## 1 Introduction  
In a semiconductor production factory, a module of equipment that has malfunctioned or shut down must generally be repaired or replaced with a new module within the shop floor system. This activity results in equipment downtime and considerable maintenance costs, which, in turn, yield loss of production profit. In most processes, a wafer-handling robot arm (WHRA) is used to transfer wafers between the cassette and the chamber. However, a deviation in WHRA positioning may result in wafer fragmentation or backward positioning in processes such as in spin coating and yellow light generation. Although machine manufacturers have provided a solution, i.e., position compensation of robot arms, in the latest generation of machines, manufacturing engineers have attempted to upgrade old machines by implementing new controller boards. However, because of the additional cost this method incurs, users are resistant to such upgrade techniques. Therefore, an effective method for predicting maintenance time and a reliable kit for adding a positioning inspection module to existing equipment are required [1]. Conventional maintenance involves breakdown maintenance, scheduled preventive maintenance, and condition-based maintenance (CBM). In CBM, experts monitor a sensorless machine's health based on data, such as the driving voltage or current, obtained by attaching sensors, such as accelerometers and microphones, at key positions or locations with well-known domain-knowledge on the machine. In previous studies [2; 3; 4], some systematic, data-driven methods were used to trace the cause of major problems occurring in the ball screw of a feed drive system or Computer Numerical Control (CNC) machine in a manufacturing process. In that research, the failure signature was identified and classified using various prediction models. With trends such as big data, the Internet of Things, and smart manufacturing, smart analytics can determine the health statuses of CNC machines. The acquisition of large volumes of sensor data and data-driven approaches have developed in recent machine-learning research. Data cleaning and feature engineering are required for fast computing for effective machinery prognostics. Current methods to predict the failure of rotating machinery through CBM are based on physics-based or data-driven prognostics models. These methods are classified as conventional reliability models, condition-based prognostics models, or those integrating reliability and prognostics models [5]. A proactive reliability assessment method for a WHRA was studied in [1]; predictions were based on a sample degradation trend obtained through the Wiener stochastic process and random sampling with controlled uncertainty using a Monte Carlo simulation. The study's aim was to create a prognostic and health management model for predicting the lifetime and monitoring the state of the WHRA prior to maintenance. The reliability of an individual unit or subsystem during shop floor use is vital to the maintenance of the life of the unit or system. The remaining useful life (RUL) indicates the ability of a unit or system to survive in the future. When operation degrades, it is essential to estimate the RUL accuracy in order to make the appropriate decision for failure prevention. In [6], the prediction of the RUL of a bearing test rig was performed on the basis of a hazard model and logistic regression (LR) model by considering hard failure and multiple degradation features. Furthermore, a systematic methodology for the prognosis, health assessment, and RUL of ball screws was proposed in [7]. Because the RUL cannot be assumed to degrade linearly with the progress of the work cycle, RUL profiles may initially be constant before degrading according to a certain mathematical function at a certain inflection point until the final failure occurs.