Change point estimation in phase I monitoring of logistic regression profile

In statistical process control, an important issue in phase I is to identify the time of a change in process parameters. Control charts monitor the process over time, but the time an alarm is signaled by a control chart is not necessarily the real time of change in the process. Finding the real time of change, called as change point, is important because it leads to saving cost and time in detecting the assignable cause. Recently, profile monitoring in which a response variable and one or more explanatory variables are modeled by a regression function is attracted by many researchers. One type of profiles considered in the literature is a logistic profile where the distribution of the response variable is binary. In this paper, we develop two methods including likelihood ratio test and clustering to estimate the real time of a step change in phase I monitoring of the logistic profiles. The performance of the proposed methods is evaluated and compared through simulation studies. The results show the efficiency of both estimator methods. A real case is also studied to show the applicability of the proposed methods in practice.