This paper deals with the surveillance of the health state and the prediction of the Remaining Useful Life (RUL) of an operating equipment unit of the semiconductor manufacturing industry. It aims at improving an existing work performed in this domain. For that, a new framework for RUL prediction is proposed based on modeling the behavior of the Health Indicator (HI). The contribution of this framework is the effective combination of the proposed HI extraction and the RUL prediction approaches. The HI extraction approach is mainly based on the Least Absolute Shrinkage and Selection Operator (LASSO) regression model. The RUL prediction approach relies on the adaptive Wiener process in which the similarity principle is introduced. An application of the proposed framework on real industrial data shows an improvement of the RUL prediction accuracy compared to the existing work.