A bayesian scheme to detect changes in the mean of a short-run process

In this article we propose a model suitable for statistical process control in short production runs. We wish to detect on-line whether the mean of the process has exceeded a prespecified upper threshold value. The theoretical basis of the model is a Bayesian formulation, leading to a mixture of normal distributions. Issues of decisions about whether the process is within specification and forecasting are addressed. The Kalman filter model is shown to be related to a special case of our model. The calculations are illustrated with a clinical chemistry example. The tool wear problem is another potential candidate for our approach.