Monitoring poisson count data with probability control limits when sample sizes are time varying

This article considers the problem of monitoring Poisson count data when sample sizes are time varying without assuming a priori knowledge of sample sizes. Traditional control charts, whose control limits are often determined before the control charts are activated, are constructed based on perfect knowledge of sample sizes. In practice, however, future sample sizes are often unknown. Making an inappropriate assumption of the distribution function could lead to unexpected performance of the control charts, for example, excessive false alarms in the early runs of the control charts, which would in turn hurt an operator's confidence in valid alarms. To overcome this problem, we propose the use of probability control limits, which are determined based on the realization of sample sizes online. The conditional probability that the charting statistic exceeds the control limit at present given that there has not been a single alarm before can be guaranteed to meet a specified false alarm rate. Simulation studies show that our proposed control chart is able to deliver satisfactory run length performance for any time‐varying sample sizes. The idea presented in this article can be applied to any effective control charts such as the exponentially weighted moving average or cumulative sum chart. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 625–636, 2013