A nonparametric CUSUM scheme for monitoring multivariate time-between-events-and-amplitude data with application to automobile painting

Monitoring time-between-events-and-amplitude (TBEA) data, including the time interval between two successive nonconforming events and the amplitude of an event, is significant in many applications, especially manufacturing and service operations. Almost all TBEA control charts consider only one quality characteristic of the event, and most of the related research is restricted to cases where data are assumed to follow specific distributions. However, an event is usually described by multiple quality characteristics of which underlying distributions are unknown. In this article, we integrate the TBEA data into a specified form and then design a nonparametric multivariate TBEA (NMTBEA) control chart based on log-linear modelling. This chart is used to monitor the location shifts of the time interval and the amplitudes in an event. Next, we investigate the performance of some improved nonparametric control charts in monitoring multivariate TBEA data. The numerical simulation results show that the NMTBEA control chart performs best in most shifts that occur in six representative distributions. A real example of the colour difference monitoring of the car body in the automotive industry is provided to illustrate the implementation of the proposed chart.