Semiparametric regression control charts. (2nd January 2017) - Chen, Yuhui; Hanson, Timothy
ABSTRACT: Control charts are screening processes that have been widely used in many areas where monitoring product quality is required. Many methods have been proposed to construct charts with different types of data. A common point in most existing methods is to monitor the quality variable only. However, in many situations, the quality variable depends on other covariates, such as environmental factors. Thus, without adjusting charts by taking the effect of covariates into consideration, the traditional charts typically have a poor performance when the quality variable is highly dependent on covariates. To this point, we propose a new type of semiparametric regression control charts by integrating a regression model into a traditional control chart. The quality monitoring process stems from a newly developed nonparametric prior called the transformed Bernstein polynomial prior (TBPP), which provides a convenient and robust way to implement the pattern recognition by assuming the unknown pattern is centered at a standard, commonly used parametric family, such as the normal. Then, by adding details via the data, any departure from the initial parametric guess will be captured and used for adjustment on estimation to guarantee robustness. In addition, this new type of control charts also inherits the merit of the smoothness property of the TBPP and thus provides an efficient estimation procedure through optimization. In practice, the proposed method is, therefore, suitable to screening a process where a large data set is presented.