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