Flexible Monitoring Methods for High-yield Processes

Abstract

In recent years, advancement in technology brought a revolutionary change in the manufacturing processes. Therefore, manufacturing systems produce a large number of conforming items with a small amount of non-conforming items. The resulting dataset usually contains a large number of zeros with a small number of count observations. It is claimed that the excess number of zeros may cause over-dispersion in the data (i.e., when variance exceeds mean), which is not entirely correct. Actually, an excess amount of zeros reduce the mean of a dataset which causes inflation in the dispersion. Hence, modeling and monitoring of the products from high-yield processes have become a challenging task for quality inspectors. From these highly efficient processes, produced items are mostly zero-defect and modeled based on zero-inflated distributions like zero-inflated Poisson (ZIP) and zero-inflated Negative Binomial (ZINB) distributions. A control chart based on the ZIP distribution is used to monitor the zero-defect process. However, when additional over-dispersion exists in the zero-defect dataset, a control chart based on the ZINB distribution is a better alternative. Usually, it is difficult to ensure that data is over-dispersed or under-dispersed. Hence, a flexible distribution named zero-inflated Conway–Maxwell–Poisson (ZICOM-Poisson) distribution is used to model over or under-dispersed zero-defect dataset. In this study, CUSUM charts are designed based on the ZICOM-Poisson distribution. These provide a flexible monitoring method for quality practitioners. A simulation study is designed to access the performance of the proposed monitoring methods and their comparison. Moreover, a real application is presented to highlight the importance of the stated proposal.