Poisson GWMA Control Chart

Abstract

A generally weighted moving average (GWMA) control chart for monitoring Poisson observations is introduced. Using simulation, its average run lengths and standard deviations of run lengths are compared with those of other control charts for Poisson data. It is shown that the Poisson GWMA chart outperforms other control charts, especially when the process shift is small.

Keywords:

• Average run length
• EWMA
• GWMA
• Poisson distribution

Mathematics Subject Classification:

• Primary 65C60
• Secondary 68U20

Acknowledgment

The authors would like to thank the referee for the insightful comments and suggestions which greatly strengthened this article.

Notes

∗Entries inside parentheses are SDRLs.

∗∗Given that the size of sample is 6,000 per simulation iteration, the c-chart does not signal through 6,000 sample points when μ₁ = 1 (μ₀ = 4). Thus, ARL₁ = 6,000 (constant) and SDRL₁ = 0.