Process Monitoring with Multivariate p-Control Chart

We assume that the operator is interested in monitoring a multinomial process. In this case the items are classified into (k+1) ordered distinct and mutually exclusive defect categories. The first category is used to classify the conforming defect-free items, while the remaining k categories are used to classify the nonconforming items in k defect grades, with increasing degrees of nonconformity. Usually the process is said to be capable if the overall proportion of nonconforming items is very small and remains low, or declines over time. Nevertheless, since we classify the nonconforming items into k distinct defect grades, the operator can also evaluate the overall level of defectiveness. This quality parameter depends on the k defect categories. Furthermore, we are interested in evaluating, over time, the proportion of nonconforming items in each category as well as the overall level of defectiveness. To achieve this goal, we propose (i) a normalized index that can be used to evaluate the capability of the process in terms of the overall level of defectiveness, and (ii) a two-sided Shewhart-type multivariate control chart to monitor the overall proportion of nonconforming items and the corresponding defectiveness level.