Monitoring a process with mixed-type and high-dimensional data

Statistical process control (SPC) techniques that originated in manufacturing have also been applied to monitoring various service processes. The quality of a service process can be characterized by one or several variables. Conventional multivariate SPC methods usually assume these process variables follow an underlying distribution, generally multivariate normal. However, in many cases, the distribution assumption cannot be easily made, or the assumption made is not appropriate. For instance, the quality characteristics of a service process may include both continuous and categorical variables (i.e., mixed-type variables). In this case there will be no specific distribution to assume. Direct application of conventional SPC techniques to monitor such mixed-type variables may cause increased false alarm rates and misleading conclusions. To further complicate the case, the number of variables is usually large (i.e., high-dimensional variables). This paper enumerates the difficulties in monitoring a process with mixed-type and high-dimensional data and discusses potential solutions.