Application of Bayesian Method for Virtual Metrology of Mobile Repeater System

Abstract

Our research purpose is to reducing measurement cost and time by testing measurements of one frequency band section to predict those of other frequency band sections during quality inspection of ICS Repeater’s test WCDMA ICS Repeater, especially one with band selective function, have complicated structure comparing to standard repeater which only used for single frequency bandwidth and require time and cost during the repeating same test process to each different frequency bandwidth. To solve this problem, modern technology need to virtual metrology and establish statistical model in order to reduce the testing process. Virtual metrology is method that uses the regression model which considers and investigates process variable and independent variable to find relationship. However it is difficult to apply to situation such as band selective ICS repeater which has only small sample data. In order to solve problem occurred during repeated tests and small sample size. This thesis suggests virtual metrology by regression model with Bayesian methods. Also this thesis compares the Bayesian regression analysis, multivariate Bayesian regression analysis and regression analysis by previously acquired sample data. In this thesis, despite the small sample data we can increase the precision of regression coefficient estimation and it is effective to virtual metrology of ICS repeater. This research applicate Bayesian regression analysis based on correlated measurement data. The Bayesian regression models use prior information from historical measurement data to predict measurements of other frequency band sections by exploiting correlation structure of measurements. In case of small size samples such as an ICS repeater, Bayesian regression can improve the accuracy of parameter estimation by using prior distribution of regression parameters. For small sized samples such as WCDMA(Wideband Code Division Multiple Access) band selective ICS repeaters, this research provides virtual inspection methods on products using correlation structure of measurement data mainly via Bayesian framework.