A Control Chart Based on Likelihood Ratio Test for Monitoring Process Mean and Variability

摘要

Recently, monitoring the process mean and variance simultaneously by using a single chart has drawn more and more attention. In this paper, we propose a new single chart that integrates the EWMA procedure with the generalized likelihood ratio (GLR) test statistics for jointly monitoring both the process mean and variance. It can be easily designed and constructed, and its average run length can be evaluated by a two-dimensional Markov chain model. Owing to the good properties of the GLR test and EMWA, computation results show that it provides quite a robust and satisfactory performance in various cases, including the detection of the decrease in variability and the individual observation at the sampling point, which are very important in many practical applications but may not be well handled by the existing approaches in the literature. The application of our proposed method is illustrated by a real data example from chemical process control.