On the monitoring of multi-attributes high-quality production processes

Over the last decade, there have been an increasing interest in the techniques of process monitoring of high-quality processes. Based upon the cumulative counts of conforming (CCC) items, Geometric distribution is particularly useful in these cases. Nonetheless, in some processes the number of one or more types of defects on a nonconforming observation is also of great importance and must be monitored simultaneously. However, there usually exist some correlations between these two measures, which obligate the use of multi-attribute process monitoring. In the literature, by assuming independence between the two measures and for the cases in which there is only one type of defect in nonconforming items, the generalized Poisson distribution is proposed to model such a problem and the simultaneous use of two separate control charts (CCC & C chats) is recommended. In this paper, we propose a new methodology to monitor multi-attribute high-quality processes in which not only there exist more than one type of defects on the observed nonconforming item but also there is a dependence structure between the two measures. To do this, first we transform multi-attribute data in a way that their marginal probability distributions have almost zero skewnesses. Then, we estimate the transformed mean vector and covariance matrix and apply the well-known x2 control chart. In order to illustrate the proposed method and evaluate its performance, we use two numerical examples by simulation and compare the results. The results of the simulation studies are encouraging.