Multivariate control chart based on the highest possibility region

Abstract

The T 2 control chart is widely adopted in multivariate statistical process control. However, when dealing with asymmetrical or multimodal distributions using the traditional T 2 control chart, some points with relatively high occurrence possibility might be excluded, while some points with relatively low occurrence possibility might be accepted. Motived by the thought of the highest posterior density credible region, we develop a control chart based on the highest possibility region to solve this problem. It is shown that the proposed multivariate control chart will not only meet the false alarm requirement, but also ensure that all the in-control points are with relatively high occurrence possibility. The advantages and effectiveness of the proposed control chart are demonstrated by some numerical examples in the end.

Process Capability Indices Based on the Highest Density Interval

“…As Tano and Vännman introduced, MPCIs can roughly be divided into four different groups: group 1, based on the ratio of a tolerance region to a process region; group 2, based on the probability of NC; group 3, based on the PCA; and group 4, others. For MPCIs belong to group 1, similar to the multivariate control charts based on the highest density region in Gang et al ., the highest density region can be used to define the process region and present the corresponding MPCIs. For MPCIs belong to group 3, the highest density interval can be utilized to define the natural tolerance for each principal component.…”