Cumulative sum charts for monitoring the COM-Poisson processes

Abstract

The COM-Poisson distribution generalizes the standard Poisson distribution, allowing for under- or over-dispersion. It is used to model defect counts in manufacturing processes with over- or under-dispersed non-conforming products. The COM-Poisson distribution has two parameters; the rate parameter (μ) and dispersion parameter (ν). This study proposes three kinds of cumulative sum (CUSUM) control charts based on either the rate parameter, dispersion parameter, or both to detect shifts. Two control charts, namely, μ-CUSUM and ν-CUSUM detect shift respectively on one of two parameters, while a single CUSUM chart, namely, s-CUSUM considers the shift in both parameters at once. The proposed μ-CUSUM chart is flexible for over- or under-dispersed data and generalizes the Bernoulli, the Poisson and the geometric CUSUM charts as its special cases. The performance of the proposed charts have been evaluated in terms of average number of signals (ANOS) and compared with the Sellers (2012) chart. The performance comparison shows that the flexible and generalized μ-CUSUM chart is better to detect small to moderate shifts in the Poisson parameter than the Sellers (2012) chart. The ν-CUSUM performs very well to detect small to moderate shifts in the dispersion parameter. The performance evaluations of the s-CUSUM chart showed that, it works better when both of the parameter increases (decreases), but very poorly if one parameter increases (decreases) and other parameter decreases (increases). Two numerical examples are given to demonstrate the application of the proposed charts on practical data sets.