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.
Highlights
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 results show that the Average Run Length (ARL) value of the ARL ZIGP Exponential Weight Moving Average (EWMA) control chart has better accuracy when compared to when using the Zero-Inflated Generalized Poisson (ZIP) EWMA control chart on ZIGP distributed data
Handling Overdispersion with Negative Binomial and Generalized Poisson Regression Models
Summary
Karakteristik kualitas tidak selalu dalam bentuk data kontinyu tapi juga dalam bentuk data atribut. Ada beberapa distribusi yang telah diperkenalkan oleh para ahli untuk mengatasi masalah overdispersi dan underdispersi. Salah satu model yang dapat mengatsi masalah tersebut adalah distribusi generalized Poisson (GP). Distribusi GP merupakan distribusi perluasan dari distribusi Poisson, Distribusi GP dapat mengatasi masalah overdispersi tetapi tidak dapat mengatasi masalah zero inflated atau kasus dengan data yang ada terlalu banyak mengandung nilai nol. Salah satu distribusi yang dapat mengatasi masalah tersebut adalan distribus zero inflated Poisson (ZIP). Model ZIP ini kurang tepat untuk mengatasi masalah underdispersi. Sehingga distribusi ZIGP ini dapat diterapkan pada data atribut yang menunjukan sifat overdispersi atau underdispersi serta mempunyai frekuensi data nol yang lebih banyak. Peta kendali Cumulatif Sum (CUSUM) dan Exponentially Weighted Moving Average (EWMA) merupakan alternatif yang tepat untuk masalah tersebut [2]. Peta kendali EWMA yang dikaji adalah untuk data berdistribusi ZIGP.
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