A one-chart scheme for joint monitoring of the two parameters of zero-inflated Poisson processes

The high-quality processes usually have more count of zeros than are expected under chance variation and are commonly modeled by zero-inflated Poisson (ZIP) distribution. A ZIP model has two parameters-phi (phi is an element of[0,1]) and lambda (lambda>0). Often separate control charts are used for monitoring the two parameters. But a one-chart scheme for joint monitoring of the two parameters offers significant operational advantages. A few one-chart schemes for joint monitoring of the two parameters are reported in literature. However, the monitoring statistic of none of these schemes is defined directly on the observed quality characteristics. This leads to difficulty in understanding of these schemes by the practitioners. Any control charting scheme developed directly on the observed quality characteristic is intuitively appealing to the practitioners and can be easy to interpretations by the practitioners. In this article, a one-chart scheme (called Gamma chart) is developed considering average number of nonconformities in the samples as the monitoring statistic. The performance of the Gamma chart is studied via simulation. The results reveal that it efficiently detect the out-of-control process conditions resulting from moderate shifts in phi and/or lambda. Finally, a case study from an Indian automobile industry is presented.