation models; Dynamic models; Failure time distribution; Estatística – Teses; Degradação - Modelos – Teses; Sistemas dinâmicos – Teses; Análise do tempo de falha – Teses

The general degradation path models assume that there is a regular functional form common to all experimental units relating time and degradation. The random effects of the environment can affect the degradation trajectories of these units and, consequently, the assumed functional form becomes a very abrupt approximation of reality and biased estimates for failure times are obtained. Considering the temporal nature of degradation data, dynamic models emerge as an alternative to model such data, as they make an approximation by parts for the true form of the degradation path. The present doctoral thesis begins by presenting the datasets that motivate our work, together with a brief review of the degradation models that recur in the literature. The introduction also provides a detailed description of the contributions of the three models proposed in this text. The first one introduces a dynamic linear degradation model to address situations where degradation paths do not evolve regularly over time. This model is an extension of what was developed in my master's, as it assumes the presence of an intercept that dynamically evolves over time. The second model is aimed at describing the behavior of positive degradation data. Degradation measures are modeled according to a gamma distribution and the degradation rate is dependent on two components. The first quantifies the physical characteristics of each unit and the other is dynamic and represents the random effects of the common environment. As in the first model, the last proposed model assumes that degradation measures are normally distributed. Extending the first proposal, this model assumes that the degradation rate breaks down into the same two factors considered in the second model. However, it assumes that the effect that quantifies the physical characteristics of the device is a function of covariates. This approach introduces more flexibility to the analysis since, in some degradation tests, multiple characteristics are observed to understand different aspects of system reliability. The text ends with a compact summary of the methods and results obtained in the studies carried out throughout the thesis, together with relevant topics for future research.