Simple linear profiles monitoring in the presence of within profile autocorrelation

Quality of some processes or products can be characterized effectively by a function referred to as profile. Many studies have been done by researchers on the monitoring of simple linear profiles when the observations within each profile are uncorrelated. However, due to spatial autocorrelation or time collapse, this assumption is violated and leads to poor performance of the proposed control charts. In this paper, we consider a simple linear profile and assume that there is a first order autoregressive model between observations in each profile. Here, we specifically focus on phase II monitoring of simple linear regression. The effect of autocorrelation within the profiles is investigated on the estimate of regression parameters as well as the performance of control charts when the autocorrelation is overlooked. In addition, as a remedial measure, transformation of Y-values is used to eliminate the effect of autocorrelation. Four methods are discussed to monitor simple linear profiles and their performances are evaluated using average run length criterion. Finally, a case study in agriculture field is investigated.