Step change point estimation in monitoring of auto-correlated simple linear profiles using clustering and maximum likelihood methods

In most of the researches in the area of profile monitoring, quality of a process is described by a relationship between a response variable and one explanatory variable, referred to as simple linear profile in the literature. Most of the papers in this field have assumed that observations within each profile are independent; however, the independency between the observations can be violated due to time collapse between two successive samplings in many real applications. On the other hand, usually real time of changes in process (change point) is different from the time control charts alarm the process is out-of-control. Finding the change point in the process saves time and money to find out root causes of the problem in the process. This paper specifically assumes that quality of process is modeled by using an AR(1) auto correlated simple linear profile. Then, the step change point of the process is estimated by using maximum likelihood and clustering methods after getting a signal from the T2 hotelling control chart in Phase II. Performance of the proposed methods is compared by using simulation studies. Finally, an application of the proposed methods is shown through a real case.