Monitoring correlated variable and attribute quality characteristics based on NORTA inverse technique

In some statistical process control applications, quality of a process or a product is characterised and monitored based on a variable or an attribute quality characteristic. However, sometimes a vector of variables or attributes describes the quality of a process. Likewise, in some cases, quality of a process or a product is characterised by a combination of several correlated variables and attributes. To the best of our knowledge, there is no method in monitoring multivariate-attribute processes in spite of numerous studies in multivariate and multi-attribute control charts. This paper describes a method to monitor a process with multiple correlated variable and attribute quality characteristics. In the proposed method, we utilise NORTA inverse technique to design a scheme in monitoring multivariate-attribute processes. First, NORTA inverse method transforms the data to a multivariate normal distribution, and then we apply multivariate control charts such as T² and MEWMA for transformed data. The performance of the proposed method considering both T² and MEWMA charts is investigated by using simulation studies in terms of average run length criterion.