In most statistical process control (SPC) applications, quality of a process or product is monitored by univariate or multivariate control charts. However, sometimes a functional relationship between a response variable and one or more explanatory variables is established and monitored over time. This relationship is called “profile” in SPC literature. In this paper, we specifically consider processes with compositional data responses, including multivariate positive observations summing to one. The relationship between compositional data responses and explanatory variables is modeled by a Dirichlet regression profile. We develop a monitoring procedure based on likelihood ratio test (lrt) for Phase I monitoring of Dirichlet regression profiles. Then, we compare the performance of the proposed method with the best method in the literature in terms of probability of signal. The results of simulation studies show that the proposed control chart has better performance in Phase I monitoring than the competing control chart. Moreover, the proposed method is able to estimate the real time of a change as well. The performance of this feature is also investigated through simulation runs which show the satisfactory performance. Finally, the application of the proposed method is illustrated based on a real case in comparison with the existing method.
Outliers Detection Models in Shewhart Control Charts; an Application in Photolithography: A Semiconductor Manufacturing Industry