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.
Filtering and smoothing methods for mixed particle count distributions
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