Phase II monitoring of simple linear profiles under decreasing step shifts

Recently, Profile monitoring in which the quality of a process or product can be characterized by a relationship between two or more variables has been considered by a lot of researchers. In different applications, the profiles can be linear or nonlinear in nature. Several methods have been proposed for monitoring simple linear profiles in Phase II. Some of these methods either have been developed to detect increasing step shifts or their performance is just evaluated under this type of shift. However, sometimes, a decreasing step shift can be occurred leading to poor performance of the process. In this paper, we modify the methods including T2, EWMA-3, and CUSUM-3 to improve their performance in detecting decreasing step shifts in Phase II. The performance of the modified methods as well as other existing methods including EWMA/R, MEWMA and LRT has been evaluated under decreasing step shifts by using simulation studies via Average Run length criterion.