In this study a Charge-coupled Device (CCD)- based robot arm fault diagnostic system was created, and a prognostic and health management (PHM) model was developed to predict the Mean-Time-to-Failure (MTTF) and Residual Useful Life (RUL) of the wafer handling robot arm. The prognostic results are used to evaluate the healthy state of the robot arm prior to maintenance. The observation of real random eccentric path of the robot arm based on the data collection from the handling position measurement represented the random walk likely and thus the Wiener stochastic process model was applied. The random sampling simulation called Monte Carlo method with the control of the uncertainty is also used to simulate all possible paths to the failure threshold. The MTTF and RUL are calculated for each prediction from the PDF on the threshold level. It is noted that the robot arm is in a healthy state to handling wafers according to the results of prognosis. The handling test of the robot arm runs continually and more measurement data were collected to validate the PHM model.