A Kernel-Density based Semi-Parametric stochastic degradation model with dependent increments

The degradation modeling of highly reliable industrial products is a significant issue for manufacturers, and stochastic process models have been widely applied to model degradation trends. However, they suffer from the two underlying assumptions: the degradation increments following a specific parametric distribution and mutually independent degradation increments. Hence some degradation trends cannot be well captured by these models. In this paper, we propose a general semi-parametric stochastic degradation model to fit the degradation data. The probability density function of the degradation increments is estimated by the adaptive kernel density estimation method, and the copula function is used to measure the dependence of the successive degradation increments. Increments are extrapolated by marginal conditional distributions. A simulation study is carried out where the degradation increments are generated under five distributions, and four degradation models are used to fit the data. The simulation results show that the proposed model can well fit the data generated from the existing stochastic process models as well as other models. Finally, several real datasets are used to verify the validity of the proposed method, which can generate more similar degradation paths to the real ones and thus can provide a more accurate lifetime prediction.