Bayesian statistical process control for Phase I count type data

Count data, most often modeled by a Poisson distribution, are common in statistical process control. They are traditionally monitored by frequentist c or u charts, by cumulative sum and by exponentially weighted moving average charts. These charts all assume that the in-control true mean is known, a common fiction that is addressed by gathering a large Phase I sample and using it to estimate the mean. "Self-starting" proposals that ameliorate the need for a large Phase I sample have also appeared. All these methods are frequentist, ie, they allow only retrospective inference during Phase I, and they have no coherent way to incorporate less-than-perfect prior information about the in-control mean. In this paper, we introduce a Bayesian procedure that can incorporate prior information, allow online inference, and should be particularly attractive for short-run settings where large Phase I calibration exercises are impossible or unreasonable.