Monitoring of simple linear profiles and change point estimation in the presence of within-profile ARMA autocorrelation

Document Type : CFP- Quality Engineering Techniques in Production and Service Systems


1 Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

2 Industrial Engineering Department, Kharazmi University, Karaj, Iran



The quality of some products can be effectively characterized by univariate or multivariate distribution in statistical process control applications. In some situations, however, the quality of a product can be characterized by a relationship between independent and response variables called a profile. There have been many studies on monitoring simple linear profiles when observations are uncorrelated. However, due to time collapse, this assumption is rarely observed in practice and leads to poor results for corresponding control charts. Many studies consider the autocorrelation structure between observations a first-order autoregressive model. But a wide range of autocorrelation between observations might not be modeled by AR(1) models. Therefore this paper examines a simple linear profile and assumes an autoregressive moving average (ARMA) autocorrelation between observations. It is assumed that in each profile, random errors follow an ARMA(p,q) model. This article focuses specifically on Phase II monitoring of simple linear profiles. Estimating the change point results in significant time and cost savings. In this paper, a maximum likelihood estimator is derived to estimate the change point. Then through some simulation experiments, the performance of the proposed control chart is compared to Hotelling’s T2 control chart, and as another part of simulation experiments, the performance of the proposed change point estimator is compared to one of the built-in change point estimators of exponentially weighted moving average (EWMA) control charts. The results indicate that the proposed estimator provides adequately accurate estimates of the change point and outperforms the built-in change point estimator of the EWMA chart.