Abstract
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.
Original language | English (US) |
---|---|
Pages (from-to) | 1192-1208 |
Number of pages | 17 |
Journal | Communications in Statistics - Theory and Methods |
Volume | 43 |
Issue number | 6 |
DOIs | |
State | Published - Mar 19 2014 |
Externally published | Yes |
Keywords
- Attribute control chart
- Average run length
- Cumulative sum control chart
- Multivariate Poisson distribution
ASJC Scopus subject areas
- Statistics and Probability