Monitoring polynomial profiles in quality control applications

In some statistical process control applications, quality of a process or product is characterized by a relationship between two or more variables which is referred to as profile. Sometimes, this relationship can be characterized by a polynomial profile. There are some methods in the literature which can be easily extended and used for monitoring polynomial profiles. In this paper, a new method is proposed for monitoring kth order polynomial profiles in phase II. In the proposed method, the polynomial profiles are transformed to orthogonal polynomial profiles, and the parameters of the transformed model are monitored by separate exponentially weighted moving average control charts. Based on the relationship between the parameters of the main and transformed model, the step shifts in the parameters of main model lead to larger step shifts in the parameters of the transformed model. Hence, this transformation leads to quicker detection in phase II. The performance of the proposed method is compared with the existing methods using numerical simulation runs in terms of average run length criterion.