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This paper presents a parameter residual-based method for predicting the remaining useful life (RUL) of multilayer ceramic capacitors (MLCCs) under temperature-humidity-bias conditions. Three performance parameters in each MLCC were monitored: capacitance, dissipation factor, and insulation resistance. A kernel regression method was used to estimate the parameters' values of interest. The residuals were generated by the difference between the estimation and the actual monitored value. Based on the features of the residual data, a linear state space model was adopted to describe the dynamics of the residuals. The future evolution of the residuals was predicted with uncertainty bounds in a Bayesian framework. The failure threshold in terms of the parameter residuals was investigated. Then, the RUL of each MLCC with uncertainty bounds was determined. By comparing the predicted results with the experimental results, it was demonstrated that the proposed prognostics approach can provide an estimation of the RUL of MLCCs.