The Design of Generalized Likelihood Ratio Control Chart for Monitoring the von Mises Distributed Data

Abstract

‎In this paper‎, ‎a new generalized likelihood ratio (GLR) control chart based on sequentially probability ratio test (SPRT) is introduced to monitor the directional mean of von Mises distribution‎. ‎Different window size of past samples are utilized to construct the GLR chart statistic‎, ‎and the performance of this chart in detecting a wide range of parameter shift is evaluated‎. ‎A simulation study is carried out to investigate the performance of the proposed control chart in comparison with cumulative sum (CUSUM) control chart‎. ‎To guide practitioners‎, ‎a real example is provided‎.

Keywords

• von mises distribution
• average run length
• maximum likelihood estimation
• cusum
• generalized likelihood ratio