A decision theoretic approach to change point estimation for binomial CUSUM control charts

Detecting when the process has changed is a classical problem in sequential analysis and is an important practical issue in statistical process control. This article is concerned about the binomial cumulative sum (CUSUM) control chart, which is extensively applied to industrial process control, health care, public health surveillance, and other fields. For the binomial CUSUM, a maximum likelihood estimator has been proposed to estimate the change point. In our article, following a decision theoretic approach, we develop a new estimator that aims to improve the existing methods. For interval estimation, we propose a parametric bootstrap procedure to construct the confidence set of the change point. We compare our proposed method with the maximum likelihood estimator and Page's last zero estimator in terms of mean squared error by simulations. We find that the proposed method gives more unbiased and robust results than the existing procedures under various parameter designs. We analyze jewelry manufacturing data for illustration.