Phase II monitoring of generalized linear profiles using weighted likelihood ratio charts

In recent years, effective profile monitoring for discrete response variables, such as binary, multinomial, ordinal or Poisson variables, has increasingly attracted interest of researchers in the area of statistical process control. Such quality characteristics are often modeled as special cases of generalized linear models. The objective of this paper is to try to provide a unified framework for Phase II monitoring of generalized linear profiles of which the explanatory variables can be fixed design or random arbitrary design. To this end, a new control chart is developed based on the weighted likelihood ratio test, and it can be readily extended to other generalized profiles or profiles with random predictors if the likelihood function can be obtained. Numerical results and illustrative example show that the proposed control chart has satisfactory in-control run length distribution and stands out at early detection.