The small sample prediction problem which commonly exists in reliability analysis was discussed with the progressive prediction method in this paper. The modeling and estimation procedure

as well as the forecast and confidence limits formula of the progressive auto regressive (PAR) method were discussed in great detail. PAR model not only inherits the simple linear features of auto regressive (AR) model

but also has applicability for nonlinear systems. An application was illustrated for predicting the future fatigue failure for Tantalum electrolytic capacitors. Forecasting results of PAR model were compared with auto regressive moving average (ARMA) model

and it can be seen that the PAR method can be considered good and shows a promise for future applications.