A combination of CUSUM charts for monitoring a Zero-inflated Poisson process

As an extension of the standard Poisson distribution, the Zero-inflated Poisson distribution (ZIP) is used to model the defects in the process with a large number of zeros in the process data. We studied a CUSUM type chart for monitoring the ZIP processes. We propose a control charting procedure using a combination of two cumulative sum (CUSUM) charts to detect increases in both parameters of the ZIP process, denoted as conforming run length (CRL) CUSUM chart, zero truncated Poisson (ZTP) CUSUM chart, and the combination of them as CRL-ZTP CUSUM chart. The control limits of the CRL-CUSUM chart and ZTP-CUSUM chart are obtained using Markov chain based methods. And both Markov chain based methods and simulations are used to determine the control limits of the CRL-ZTP CUSUM chart. Simulation experiments show that the CRL-ZTP CUSUM chart outperforms an existing method. And the CRL-ZTP CUSUM chart is more practical in detecting the increase in one or both of the parameters of the ZIP process. Finally, a real example is presented to illustrate the implementation of our proposed methods in a manufacturing application.