A wavelet-analysis-based change point model for process monitoring

The change-point problem originates from the applied research area of industry. Many approaches have been proposed in literature to solve the change point problems, such as likelihood method, Bayesian method, nonparametric method, information criterion method, and etc. However, these existing approaches mostly have to know the distribution or the number of the change point of observations in a process previously. And they also need a certain amount of historical data. However, data from most practical processes contain information both in time domain and frequency domain. The distributions of the data or the number of the change point the data have are always unknown. In this case, the wavelet theory is more capable of solving the change point problem then other existing approaches. In this paper, we present an approach for how to use the wavelet theory to find out change points in a time series, including the probability analysis, the identification of a change point, the method of choosing types of wavelet, and a general frame work of this approach. A case study is carried out to show that the wavelet method suggested in this paper has good properties.