Statistical process monitoring based on maximum entropy density approximation and level set principle

Most control charts are based on the idea of separating the sample space of the quantity being monitored into an in-control region and an out-of-control region. This article proposes a control chart scheme that is based on the following ideas. First, a maximum entropy density is fitted to the null distribution of the quantity being monitored. Then the in-control region is selected as the one with the minimum volume from a set of acceptable in-control regions. The proposed control chart method utilizes the idea of density level sets being the minimum volume sets and thus a level set is selected as the optimal in-control region. The proposed control chart scheme defined by the level set is shown to be effective in detecting changes in the distribution of the quantity being monitored. Various numerical case studies are presented to illustrate the effectiveness of the proposed method.