Phase II Monitoring of Autocorrelated Polynomial Pro les in AR(1) Processes

In many practical situations, the quality of a process or product can be characterized by a function or pro le. Here, we consider a polynomial pro le and investigate the e ect of the violation of a common independence assumption, implicitly considered in most control charting applications, on the performance of the existing monitoring techniques. We speci cally consider a case when there is autocorrelation between pro les over time. An autoregressive model of order one is used to model the autocorrelation structure between error terms in successive pro les. In addition, two remedial methods, based on time series approaches, are presented for monitoring autocorrelated polynomial pro les in phase II. Their performances are compared using a numerical simulation runs in terms of an Average Run Length (ARL) criterion. The e ects of assignable cause and autocorrelation coe cient on the shape of pro les are also investigated.