Avaliação do desempenho e aplicação do gráfico de controle EWMA para o processo estocástico POMINAR(1)
In this work we propose to evaluate the performance of the EWMA control chart, adapting it to the first-order mixed autoregressive model with Poisson innovations, called POMINAR(1), which is composed of two operators known as thinning binomial and thinning Poisson. The objective is to compare the...
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| Formato: | Dissertação |
| Idioma: | pt_BR |
| Publicado em: |
Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/handle/123456789/52331 |
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| Resumo: | In this work we propose to evaluate the performance of the EWMA control chart, adapting
it to the first-order mixed autoregressive model with Poisson innovations, called POMINAR(1), which is composed of two operators known as thinning binomial and thinning
Poisson. The objective is to compare the results obtained with those of the Shewhart
control chart, and to show that the EWMA control chart is more efficient to detect
deviations in the process mean below 1.5 standard deviation. For this, the EWMA control
chart and its expectation are defined. Two theorems and two corollaries are proposed
in order to define the variance according to the size of the rational subgroup. Moreover,
the EWMA upper and lower control limits will be set, to analyze its performance. After
that, an analysis will be made comparing the values found in a simulation using the
EWMA control chart with the results obtained using the Shewhart control chart. Finally,
two applications with real data using the EWMA control chart are presented. The first
situation relates to the Criminal Data Section on the Forecasting Principles website. The
chosen variable represents the number of monthly robberies reported in political district
nº 12, in Pittsburgh (USA), from Jan/1990 to Dec/2001, with a total of 144 observations.
The second situation is the count of different IP addresses recorded in a period of two
minutes in duration on the server of the Department of Statistics of the University of
Wüsrzburg, on November 29, 2005, between 10 a.m. and 6 p.m. with 241 observations. |
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