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Abstrak :
Over-dispersi dan under-dispersi adalah beberapa masalah umum ketika pemodelan dihitung data. Karena kondisi seperti itu, distribusi Poisson tidak lagi cocok untuk data cacah pemodelan, karena melanggar asumsi kesetaraan (mean equal variance). Di studi sebelumnya, beberapa distribusi telah diperkenalkan sebagai alternatif untuk Distribusi poisson, untuk menangani kondisi dispersi. Namun, distribusinya bisa hanya menangani overdispersion atau underdispersion. Oleh karena itu, distribusi baru adalah dikembangkan untuk menangani data dengan dispersi kurang dan penyebaran berlebihan. Distribusi ini adalah disebut distribusi Conway Maxwell Poisson (COM-Poisson). COM-Poisson distribusi pertama kali diperkenalkan oleh Conway dan Maxwell pada tahun 1962, sebagai solusi untuk sistem antrian dengan tarif layanan yang tergantung pada negara. Modifikasi Poisson ini distribusi memiliki dua parameter, λ dan parameter tambahan v, yang disebut dispersi parameter. Karena parameter tambahan, distribusi ini dapat digunakan di dispersi berlebihan (jika v <1), equidispersion (jika v = 1), dan dispersi kurang (jika v> 1). Melalui contoh data nyata, tesis ini akan menggunakan distribusi COM-Poisson untuk pemodelan data dengan kondisi penyebaran berlebihan dan kurang penyebaran. ......Over-dispersion and under-dispersion are some common problems compiling calculated data modeling. Because of such conditions, the Poisson distribution is no longer suitable for modeling data, because of the testing of the equality equation (mean equal variance). In previous studios, several distributions have been introduced as alternatives to Poisson distribution, to support the terms of dispersion. However, its distribution can only overcome overdispersion or underdispersion. Therefore, new distributions have been developed to support data with less dispersion and excessive distribution. This distribution is called the Conway Maxwell Poisson (COM-Poisson) distribution. COM-Poisson distribution was first introduced by Conway and Maxwell in 1962, as a solution for queuing systems with service rates that depend on the country. This Poisson modification distribution has two parameters, λ and an additional parameter v, which is called parameter dispersion. Because of the additional parameters, this distribution can be used in excessive dispersion (if v <1), equation (if v = 1), and less dispersion (if v> 1). Through real data examples, this thesis will use the COM-Poisson distribution for data modeling with the use of redundant and less-spread distributions.

Abstrak :
ABSTRACT
Count data are often described by the Poisson distribution, which requires identical mean and variance, namely equi dispersion. However, in practical situations, count data usually exhibit either over dispersion with variance larger than mean, or under dispersion with variance smaller than mean. Therefore, traditional approaches that focus on only mean shifts, such as the c chart, cannot monitor count data with over/under dispersion efficiently.To monitor mean and dispersion of count data simultaneously, this paper adopts Conway MaxwelI Poisson (COMPoisson) distributions to ht count data with over/under dispersion, and constructs a control chart based on the likelihood ratio test. The proposed chart is powerful in detecting both mean and dispersion shifts of count data with either over dispersion or under dispersion. Numerical simulations have demonstrated its performance in various cases.