A hybrid root transformation and decision on belief approach to monitor multiattribute Poisson processes

Most of industrial applications of statistical process control involve more than one quality characteristics to be monitored. These characteristics are usually correlated, causing challenges for the monitoring methods. These challenges are resolved using multivariate quality control charts that have been widely developed in recent years. Nonetheless, multivariate process monitoring methods encounter a problem when the quality characteristics are of the attribute type and follow nonnormal distributions such as multivariate binomial or multivariate Poisson. Since the data analysis in the latter case is not as easy as the normal case, more complexities are involved to monitor multiattribute processes. In this paper, a hybrid procedure is developed to monitor multiattribute correlated processes, in which number of defects in each characteristic is important. Two phases are proposed to design the monitoring scheme. In the first phase, the inherent skewness of multiattribute Poisson data is almost removed using a root transformation technique. In the second phase, a method based on the decision on belief concept is employed. The transformed data obtained from the first phase are implemented on the decision on belief (DOB) method. Finally, some simulation experiments are performed to compare the performances of the proposed methodology with the ones obtained using the Hotelling T2 and the MEWMA charts in terms of in-control and out-of-control average run length criteria. The simulation results show that the proposed methodology outperforms the other two methods.