Semi-parametric models for heterogeneous degradation data
Degradation data are commonly considered to make reliability assessments in highly reliable systems. General path models are a possible approach to model the degradation behavior. This class of models includes random effects in its structure to account for correlation among the measures in a single unit. Distributions for random effects, which may have a nice interpretation in terms of the degradation rate, are usually specified assuming that degradation comes from homogeneous populations. Homogeneity can be a strong assumption if there is high variability in the manufacturing process or whenever there is no guarantee that the devices works on similar conditions. We develop semi-parametric degradation models that simultaneously accommodate skewness, multimodality and heavy-tail behavior. That is achieved by assuming a Dirichlet process mixture of both normal and skew-normal distributions for the random effects. We also prove that the proposed model account for multi-modality in the lifetime distribution as it is also a Dirichlet process mixture. We carry out simulation studies and data analysis to show the flexibility of the proposed model in modeling skewness, heavy tail and multi-modal behavior of the random effects.
We conclude that the prior specification for the precision parameter and initial number of components in the DP does not substantially affect the posterior inference for the failure time. Thus, the proposed model may be implemented starting from a more parsimonious structure. In comparison to Weibull model and the finite mixture of normal model, the Monte Carlo study showed that the proposed models are a competitive approach providing better inference for the failure time of a future observation in heterogeneous population. Their behavior, in terms of biases, is also comparable to that obtained under Weibull model for Weibull data.
Joint work with Cristiano C. Santos