Accuracy of Zero Inflated Generalized Poisson Exponentially Moving Average Control Chart

Authors

  • L.M. JAMALUDDIN Al AFGANI universitas hasanuddin

DOI:

https://doi.org/10.20956/j.v18i1.14035

Keywords:

Overdispersion, Underdispersion, Poisson distribution, Generalized Poisson distribution (GP), Zero-Inflated Poisson distribution (ZIP), Zero-Inflated Generalized Poisson distribution (ZIGP), EWMA 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.  

Downloads

Download data is not yet available.

References

Alevizakos, V., & Christos K., 2019. Monitoring Of Zero-Inflated Poisson Processes With EWMA and DEWMA Control Charts. Quality and Reliabilty Engineering Intrnational, Vol. 36, No. 1, pp. 88-111. https://doi.org/10.1002/qre.2561.

Aya, A.A., Nesma A.S., & Mahmoud A.M., 2019. An Adaptive EWMA Control Chart For Monitoring Zero-Inflated Poisson Processes . Communications in Statistics - Simulation and Computation. http://doi.org/10.1080/03610918.2019.1676437.

Consul, P.C., Jain G.C., 1973. A Generalized Of The Poisson Distributions. Technometrics, Vol. 15, No.4, pp. 791–799. http://doi.org/10.1080/00401706.1973.10489112.

Edwin R, Van Den Heuvel., Stephan Van Driel A.W., & Zhuozhao Zhan., 2020. A Bivariate Zero-Inflated Poisson Control Chart: Comments And Corrections On Earlier Results. Communications in Statistics - Theory and Methods. http://doi.org/10.1080/03610926.2020.1736304.

Famoye, F., Singh K.P., 2003. On inflated Generalized Poisson Regression Models. Advance and Applied Statistics, Vol. 3, No.2, pp. 145–158.

Famoye, F., Singh K.P., 2006. Zero-Inflated Generalized Poisson Regression Model With An Application To Domestic Violence Data, Journal of Data Science, Vol. 4, No. 1, pp. 117–130. http://doi.org/10.6339/JDS.2006.04(1).257 .

Katemee, N., Tidadeaw M., 2016. Control Charts for Monitoring the Zero-Inflated Generalized Poisson Processes. International J. of Math. Sci. & Engg. Appls, Vol. 10, No.3, pp. 173–181.

Montgomery, D.C., 2006. Introduction to Statistical Quality Control 5th Edition. John Wiley & Sons Inc., New York.

Montgomery, D.C., 2009. Introduction To Statistical Quality Control Sixth Edition. John Wiley & Sons Inc., New York.

Noriszura, I., Jemain, A.A., 2007. Handling Overdispersion with Negative Binomial and Generalized Poisson Regression Models. Casualty Actuarial Society Forum. https://www.researchgate.net/publication/252461712_Handling_Overdispersion_with_Negative_Binomial_and_Generalized_Poisson_Regression_Models. [21 Oktober 2020].

Patel, A.K., Divecha J., 2011. Modified Exponentially Weighted Moving Average (EWMA) Control Chart for an Analytical Process Data. Journal of Chemical engineering and Material Sciense, Vol. 2, No.1, 12-20. https://academicjournals.org/journal/JCEMS/article-full-text-pdf/466796E1469. [21 Oktober 2020].

Walpole, R.E., Dkk., 2003. Probabilitas dan Statistika untuk Teknik dan Sains. PT Prehallindo, Jakarta.

Woodall, W.H., Mahmoud A. M., 2005. The Inertial Properties of Quality Control Charts. Technometrics, Vol. 47, No. 4, pp. 425-436. https://doi.org/10.1198/004017005000000256.

Downloads

Published

2021-09-02

Issue

Section

Research Articles