Inverse Gaussian cumulative sum control charts for location and shape

Cumulative sum (CUSUM) control charts are very effective at detecting persisting special causes. The most common CUSUM chart assumes that the process measurement being monitored follows the normal distribution. Many industrial problems yield measures with skewed, positive distributions-examples are component reliabilities, times to completion of tasks and insurance claims. Non-normal measures such as these should not be monitored using procedures based an the normal distribution. The inverse Gaussian distribution provides a flexible distribution that can be used to model positive skew quantities, and therefore provides an effective framework for statistical process control on processes producing such measures. This paper defines the optimal CUSUM control chart schemes for location and shape of the inverse Gaussian distribution and evaluates its performance in detecting step changes in each of these parameters. The inverse Gaussian distribution has been shown to be a good fit to a long record of task completion times on a General Motors assembly line. We extend this application, showing how our CUSUMS may be used to detect changes in the distribution of these task completion times.