Monitoring Multi-Attribute Processes Based on NORTA Inverse Transformed Vectors

Abstract

Although multivariate statistical process control has been receiving a well-deserved attention in the literature, little work has been done to deal with multi-attribute processes. While by the NORTA algorithm one can generate an arbitrary multi-dimensional random vector by transforming a multi-dimensional standard normal vector, in this article, using inverse transformation method, we initially transform a multi-attribute random vector so that the marginal probability distributions associated with the transformed random variables are approximately normal. Then, we estimate the covariance matrix of the transformed vector via simulation. Finally, we apply the well-known T ² control chart to the transformed vector. We use some simulation experiments to illustrate the proposed method and to compare its performance with that of the deleted-Y method. The results show that the proposed method works better than the deleted-Y method in terms of the out-of-control average run length criterion.

Keywords:

• Multivariate statistics
• Multi-attribute control chart
• Normal transformation
• NORTA method
• Quality control

Mathematics Subject Classification:

• Primary 62H99
• Secondary 62P30