Modelos robustos para degradação linear e tempo de falha - Rívert Paulo Braga Oliveira (2015)
In statistics the reliability is a branch that seeks to describe the time to failure distribution of objects of interest. For certain situations where failures are not frequent or virtually nonexistent, the estimation of quantities describing the failure times is compromised. The general degradation models have been developed to overcome this problem by measuring a feature linked to failure, not the failure itself. When this feature is monitored it becomes possible to improve the estimates of the time to failure quantities of interest. In this paper we introduce exible classes of failure time models and degradation that are able to accommodate asymmetric behavior and heavy tails. For the degradation path models this goal is achieved by assuming the degradationand reciprocal degradation rates have distributions in both classes of distributions, the scale mixture of skew-normal and scale mixture of log skew normal families of distributions. We also consider the same families to perform conventional time to failure analysis. For both models we build up algorithms based on the data augmentation technique in order to sample parameters from the posterior distribution. The new methodologies are applied to simulated databases with dierent characteristics, considering the presence or absence asymmetry, heavy tails and light tails. The modeling of known literature practical situations is also explored, namely the train wheels and lasers degradation data, and the lung cancer lifetime data. The results of the new modeling are compared with current approaches to model degradation and conventional failure times. Due to its exibility characteristics, the proposed methods show promise even in cases of misspecication. The work also has a rich discussion on general degradation path models, and conventional failure time models, in terms of the Bayesian paradigm. Some formal proofs and propositions also provide interesting theoretical results not yet explored in the literature. Finally, the developed methodology leaves several open issues and results to encourage further research.