A Review of Sequential Changepoint Detection in Quality Control and Dynamical Systems

Abstract

This thesis introduces concepts of control chart and its operation, and review various control charts that have been suggested: Shewharts ¯X chart, exponentially weighted moving average (EWMA) chart, cumulative sum (CUSUM) chart, generalized likelihood ratio (GLR) chart and mixture liklihood ratio chart using integrated likelihood ratio. Then, we discuss procedure and advantages of Poisson CUSUM chart. Also, two kinds of parameter change test for Poisson autoregressive models are considered: an estimate-based test using CMLE and a residual-based test. Finally, we perform a simulation study for illustration. We are going to simulate Poisson CUSUM chart with INGARCH(1,1) data if it is usable in spite of the autocorrelation. For the simulation, we deal with various cases of λ, α and β values to see if Poisson CUSUM chart is also valid for autocorrelated Poisson data.