A Phase II control chart based on the weighted likelihood ratio test for monitoring polynomial profiles

In this paper, a new Phase II control chart based on the weighted likelihood ratio test (WLRT) is proposed for monitoring polynomial profiles. The new chart can be easily designed and constructed. Due to the good properties of the likelihood ratio test, computation results show that it provides quite satisfactory performance in various cases, including the detection of the decrease in variance which is very important in many practical applications but may not be well handled by the existing approaches in the literature. Average run length (ARL) comparisons between some other procedures and the new chart are presented. The effect of parameter estimates on the WLRT chart is considered. The application of our proposed method is illustrated by a simulation example.