Rank-based process control for mixed-type data

Conventional statistical process control tools target either continuous or categorical data but seldom both at the same time. However, mixed-type data consisting of both continuous and categorical observations are becoming more common in modern manufacturing processes and service management. However, they cannot be analyzed using traditional methods. By assuming that there is a latent continuous variable that determines the attribute levels of a categorical variable, the ordinal information among the attribute levels can be exploited. This enables us to simultaneously describe and monitor continuous and categorical data in a unified framework of standardized ranks, based on which a multivariate exponentially weighted moving average control chart is proposed. This control chart specializes in detecting location shifts in continuous data and in latent continuous distributions of categorical data. Numerical simulations show that our proposed chart can efficiently detect location shifts and is robust to various distributions.