A CUSUM-based method for monitoring simple linear profiles

In most statistical process control applications, the quality of a process or product is characterized by univariate or multivariate quality characteristics and monitored by the corresponding univariate and multivariate control charts, respectively. However, sometimes, the quality of a process or a product is better characterized by a relationship between a response variable and one or more explanatory variables. This relationship, which can be linear, nonlinear, or even a complicated model, is referred to as a profile. So far, several methods have been proposed for monitoring simple linear profiles. In this paper, a new method based on cumulative sum statistics is proposed to enhance monitoring of linear profiles in phase II. The performance of the proposed method is evaluated by average run length criterion. A comprehensive comparison is also conducted between the performance of the proposed method and the existing methods for monitoring simple linear profiles. The results show that the proposed method performs satisfactorily. In addition, the effects of reference value, sample size, and corrected sum of squares of explanatory variables on the performance of the proposed method are investigated.