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The inverse gaussian distribution can be used to model processes with skewed output. In this thesis, several Shewhard and CUSUM control schemes are developed for the inverse gaussian distribution. The behavior of these schemes is described. A new type of Shewhart chart, a self-starting Shewhart chart, is developed and applied to the inverse gaussian distribution. A second new type of control chart, which controls simultaneously for multiple parameters, is developed and shown to have some useful properties. Predictive Shewhart schemes, based on a diffuse prior, are developed and used for control.