Change-point Detection in Phase I for Profiles with Binary Data and Random Predictors

In some applications, the quality of a process must be characterized by a profile, which describes the relationship between the response variable and explanatory variables. Moreover, for some processes, especially service processes, categorical response variables are common, making statistical process control techniques for profiles with categorical response data a must. We study Phase I analysis of profiles with binary data and random explanatory variables to identify the presence of change-points in the reference profile dataset. The change-point detection method based on logistic regression models is proposed. The method exploits directional shift information and integrates change-point algorithm with the generalized likelihood ratio. A diagnostic scheme for identifying the change-point location and the shift direction is also suggested. Numerical simulations are conducted to demonstrate the detection effectiveness and the diagnostic accuracy. A real example is used to illustrate the implementation of the proposed method.