Advances and Applications in Statistics
Volume 18, Issue 1, Pages 89 - 107
(September 2010)
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CONTROL CHARTS FOR GENERALIZED LOG-GAMMA PROCESSES
Eduardo Gutierrez Gonzalez and Olga Vladimirovna Panteleeva
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Abstract: Production processes do not always follow normal behaviors, as is the classic case of control charts, for these reasons, this paper proposes a new Shewhart-type control chart for the quantiles of the generalized log-gamma distribution. For this, it?s used the fact that this distribution, under a fixed value of the shape parameter, belongs to the family of location and scale distributions, and thus the problem is simplified by working with only the shape parameter; for which is used its maximum likelihood estimator. The delta method is used to find the distribution of the sample standard deviation. To do this, it is necessary to show the way to calculate the central moments of the generalized log-gamma distribution. Finally, the results are applied to a production problem. |
Keywords and phrases: control charts, Shewhart-type control charts, generalized log-gamma distribution, delta method, central moments. |
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