The estimation of the failure rate is one of the most important subjects in PRA. The Bayes`` theorem has been applied to the program of predicting the failure rate of a specific component in the several recent studies. The new method is developed in this study to estimate the time varying failure rate of the component when the component is affected by aging. The developed method consists of the dynamics modeling, time update and measurement update, for which the Kalman filter technique is modified. The discrete probability distributions(DPDs) are used in all processes of the developed method instead of the continuous distributions for simplicity and accuracy. The results of the typical Bayesian approach and the developed method are compared using the Monte-Carlo simulation. And the results of the developed method are applied to the problem of the preventive replacement.