Filtering and smoothing methods for mixed particle count distributions

A particle count data stream is examined. The data are shown to consist of two mixed process distributions, a base Poisson count process and an outlier process. A model is developed that describes the mixed data stream. A smoothing and filtering method, using an exponentially weighted moving average (EWMA) and Poisson probabilities, is developed that separates the two process distributions into a base process and an outlier process. By separating the two distributions, statistical monitoring schemes can be applied to each. A Bernoulli EWMA is introduced for monitoring the outlier process. Average run length (ARL) evaluation is performed using Markov chain methodology, and suggestions for implementation are provided.