Identifying the mean step change of UBM chart

Abstract

The traditional control charts are developed based on the assumption that the successive observations are independent and identically distributed. In some processes, the independence assumption is violated when there is autocorrelation between observations. To solve this problem, two methods, classified as model-based and model-free, could be applied. When a control chart alarms an assignable cause, it is essential to detect the process change point in order to remove the root cause. In the presence of autocorrelated data, different methods for change-point identification have been applied only for model-based methods. Hence, this is considered as the research gap and an attempt is made to fill this gap by applying maximum likelihood function in unweighted batch mean control chart, one of the most applied model-free methods. In this article, an estimator is presented to determine the change point for the first-order autoregressive process, AR(1). When a real change occurs, the performance of proposed estimator is evaluated through simulation.