Control Charts Based on Zero to k Inflated Power Series Regression Models and Their Applications

In many different fields and industries, count data are publicly accessible. Control charts are used in quality studies to track count procedures. These control charts, however, only have a limited impact on zero-inflated data that contains extra zeros. The Zero-inflated power series (ZIPS) models, particularly its crucial sub-models, the Zero-inflated Poisson (ZIP), the Zero-inflated Negative binomial (ZINB), and the Zero-inflated Logarithmic (ZIL) models, are crucial approaches to handle the count data, and some control charts based on them have been proposed. However, there are situations when inflation can happen at one or more points other than zero (for instance, at one) or at more than one point (for instance, zero, one, and two). In these situations, the family of zero to k inflated power series (ZKIPS) models must be used in the control. In this work, we use a weighted score test statistic to examine upper-sided Shewhart, exponentially weighted moving average, and exponentially weighted moving average control charts. We only conducted numerical experiments on the zero to k Poisson model, which is one of the zero to k power series models, as an example. In ZKIPS models, the exponentially weighted moving average control chart can identify positive changes in the basis distribution’s characteristics. By adding random effects, this method, in particular, enables boosting the capability of detecting unnatural heterogeneity variability. For detecting small to moderate shifts, the proposed strategy is more effective than the current Shewhart chart, according to simulation findings obtained using the Monte Carlo methodology. To show the charts’ usefulness, they are also applied to a real example.