عنوان مقاله [English]
In statistical process control, traditionally, the assumption is made that successive observations of a quality characteristic are independently distributed. However, in practice, the observations are often serially correlated. This point has received considerable
attention in the literature in the last decade and the modified Shewhart and the residuals charts have been proposed to deal
with this situation. In this paper, it is investigated how well these control charts are able to detect a shift in the mean of AR(1) and AR(2) data. It is shown that for negative auto-conrrelation, the residuals chart is the better of these two and, for positive auto-correlation, it is better to choose the modified shewhart chart. Then, a modification of the residuals chart was made that outperforms both charts in the case of positive auto-correlation. Moreover, in order to improve the performance of the existing
control charts, three kinds of control charts namely modified EWMA, EWMA residuals and EWMA of modified residuals were
developed, . Through a simulation study, it is shown that, in terms of negative auto -correlation, the EWMA residuals chart is the best and for positive auto-correlation it is best to choose the EWMA chart of the modified residuals. Finally, an algorithm was proposed to control AR(1) and AR(2) data. This algorithm was implemented to a real-world problem and the results were reported.