Aiming at the non-stationarity and nonlinear failure rate data and existing problems of prediction methods, a relevance vector empirical mode decomposition(RVEMD) and group method of data handling(GMDH) is presented. First of all through the fluctuation and trend of failure rate time series decomposition by RVEMD, the intrinsic mode function(IMF) and residual function(RF) can be gotten, and the relevance vector machine(RVM) method is used to predict the endpoint of local extremum suppression of the existence of end effects by traditional empirical mode decomposition(EMD). Furthermore, RVM regression is used to generate the upper and lower envelopes of the sequence, instead of the conventional three spline interpolation method; and then, the forecasting model using RVM and the grey forecasting model using RF are established for each IMF component, which has made the improvement to the standard RVM regression model, through the construction of a variance Gauss kernel function(VGKF) to improve the kernel function of the overall performance and generalization ability of prediction of embedding dimension by H-Q criterion, avoiding the blindness of subjective selection, and a background value of grey prediction model based on the optimization of background value and development is constructed; finally, the optimal combination model of GMDH algorithm is used to get the final prediction results. The proposed method has better prediction performance than the conventional EMD decomposition.