Accuracy of Zero Inflated Generalized Poisson Exponentially Moving Average Control Chart

Abstract

The Zero-Inflated Generalized Poisson (ZIGP) distribution is a case-based distribution where the discrete data has a large number of zeros and an overdispersion occurs, i.e. the variance is greater than the mean value. The purpose of this study is to determine the Exponential Weight Moving Average (EWMA) control chart with the assumption that the data has a Zero-Inflated Generalized Poisson (ZIP) distribution. The results show that the ARL value of the ARL ZIGP EWMA control chart has better accuracy when compared to when using the ZIP EWMA control chart on ZIGP distributed data. This is indicated by the smaller ARL value compared to the ZIP EWMA control chart, namely when φ = 1.4, and φ = 0.6. So that the ARL ZIGP EWMA control chart has a fairly good accuracy in detecting out of control conditions for ZIGP distributed data. In addition, the modified ARL shows the same values ​​before and after the modification for the underdispersion data and shows a larger or negative value for the overdispersion data. This can eliminate or reduce errors in analyzing the accuracy of the control chart.