A change point approach for phase I analysis in multistage processes

We study the phase I analysis of a multistage process where the input of the current process stage may be closely related to the output(s) of the earlier stage(s). We frame univariate observations from each of the stages in a multistage process as a single vector and recognize that the directions in which these vectors can shift are limited when attention is restricted to a single step shift in the mean of one stage. This allows us to focus detection power on a limited subspace with improved sensitivity. Taking advantage of this particular characteristic, we propose a change point approach that integrates the classical binary segmentation test with the directional information based on the state-space model for testing the stability of a batch of historical data. We give an accurate approximation for the significance level of the proposed test. Our simulation results show that the proposed approach consistently outperforms existing methods for multistage processes.