CUSUM control charts for multivariate poisson distribution

A cumulative sum control chart for multivariate Poisson distribution (MP-CUSUM) is proposed. The MP-CUSUM chart is constructed based on log-likelihood ratios with in-control parameters, Φ₀, and shifts to be detected quickly, Φ₁. The average run length (ARL) values are obtained using a Markov Chain-based method. Numerical experiments show that the MP-CUSUM chart is effective in detecting parameter shifts in terms of ARL. The MP-CUSUM chart with smaller Φ₁ is more sensitive than that with greater Φ₁ to smaller shifts, but more insensitive to greater shifts. A comparison shows that the proposed MP-CUSUM chart outperforms an existing MP chart.