Control chart for multivariate attribute processes

Many industrial processes are multivariate in nature since the quality of a product depends on more than one variable. Multivariate control procedures can be used to capture the relationship between the variables and to provide more sensitive control than that provided by the application of univariate control procedures on each variable. Much has been done on the multivariate variable processes, such as embodied in control procedures based on Hotelling's T-2 statistic. However, little work has been done to deal with the control of multivariate attribute processes, which is very important in practical production processes. In this paper, we develop a Shewhart-type control chart to deal with multivariate attribute processes, which is called the multivariate np chart (MNP chart). The control chart uses the weighted sum of the counts of nonconforming units with respect to all the quality characteristics as the plotted statistics. It enhances the efficiency of identifying the critical assignable cause when an out-of-control signal appears. It is also simple to interpret for out-of-control signals. The practical application of the MNP chart is also discussed in this paper with an example presented to demonstrate the approach of the MNP chart and to compare with the univariate np control charts which are commonly used in industry.