Monitoring of zero-inflated binomial processes with a DEWMA control chart

Abstract

Control charts are widely used for monitoring quality characteristics of high-yield processes. In such processes where a large number of zero observations exists in count data, the zero-inflated binomial (ZIB) models are more appropriate than the ordinary binomial models. In ZIB models, random shocks occur with probability θ, and upon the occurrence of random shocks, the number of non-conforming items in a sample of size n follows the binomial distribution with proportion p. In the present article, we study in more detail the exponentially weighted moving average control chart based on ZIB distribution (ZIB-EWMA) and we also propose a new control chart based on the double exponentially weighted moving average statistic for monitoring ZIB data (ZIB-DEWMA). The two control charts are studied in detecting upward shifts in θ or p individually, as well as in both parameters simultaneously. Through a simulation study, we compare the performance of the proposed chart with the ZIB-Shewhart, ZIB-EWMA and ZIB-CUSUM charts. Finally, an illustrative example is also presented to display the practical application of the ZIB charts.